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Observation of a rare beta decay of the charmed baryon with a Graph Neural Network
BESIII Collaboration, M. Ablikim, M. N. Achasov, P. Adlarson, O. Afedulidis, X. C. Ai, R. Aliberti, A. Amoroso, Q. An, Y. Bai, O. Bakina, I. Balossino, Y. Ban, H.-R. Bao, V. Batozskaya, K. Begzsuren, N. Berger, M. Berlowski, M. Bertani, D. Bettoni, et al (642)
Oct 18 2024 hep-ex hep-lat hep-ph nucl-ex arXiv:2410.13515v1

@misc{2410.13515, author = {BESIII Collaboration and M.~Ablikim and M.~N.~Achasov and P.~Adlarson and O.~Afedulidis and X.~C.~Ai and R.~Aliberti and A.~Amoroso and Q.~An and Y.~Bai and O.~Bakina and I.~Balossino and Y.~Ban and H.-R.~Bao and V.~Batozskaya and K.~Begzsuren and N.~Berger and M.~Berlowski and M.~Bertani and D.~Bettoni and F.~Bianchi and E.~Bianco and A.~Bortone and I.~Boyko and R.~A.~Briere and A.~Brueggemann and H.~Cai and X.~Cai and A.~Calcaterra and G.~F.~Cao and N.~Cao and S.~A.~Cetin and J.~F.~Chang and G.~R.~Che and G.~Chelkov and C.~Chen and C.~H.~Chen and Chao Chen and G.~Chen and H.~S.~Chen and H.~Y.~Chen and M.~L.~Chen and S.~J.~Chen and S.~L.~Chen and S.~M.~Chen and T.~Chen and X.~R.~Chen and X.~T.~Chen and Y.~B.~Chen and Y.~Q.~Chen and Z.~J.~Chen and Z.~Y.~Chen and S.~K.~Choi and G.~Cibinetto and F.~Cossio and J.~J.~Cui and H.~L.~Dai and J.~P.~Dai and A.~Dbeyssi and R.~E.~de Boer and D.~Dedovich and C.~Q.~Deng and Z.~Y.~Deng and A.~Denig and I.~Denysenko and M.~Destefanis and F.~De Mori and B.~Ding and X.~X.~Ding and Y.~Ding and Y.~Ding and J.~Dong and L.~Y.~Dong and M.~Y.~Dong and X.~Dong and M.~C.~Du and S.~X.~Du and Y.~Y.~Duan and Z.~H.~Duan and P.~Egorov and Y.~H.~Fan and J.~Fang and J.~Fang and S.~S.~Fang and W.~X.~Fang and Y.~Fang and Y.~Q.~Fang and R.~Farinelli and L.~Fava and F.~Feldbauer and G.~Felici and C.~Q.~Feng and J.~H.~Feng and Y.~T.~Feng and M.~Fritsch and C.~D.~Fu and J.~L.~Fu and Y.~W.~Fu and H.~Gao and X.~B.~Gao and Y.~N.~Gao and Yang Gao and S.~Garbolino and I.~Garzia and L.~Ge and P.~T.~Ge and Z.~W.~Ge and C.~Geng and E.~M.~Gersabeck and A.~Gilman and K.~Goetzen and L.~Gong and W.~X.~Gong and W.~Gradl and S.~Gramigna and M.~Greco and M.~H.~Gu and Y.~T.~Gu and C.~Y.~Guan and A.~Q.~Guo and L.~B.~Guo and M.~J.~Guo and R.~P.~Guo and Y.~P.~Guo and A.~Guskov and J.~Gutierrez and K.~L.~Han and T.~T.~Han and F.~Hanisch and X.~Q.~Hao and F.~A.~Harris and K.~K.~He and K.~L.~He and F.~H.~Heinsius and C.~H.~Heinz and Y.~K.~Heng and C.~Herold and T.~Holtmann and P.~C.~Hong and G.~Y.~Hou and X.~T.~Hou and Y.~R.~Hou and Z.~L.~Hou and B.~Y.~Hu and H.~M.~Hu and J.~F.~Hu and S.~L.~Hu and T.~Hu and Y.~Hu and G.~S.~Huang and K.~X.~Huang and L.~Q.~Huang and X.~T.~Huang and Y.~P.~Huang and T.~Hussain and F.~Hölzken and N.~Hüsken and N.~in der Wiesche and J.~Jackson and S.~Janchiv and J.~H.~Jeong and Q.~Ji and Q.~P.~Ji and W.~Ji and X.~B.~Ji and X.~L.~Ji and Y.~Y.~Ji and X.~Q.~Jia and Z.~K.~Jia and D.~Jiang and H.~B.~Jiang and P.~C.~Jiang and S.~S.~Jiang and T.~J.~Jiang and X.~S.~Jiang and Y.~Jiang and J.~B.~Jiao and J.~K.~Jiao and Z.~Jiao and S.~Jin and Y.~Jin and M.~Q.~Jing and X.~M.~Jing and T.~Johansson and S.~Kabana and N.~Kalantar-Nayestanaki and X.~L.~Kang and X.~S.~Kang and M.~Kavatsyuk and B.~C.~Ke and V.~Khachatryan and A.~Khoukaz and R.~Kiuchi and O.~B.~Kolcu and B.~Kopf and M.~Kuessner and X.~Kui and N.~Kumar and A.~Kupsc and W.~Kühn and J.~J.~Lane and P.~Larin and L.~Lavezzi and T.~T.~Lei and Z.~H.~Lei and M.~Lellmann and T.~Lenz and C.~Li and C.~Li and C.~H.~Li and Cheng Li and D.~M.~Li and F.~Li and G.~Li and H.~B.~Li and H.~J.~Li and H.~N.~Li and Hui Li and J.~R.~Li and J.~S.~Li and K.~Li and L.~J.~Li and L.~K.~Li and Lei Li and M.~H.~Li and P.~R.~Li and Q.~M.~Li and Q.~X.~Li and R.~Li and S.~X.~Li and T.~Li and W.~D.~Li and W.~G.~Li and X.~Li and X.~H.~Li and X.~L.~Li and X.~Y.~Li and X.~Z.~Li and Y.~G.~Li and Z.~J.~Li and Z.~Y.~Li and C.~Liang and H.~Liang and H.~Liang and Y.~F.~Liang and Y.~T.~Liang and G.~R.~Liao and L.~Z.~Liao and Y.~P.~Liao and J.~Libby and A.~Limphirat and C.~C.~Lin and D.~X.~Lin and T.~Lin and B.~J.~Liu and B.~X.~Liu and C.~Liu and C.~X.~Liu and F.~Liu and F.~H.~Liu and Feng Liu and G.~M.~Liu and H.~Liu and H.~B.~Liu and H.~H.~Liu and H.~M.~Liu and Huihui Liu and J.~B.~Liu and J.~Y.~Liu and K.~Liu and K.~Y.~Liu and Ke Liu and L.~Liu and L.~C.~Liu and Lu Liu and M.~H.~Liu and P.~L.~Liu and Q.~Liu and S.~B.~Liu and T.~Liu and W.~K.~Liu and W.~M.~Liu and X.~Liu and X.~Liu and Y.~Liu and Y.~Liu and Y.~B.~Liu and Z.~A.~Liu and Z.~D.~Liu and Z.~Q.~Liu and X.~C.~Lou and F.~X.~Lu and H.~J.~Lu and J.~G.~Lu and X.~L.~Lu and Y.~Lu and Y.~P.~Lu and Z.~H.~Lu and C.~L.~Luo and J.~R.~Luo and M.~X.~Luo and T.~Luo and X.~L.~Luo and X.~R.~Lyu and Y.~F.~Lyu and F.~C.~Ma and H.~Ma and H.~L.~Ma and J.~L.~Ma and L.~L.~Ma and M.~M.~Ma and Q.~M.~Ma and R.~Q.~Ma and T.~Ma and X.~T.~Ma and X.~Y.~Ma and Y.~Ma and Y.~M.~Ma and F.~E.~Maas and M.~Maggiora and S.~Malde and Y.~J.~Mao and Z.~P.~Mao and S.~Marcello and Z.~X.~Meng and J.~G.~Messchendorp and G.~Mezzadri and H.~Miao and T.~J.~Min and R.~E.~Mitchell and X.~H.~Mo and B.~Moses and N.~Yu.~Muchnoi and J.~Muskalla and Y.~Nefedov and F.~Nerling and L.~S.~Nie and I.~B.~Nikolaev and Z.~Ning and S.~Nisar and Q.~L.~Niu and W.~D.~Niu and Y.~Niu and S.~L.~Olsen and Q.~Ouyang and S.~Pacetti and X.~Pan and Y.~Pan and A.~Pathak and P.~Patteri and Y.~P.~Pei and M.~Pelizaeus and H.~P.~Peng and Y.~Y.~Peng and K.~Peters and 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Y.~J.~Sun and Y.~Z.~Sun and Z.~Q.~Sun and Z.~T.~Sun and C.~J.~Tang and G.~Y.~Tang and J.~Tang and M.~Tang and Y.~A.~Tang and L.~Y.~Tao and Q.~T.~Tao and M.~Tat and J.~X.~Teng and V.~Thoren and W.~H.~Tian and Y.~Tian and Z.~F.~Tian and I.~Uman and Y.~Wan and S.~J.~Wang and B.~Wang and B.~L.~Wang and Bo Wang and D.~Y.~Wang and F.~Wang and H.~J.~Wang and J.~J.~Wang and J.~P.~Wang and K.~Wang and L.~L.~Wang and M.~Wang and N.~Y.~Wang and S.~Wang and S.~Wang and T.~Wang and T.~J.~Wang and W.~Wang and W.~Wang and W.~P.~Wang and X.~Wang and X.~F.~Wang and X.~J.~Wang and X.~L.~Wang and X.~N.~Wang and Y.~Wang and Y.~D.~Wang and Y.~F.~Wang and Y.~L.~Wang and Y.~N.~Wang and Y.~Q.~Wang and Yaqian Wang and Yi Wang and Z.~Wang and Z.~L.~Wang and Z.~Y.~Wang and Ziyi Wang and D.~H.~Wei and F.~Weidner and S.~P.~Wen and Y.~R.~Wen and U.~Wiedner and G.~Wilkinson and M.~Wolke and L.~Wollenberg and C.~Wu and J.~F.~Wu and L.~H.~Wu and L.~J.~Wu and X.~Wu and X.~H.~Wu and Y.~Wu and Y.~H.~Wu and Y.~J.~Wu and Z.~Wu and L.~Xia and X.~M.~Xian and B.~H.~Xiang and T.~Xiang and D.~Xiao and G.~Y.~Xiao and S.~Y.~Xiao and Y.~L.~Xiao and Z.~J.~Xiao and C.~Xie and X.~H.~Xie and Y.~Xie and Y.~G.~Xie and Y.~H.~Xie and Z.~P.~Xie and T.~Y.~Xing and C.~F.~Xu and C.~J.~Xu and G.~F.~Xu and H.~Y.~Xu and M.~Xu and Q.~J.~Xu and Q.~N.~Xu and W.~Xu and W.~L.~Xu and X.~P.~Xu and Y.~C.~Xu and Z.~P.~Xu and Z.~S.~Xu and F.~Yan and L.~Yan and W.~B.~Yan and W.~C.~Yan and X.~Q.~Yan and H.~J.~Yang and H.~L.~Yang and H.~X.~Yang and T.~Yang and Y.~Yang and Y.~F.~Yang and Y.~F.~Yang and Y.~X.~Yang and Z.~W.~Yang and Z.~P.~Yao and M.~Ye and M.~H.~Ye and J.~H.~Yin and Z.~Y.~You and B.~X.~Yu and C.~X.~Yu and G.~Yu and J.~S.~Yu and T.~Yu and X.~D.~Yu and Y.~C.~Yu and C.~Z.~Yuan and J.~Yuan and J.~Yuan and L.~Yuan and S.~C.~Yuan and Y.~Yuan and Z.~Y.~Yuan and C.~X.~Yue and A.~A.~Zafar and F.~R.~Zeng and S.~H.~Zeng and X.~Zeng and Y.~Zeng and Y.~J.~Zeng and Y.~J.~Zeng and X.~Y.~Zhai and Y.~C.~Zhai and Y.~H.~Zhan and A.~Q.~Zhang and B.~L.~Zhang and B.~X.~Zhang and D.~H.~Zhang and G.~Y.~Zhang and H.~Zhang and H.~Zhang and H.~C.~Zhang and H.~H.~Zhang and H.~H.~Zhang and H.~Q.~Zhang and H.~R.~Zhang and H.~Y.~Zhang and J.~Zhang and J.~Zhang and J.~J.~Zhang and J.~L.~Zhang and J.~Q.~Zhang and J.~S.~Zhang and J.~W.~Zhang and J.~X.~Zhang and J.~Y.~Zhang and J.~Z.~Zhang and Jianyu Zhang and L.~M.~Zhang and Lei Zhang and P.~Zhang and Q.~Y.~Zhang and R.~Y.~Zhang and S.~H.~Zhang and Shulei Zhang and X.~D.~Zhang and X.~M.~Zhang and X.~Y.~Zhang and Y.~Zhang and Y.~Zhang and Y.~T.~Zhang and Y.~H.~Zhang and Y.~M.~Zhang and Yan Zhang and Z.~D.~Zhang and Z.~H.~Zhang and Z.~L.~Zhang and Z.~Y.~Zhang and Z.~Y.~Zhang and Z.~Z.~Zhang and G.~Zhao and J.~Y.~Zhao and J.~Z.~Zhao and L.~Zhao and Lei Zhao and M.~G.~Zhao and N.~Zhao and R.~P.~Zhao and S.~J.~Zhao and Y.~B.~Zhao and Y.~X.~Zhao and Z.~G.~Zhao and A.~Zhemchugov and B.~Zheng and B.~M.~Zheng and J.~P.~Zheng and W.~J.~Zheng and Y.~H.~Zheng and B.~Zhong and X.~Zhong and H.~Zhou and J.~Y.~Zhou and L.~P.~Zhou and S.~Zhou and X.~Zhou and X.~K.~Zhou and X.~R.~Zhou and X.~Y.~Zhou and Y.~Z.~Zhou and J.~Zhu and K.~Zhu and K.~J.~Zhu and K.~S.~Zhu and L.~Zhu and L.~X.~Zhu and S.~H.~Zhu and S.~Q.~Zhu and T.~J.~Zhu and W.~D.~Zhu and Y.~C.~Zhu and Z.~A.~Zhu and J.~H.~Zou and J.~Zu}, title = {{O}bservation of a rare beta decay of the charmed baryon with a {G}raph {N}eural {N}etwork}, year = {2024}, eprint = {2410.13515}, note = {arXiv:2410.13515v1} }
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The study of beta decay of the charmed baryon provides unique insights into the fundamental mechanism of the strong and electro-weak interactions. The $\Lambda_c^+$, being the lightest charmed baryon, undergoes disintegration solely through the charm quark weak decay. Its beta decay provides an ideal laboratory for investigating non-perturbative effects in quantum chromodynamics and for constraining the fundamental parameters of the Cabibbo-Kobayashi-Maskawa matrix in weak interaction theory. This article presents the first observation of the Cabibbo-suppressed $\Lambda_c^+$ beta decay into a neutron $\Lambda_c^+ \rightarrow n e^+ \nu_{e}$, based on $4.5~\mathrm{fb}^{-1}$ of electron-positron annihilation data collected with the BESIII detector in the energy region above the $\Lambda^+_c\bar{\Lambda}^-_c$ threshold. A novel machine learning technique, leveraging Graph Neural Networks, has been utilized to effectively separate signals from dominant backgrounds, particularly $\Lambda_c^+ \rightarrow \Lambda e^+ \nu_{e}$. This approach has yielded a statistical significance of more than $10\sigma$. The absolute branching fraction of $\Lambda_c^+ \rightarrow n e^+ \nu_{e}$ is measured to be $(3.57\pm0.34_{\mathrm{stat}}\pm0.14_{\mathrm{syst}})\times 10^{-3}$. For the first time, the CKM matrix element $\left|V_{cd}\right|$ is extracted via a charmed baryon decay to be $0.208\pm0.011_{\rm exp.}\pm0.007_{\rm LQCD}\pm0.001_{\tau_{\Lambda_c^+}}$. This study provides a new probe to further understand fundamental interactions in the charmed baryon sector, and demonstrates the power of modern machine learning techniques in enhancing experimental capability in high energy physics research.
Charm physics with overlap fermions on 2+1-flavor domain wall fermion configurations
Donghao Li, Ying Chen, Ming Gong, Keh-Fei Liu, Zhaofeng Liu, Tingxiao Wang
Jul 08 2024 hep-lat hep-ex hep-ph arXiv:2407.03697v2

@misc{2407.03697, author = {Donghao Li and Ying Chen and Ming Gong and Keh-Fei Liu and Zhaofeng Liu and Tingxiao Wang}, title = {{C}harm physics with overlap fermions on 2+1-flavor domain wall fermion configurations}, year = {2024}, eprint = {2407.03697}, note = {arXiv:2407.03697v2} }
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Decay constants of pseudoscalar mesons $D$, $D_s$, $\eta_c$ and vector mesons $D^*$, $D_s^*$, $J/\psi$ are determined from $N_f=2+1$ lattice QCD at a lattice spacing $a\sim0.08$ fm. For vector mesons, the decay constants defined by tensor currents are given in the $\overline{\rm MS}$ scheme at $2$ GeV. The calculation is performed on domain wall fermion configurations generated by the RBC-UKQCD Collaborations and the overlap fermion action is used for the valence quarks. Comparing the current results with our previous ones at a coarser lattice spacing $a\sim0.11$ fm gives us a better understanding of the discretization error. We obtain $f_{D_s^*}^T(\overline{\rm MS},\text{2 GeV})/f_{D_s^*}=0.907(20)$ with a better precision than our previous result. Combining our $f_{D_s^*}=277(11)$ MeV with the total width of $D_s^*$ determined in a recent work gives a branching fraction $4.26(52)\times10^{-5}$ for $D_s^*$ leptonic decay.
Trace anomaly form factors from lattice QCD
Bigeng Wang, Fangcheng He, Gen Wang, Terrence Draper, Jian Liang, Keh-Fei Liu, Yi-Bo Yang
Jan 12 2024 hep-lat hep-ph nucl-th arXiv:2401.05496v3

@misc{2401.05496, author = {Bigeng Wang and Fangcheng He and Gen Wang and Terrence Draper and Jian Liang and Keh-Fei Liu and Yi-Bo Yang}, title = {{T}race anomaly form factors from lattice {QCD}}, year = {2024}, eprint = {2401.05496}, doi = {10.1103/PhysRevD.109.094504}, note = {arXiv:2401.05496v3} }
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The hadron mass can be obtained through the calculation of the trace of the energy-momentum tensor in the hadron which includes the trace anomaly and sigma terms. The anomaly due to conformal symmetry breaking is believed to be an important ingredient for hadron mass generation and confinement. In this work, we will present the calculation of the glue part of the trace anomaly form factors of the pion up to $Q^2\sim 4.3~\mathrm{GeV}^2$ and the nucleon up to $Q^2\sim 1~\mathrm{GeV}^2$. The calculations are performed on a domain wall fermion ensemble with overlap valence quarks at seven valence pion masses varying from $\sim 250$ to $\sim 540$ MeV, including the unitary point $\sim 340$ MeV. We calculate the radius of the glue trace anomaly for the pion and the nucleon from the $z$ expansion. By performing a two-dimensional Fourier transform on the glue trace anomaly form factors in the infinite momentum frame with no energy transfer, we also obtain their spatial distributions for several valence quark masses. The results are qualitatively extrapolated to the physical valence pion mass with systematic errors from the unphysical sea quark mass, discretization effects in the renormalization sum rule, and finite-volume effects to be addressed in the future. We find the pion's form factor changes sign, as does its spatial distribution, for light quark masses. This explains how the trace anomaly contribution to the pion mass approaches zero toward the chiral limit.
Elastic and resonance structures of the nucleon from hadronic tensor in lattice QCD: implications for neutrino-nucleon scattering and hadron physics
Jian Liang, Raza Sabbir Sufian, Bigeng Wang, Terrence Draper, Tanjib Khan, Keh-Fei Liu, Yi-Bo Yang
Nov 08 2023 hep-lat hep-ph nucl-th arXiv:2311.04206v1

@misc{2311.04206, author = {Jian Liang and Raza Sabbir Sufian and Bigeng Wang and Terrence Draper and Tanjib Khan and Keh-Fei Liu and Yi-Bo Yang}, title = {{E}lastic and resonance structures of the nucleon from hadronic tensor in lattice {QCD}: implications for neutrino-nucleon scattering and hadron physics}, year = {2023}, eprint = {2311.04206}, note = {arXiv:2311.04206v1} }
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Understanding the transitions of nucleons into various resonance structures through electromagnetic interactions plays a pivotal role in advancing our comprehension of the strong interactions within the domain of quark confinement. Furthermore, gaining precise insights into the elastic and resonance structures of nucleons is indispensable for deciphering the physics from neutrino-nucleus scattering cross sections experimental data, which remain theoretically challenging, even in the context of neutrino-nucleon interactions whose profound understanding is imperative for the neutrino oscillation experiments. One promising avenue involves the direct evaluation of the lepton-nucleon scattering cross sections across quasi-elastic, resonance, shallow-inelastic, and deep inelastic regions, which can be achieved through the hadronic tensor formalism in lattice QCD. In this work, we present the determination of the nucleon's Sachs electric form factor using the hadronic tensor formalism and verify that it is consistent with that from the conventional three-point function calculation. We additionally obtain the transition form factor from the nucleon to its first radial excited state within a finite volume. Consequently, we identify the latter with the nucleon-to-Roper transition form factor $G_E^*(Q^2)$, determine the corresponding longitudinal helicity amplitude $S_{1/2}(Q^2)$ and compare our findings with experimental measurements, for the first time using the hadronic tensor formalism. The limitations and systematic improvements of the approach are also discussed.
Fast Fermion Smearing Scheme with Gaussian-like Profile
ChuanYang Li, Terrence Draper, Jun Hua, Jian Liang, Keh-Fei Liu, Jun Shi, Nan Wang, Yi-bo Yang
Oct 04 2023 hep-lat arXiv:2310.02179v3

@misc{2310.02179, author = {ChuanYang Li and Terrence Draper and Jun Hua and Jian Liang and Keh-Fei Liu and Jun Shi and Nan Wang and Yi-bo Yang}, title = {{F}ast {F}ermion {S}mearing {S}cheme with {G}aussian-like {P}rofile}, year = {2023}, eprint = {2310.02179}, note = {arXiv:2310.02179v3} }
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We propose a novel smearing scheme which gives a Gaussian-like profile and is more efficient than the traditional Gaussian smearing in terms of computer time consumption. We also carry out a detailed analysis of the profiles, smearing sizes, and the behaviors of hadron effective masses of different smearing schemes, and point out that having a sufficient number of gauge paths in a smearing scheme is essential to produce strong smearing effects. For a moderate smearing size $\bar{r}\sim 10a$, the time cost for the novel smearing is less than $1/8$ of that for the traditional Gaussian smearing. In practical lattice calculations with larger smearing sizes or finer lattice spacings the improvement will be more substantial.
Lattice QCD Calculation of Electroweak Box Contributions to Superallowed Nuclear and Neutron Beta Decays
Peng-Xiang Ma, Xu Feng, Mikhail Gorchtein, Lu-Chang Jin, Keh-Fei Liu, Chien-Yeah Seng, Bi-Geng Wang, Zhao-Long Zhang
Sep 01 2023 hep-lat hep-ph nucl-ex arXiv:2308.16755v2

@misc{2308.16755, author = {Peng-Xiang Ma and Xu Feng and Mikhail Gorchtein and Lu-Chang Jin and Keh-Fei Liu and Chien-Yeah Seng and Bi-Geng Wang and Zhao-Long Zhang}, title = {{L}attice {QCD} {C}alculation of {E}lectroweak {B}ox {C}ontributions to {S}uperallowed {N}uclear and {N}eutron {B}eta {D}ecays}, year = {2023}, eprint = {2308.16755}, note = {arXiv:2308.16755v2} }
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We present the first lattice QCD calculation of the universal axial $\gamma W$-box contribution $\square_{\gamma W}^{VA}$ to both superallowed nuclear and neutron beta decays. This contribution emerges as a significant component within the theoretical uncertainties surrounding the extraction of $|V_{ud}|$ from superallowed decays. Our calculation is conducted using two domain wall fermion ensembles at the physical pion mass. To construct the nucleon 4-point correlation functions, we employ the random sparsening field technique. Furthermore, we incorporate long-distance contributions to the hadronic function using the infinite-volume reconstruction method. Upon performing the continuum extrapolation, we arrive at $\square_{\gamma W}^{VA}=3.65(8)_{\mathrm{lat}}(1)_{\mathrm{PT}}\times10^{-3}$. Consequently, this yields a slightly higher value of $|V_{ud}|=0.97386(11)_{\mathrm{exp.}}(9)_{\mathrm{RC}}(27)_{\mathrm{NS}}$, reducing the previous $2.1\sigma$ tension with the CKM unitarity to $1.8\sigma$. Additionally, we calculate the vector $\gamma W$-box contribution to the axial charge $g_A$, denoted as $\square_{\gamma W}^{VV}$, and explore its potential implications.
Separation of Infrared and Bulk in Thermal QCD
Xiao-Lan Meng, Peng Sun, Andrei Alexandru, Ivan Horváth, Keh-Fei Liu, Gen Wang, Yi-Bo Yang
May 17 2023 hep-lat hep-ph arXiv:2305.09459v3

@misc{2305.09459, author = {Xiao-Lan Meng and Peng Sun and Andrei Alexandru and Ivan Horváth and Keh-Fei Liu and Gen Wang and Yi-Bo Yang}, title = {{S}eparation of {I}nfrared and {B}ulk in {T}hermal {QCD}}, year = {2023}, eprint = {2305.09459}, note = {arXiv:2305.09459v3} }
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New thermal phase of QCD, featuring scale invariance in the infrared (IR), was proposed to exist both in the pure-glue (N$_f$=0) and the ``real-world" (N$_f$=2+1) settings. Among key aspects of the proposal is that the system in this \it IR phase separates into two independent components: the scale-invariant IR part and the non-invariant bulk. Such scenario requires non-analyticities in the theory and, in case of pure-glue QCD, they were found to arise via Anderson-like mobility edges in Dirac spectra ($\lambda_\fir \!=\! 0$, $\pm \lambda_\text{A} \!\neq\! 0$) manifested in dimension function $d_\fir(\lambda)$. Here we present first evidence that this mechanism is also at work in ``real-world QCD" (N$_f$=2+1 theory at physical quark masses and $a\!=\!0.105\,$fm), supporting the existence of the proposed IR regime. Indeed, at $T\!=\!234\,$MeV, we find the dimensional jump between zero modes and lowest near-zero modes very close to unity ($d_\fir\!=\!3$ to $d_\fir \!\simeq \!2$), exactly like in pure-glue QCD in IR phase. However, no jump is found at $T\!=\!187\,$ MeV which is in the intermediate region between chiral crossover at $T_c \approx 155\,$MeV and the onset $T_\fir$ of IR phase, originally estimated at $200 < T_\fir < 250\,$MeV.
TMD Handbook
Renaud Boussarie, Matthias Burkardt, Martha Constantinou, William Detmold, Markus Ebert, Michael Engelhardt, Sean Fleming, Leonard Gamberg, Xiangdong Ji, Zhong-Bo Kang, Christopher Lee, Keh-Fei Liu, Simonetta Liuti, Thomas Mehen, Andreas Metz, John Negele, Daniel Pitonyak, Alexei Prokudin, Jian-Wei Qiu, Abha Rajan, et al (9)
Apr 10 2023 hep-ph hep-lat nucl-th arXiv:2304.03302v1

@misc{2304.03302, author = {Renaud Boussarie and Matthias Burkardt and Martha Constantinou and William Detmold and Markus Ebert and Michael Engelhardt and Sean Fleming and Leonard Gamberg and Xiangdong Ji and Zhong-Bo Kang and Christopher Lee and Keh-Fei Liu and Simonetta Liuti and Thomas Mehen and Andreas Metz and John Negele and Daniel Pitonyak and Alexei Prokudin and Jian-Wei Qiu and Abha Rajan and Marc Schlegel and Phiala Shanahan and Peter Schweitzer and Iain W.~Stewart and Andrey Tarasov and Raju Venugopalan and Ivan Vitev and Feng Yuan and Yong Zhao}, title = {{TMD} {H}andbook}, year = {2023}, eprint = {2304.03302}, note = {arXiv:2304.03302v1} }
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This handbook provides a comprehensive review of transverse-momentum-dependent parton distribution functions and fragmentation functions, commonly referred to as transverse momentum distributions (TMDs). TMDs describe the distribution of partons inside the proton and other hadrons with respect to both their longitudinal and transverse momenta. They provide unique insight into the internal momentum and spin structure of hadrons, and are a key ingredient in the description of many collider physics cross sections. Understanding TMDs requires a combination of theoretical techniques from quantum field theory, nonperturbative calculations using lattice QCD, and phenomenological analysis of experimental data. The handbook covers a wide range of topics, from theoretical foundations to experimental analyses, as well as recent developments and future directions. It is intended to provide an essential reference for researchers and graduate students interested in understanding the structure of hadrons and the dynamics of partons in high energy collisions.
Hadrons, Superconductor Vortices, and Cosmological Constant
Keh-Fei Liu
Feb 24 2023 hep-ph gr-qc hep-lat hep-th nucl-ex arXiv:2302.11600v3

@misc{2302.11600, author = {Keh-Fei Liu}, title = {{H}adrons, {S}uperconductor {V}ortices, and {C}osmological {C}onstant}, year = {2023}, eprint = {2302.11600}, note = {arXiv:2302.11600v3} }
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We explore the roles of the trace anomaly in several hadron properties. We derive the scale invariant expression for the pressure from the gravitational form factors (GFF) of QCD which results in consistent results for the mass and rest energy from the GFF and those from the trace and the Hamiltonian of the energy-momentum tensor (EMT) operators. It is shown that the energy-equilibrium correspondence of hadrons infers an equation of state where the trace anomaly matrix element, emerging from the glue condensate in the vacuum, gives a negative constant pressure that leads to confinement, much like the confinement mechanism for the vortices in type II superconductors where the negative constant pressure is due to the cost of depleting the superconducting condensate. We also note that both the trace anomaly in the QCD energy-momentum tensor and the cosmological constant in Einstein's equation are associated with the metric term which contributes to both energy and pressure. Their difference in terms of the role the pressure plays is discussed. Finally, we note that a lattice calculation of the trace anomaly distribution in the pion has addressed a question about the trace anomaly contribution to the pion mass and suggests that there might be a connection between the conformal symmetry breaking and chiral symmetry breaking in this case.
RI/(S)MOM renormalizations of overlap quark bilinears with different levels of hypercubic smearing
Yujiang Bi, Ying Chen, Ming Gong, Fangcheng He, Keh-Fei Liu, Zhaofeng Liu, Yi-Bo Yang, Dian-Jun Zhao
Feb 06 2023 hep-lat arXiv:2302.01659v2

@misc{2302.01659, author = {Yujiang Bi and Ying Chen and Ming Gong and Fangcheng He and Keh-Fei Liu and Zhaofeng Liu and Yi-Bo Yang and Dian-Jun Zhao}, title = {{RI}/({S}){MOM} renormalizations of overlap quark bilinears with different levels of hypercubic smearing}, year = {2023}, eprint = {2302.01659}, howpublished = {Phys.Rev.D 108 (2023) 5, 054506}, doi = {10.1103/PhysRevD.108.054506}, note = {arXiv:2302.01659v2} }
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On configurations with 2+1-flavor dynamical domain-wall fermions, we calculate the RI/(S)MOM renormalization constants (RC) of overlap quark bilinears. Hypercubic (HYP) smearing is used to construct the overlap Dirac operator. We investigate the possible effects of the smearing on discretization errors in the RCs by varying the level of smearing from 0 to 1 and 2. The lattice is of size $32^3\times64$ and with lattice spacing $1/a=2.383(9)$ GeV. The RCs in the $\overline{\rm MS}$ scheme at 2 GeV are given at the end, with the uncertainty of $Z_T$ reaching $\le1$% for the tensor current. Results of the renormalized quark masses and hadron matrix elements show that the renormalization procedure suppresses the $\sim$ 30% difference of the bare quantities with or without HYP smearing into the 3%-5% level.
Nucleon Electric Dipole Moment from the $\theta$ Term with Lattice Chiral Fermions
Jian Liang, Andrei Alexandru, Terrence Draper, Keh-Fei Liu, Bigeng Wang, Gen Wang, Yi-Bo Yang
Jan 12 2023 hep-lat hep-ph arXiv:2301.04331v1

@misc{2301.04331, author = {Jian Liang and Andrei Alexandru and Terrence Draper and Keh-Fei Liu and Bigeng Wang and Gen Wang and Yi-Bo Yang}, title = {{N}ucleon {E}lectric {D}ipole {M}oment from the $\theta$ {T}erm with {L}attice {C}hiral {F}ermions}, year = {2023}, eprint = {2301.04331}, note = {arXiv:2301.04331v1} }
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We calculate the nucleon electric dipole moment (EDM) from the $\theta$ term with overlap fermions on three domain wall lattices with different sea pion masses at lattice spacing 0.11 fm. Due to the chiral symmetry conserved by the overlap fermions, we have well defined topological charge and chiral limit for the EDM. Thus, the chiral extrapolation can be carried out reliably at nonzero lattice spacings. We use three to four different partially quenched valence pion masses for each sea pion mass and find that the EDM dependence on the valence and sea pion masses behaves oppositely, which can be described by partially quenched chiral perturbation theory. With the help of the cluster decomposition error reduction (CDER) technique, we determine the neutron and proton EDM at the physical pion mass to be $d_{n}=-0.00148\left(14\right)\left(31\right)\bar\theta$ e$\cdot$fm and $d_{p}=0.0038\left(11\right)\left(8\right)\bar\theta$ e$\cdot$fm. This work is a clear demonstration of the advantages of using chiral fermions in the nucleon EDM calculation and paves the road to future precise studies of the strong $CP$ violation effects.
Partial wave analysis of the charmed baryon hadronic decay $\Lambda_c^+\to\Lambda\pi^+\pi^0$
BESIII Collaboration, M. Ablikim, M. N. Achasov, P. Adlarson, M. Albrecht, R. Aliberti, A. Amoroso, M. R. An, Q. An, X. H. Bai, Y. Bai, O. Bakina, R. Baldini Ferroli, I. Balossino, Y. Ban, V. Batozskaya, D. Becker, K. Begzsuren, N. Berger, M. Bertani, et al (560)
Sep 20 2022 hep-ex hep-lat hep-ph arXiv:2209.08464v3

@misc{2209.08464, author = {BESIII Collaboration and M.~Ablikim and M.~N.~Achasov and P.~Adlarson and M.~Albrecht and R.~Aliberti and A.~Amoroso and M.~R.~An and Q.~An and X.~H.~Bai and Y.~Bai and O.~Bakina and R.~Baldini Ferroli and I.~Balossino and Y.~Ban and V.~Batozskaya and D.~Becker and K.~Begzsuren and N.~Berger and M.~Bertani and D.~Bettoni and F.~Bianchi and J.~Bloms and A.~Bortone and I.~Boyko and R.~A.~Briere and A.~Brueggemann and H.~Cai and X.~Cai and A.~Calcaterra and G.~F.~Cao and N.~Cao and S.~A.~Cetin and J.~F.~Chang and W.~L.~Chang and G.~Chelkov and C.~Chen and Chao Chen and G.~Chen and H.~S.~Chen and M.~L.~Chen and S.~J.~Chen and S.~M.~Chen and T.~Chen and X.~R.~Chen and X.~T.~Chen and Y.~B.~Chen and Z.~J.~Chen and W.~S.~Cheng and S.~K.~Choi and X.~Chu and G.~Cibinetto and S.~C.~Coen and F.~Cossio and J.~J.~Cui and H.~L.~Dai and J.~P.~Dai and A.~Dbeyssi and R.~E.~de Boer and D.~Dedovich and Z.~Y.~Deng and A.~Denig and I.~Denysenko and M.~Destefanis and F.~De Mori and Y.~Ding and J.~Dong and L.~Y.~Dong and M.~Y.~Dong and X.~Dong and S.~X.~Du and P.~Egorov and Y.~L.~Fan and J.~Fang and S.~S.~Fang and W.~X.~Fang and Y.~Fang and R.~Farinelli and L.~Fava and F.~Feldbauer and G.~Felici and C.~Q.~Feng and J.~H.~Feng and K Fischer and M.~Fritsch and C.~Fritzsch and C.~D.~Fu and H.~Gao and Y.~N.~Gao and Yang Gao and S.~Garbolino and I.~Garzia and P.~T.~Ge and Z.~W.~Ge and C.~Geng and E.~M.~Gersabeck and A Gilman and K.~Goetzen and L.~Gong and W.~X.~Gong and W.~Gradl and M.~Greco and L.~M.~Gu and M.~H.~Gu and Y.~T.~Gu and C.~Y Guan and A.~Q.~Guo and L.~B.~Guo and R.~P.~Guo and Y.~P.~Guo and A.~Guskov and T.~T.~Han and W.~Y.~Han and X.~Q.~Hao and F.~A.~Harris and K.~K.~He and K.~L.~He and F.~H.~Heinsius and C.~H.~Heinz and Y.~K.~Heng and C.~Herold and T.~Holtmann and G.~Y.~Hou and Y.~R.~Hou and Z.~L.~Hou and H.~M.~Hu and J.~F.~Hu and T.~Hu and Y.~Hu and G.~S.~Huang and K.~X.~Huang and L.~Q.~Huang and X.~T.~Huang and Y.~P.~Huang and T.~Hussain and N Hüsken and W.~Imoehl and M.~Irshad and J.~Jackson and S.~Jaeger and S.~Janchiv and E.~Jang and J.~H.~Jeong and Q.~Ji and Q.~P.~Ji and X.~B.~Ji and X.~L.~Ji and Y.~Y.~Ji and Z.~K.~Jia and H.~B.~Jiang and S.~S.~Jiang and X.~S.~Jiang and Y.~Jiang and J.~B.~Jiao and Z.~Jiao and S.~Jin and Y.~Jin and M.~Q.~Jing and T.~Johansson and N.~Kalantar-Nayestanaki and X.~S.~Kang and R.~Kappert and M.~Kavatsyuk and B.~C.~Ke and I.~K.~Keshk and A.~Khoukaz and R.~Kiuchi and R.~Kliemt and L.~Koch and O.~B.~Kolcu and B.~Kopf and M.~Kuemmel and M.~Kuessner and A.~Kupsc and W.~Kühn and J.~J.~Lane and J.~S.~Lange and P.~Larin and A.~Lavania and L.~Lavezzi and T.~T.~Lei and Z.~H.~Lei and H.~Leithoff and M.~Lellmann and T.~Lenz and C.~Li and C.~Li and C.~H.~Li and Cheng Li and D.~M.~Li and F.~Li and G.~Li and H.~Li and H.~B.~Li and H.~J.~Li and H.~N.~Li and J.~Q.~Li and J.~S.~Li and J.~W.~Li and Ke Li and L.~J Li and L.~K.~Li and Lei Li and M.~H.~Li and P.~R.~Li and S.~X.~Li and S.~Y.~Li and T.~Li and W.~D.~Li and W.~G.~Li and X.~H.~Li and X.~L.~Li and Xiaoyu Li and Y.~G.~Li and Z.~X.~Li and Z.~Y.~Li and H.~Liang and H.~Liang and H.~Liang and Y.~F.~Liang and Y.~T.~Liang and G.~R.~Liao and L.~Z.~Liao and J.~Libby and A.~Limphirat and D.~X.~Lin and T.~Lin and B.~J.~Liu and C.~X.~Liu and D.~Liu and F.~H.~Liu and Fang Liu and Feng Liu and G.~M.~Liu and H.~Liu and H.~B.~Liu and H.~M.~Liu and Huanhuan Liu and Huihui Liu and J.~B.~Liu and J.~L.~Liu and J.~Y.~Liu and K.~Liu and K.~Y.~Liu and Ke Liu and L.~Liu and Lu Liu and M.~H.~Liu and P.~L.~Liu and Q.~Liu and S.~B.~Liu and T.~Liu and W.~K.~Liu and W.~M.~Liu and X.~Liu and Y.~Liu and Y.~B.~Liu and Z.~A.~Liu and Z.~Q.~Liu and X.~C.~Lou and F.~X.~Lu and H.~J.~Lu and J.~G.~Lu and X.~L.~Lu and Y.~Lu and Y.~P.~Lu and Z.~H.~Lu and C.~L.~Luo and M.~X.~Luo and T.~Luo and X.~L.~Luo and X.~R.~Lyu and Y.~F.~Lyu and F.~C.~Ma and H.~L.~Ma and L.~L.~Ma and M.~M.~Ma and Q.~M.~Ma and R.~Q.~Ma and R.~T.~Ma and X.~Y.~Ma and Y.~Ma and F.~E.~Maas and M.~Maggiora and S.~Maldaner and S.~Malde and Q.~A.~Malik and A.~Mangoni and Y.~J.~Mao and Z.~P.~Mao and S.~Marcello and Z.~X.~Meng and J.~G.~Messchendorp and G.~Mezzadri and H.~Miao and T.~J.~Min and R.~E.~Mitchell and X.~H.~Mo and N.~Yu.~Muchnoi and Y.~Nefedov and F.~Nerling and I.~B.~Nikolaev and Z.~Ning and S.~Nisar and Y.~Niu and S.~L.~Olsen and Q.~Ouyang and S.~Pacetti and X.~Pan and Y.~Pan and A.~Pathak and Y.~P.~Pei and M.~Pelizaeus and H.~P.~Peng and K.~Peters and J.~L.~Ping and R.~G.~Ping and S.~Plura and S.~Pogodin and V.~Prasad and F.~Z.~Qi and H.~Qi and H.~R.~Qi and M.~Qi and T.~Y.~Qi and S.~Qian and W.~B.~Qian and Z.~Qian and C.~F.~Qiao and J.~J.~Qin and L.~Q.~Qin and X.~P.~Qin and X.~S.~Qin and Z.~H.~Qin and J.~F.~Qiu and S.~Q.~Qu and K.~H.~Rashid and C.~F.~Redmer and K.~J.~Ren and A.~Rivetti and V.~Rodin and M.~Rolo and G.~Rong and Ch.~Rosner and S.~N.~Ruan and A.~Sarantsev and Y.~Schelhaas and C.~Schnier and K.~Schoenning and M.~Scodeggio and K.~Y.~Shan and W.~Shan and X.~Y.~Shan and J.~F.~Shangguan and L.~G.~Shao and M.~Shao and C.~P.~Shen and H.~F.~Shen and X.~Y.~Shen and B.~A.~Shi and H.~C.~Shi and J.~Y.~Shi and Q.~Q.~Shi and R.~S.~Shi and X.~Shi and X.~D.~Shi and J.~J.~Song and W.~M.~Song and Y.~X.~Song and S.~Sosio and S.~Spataro and F.~Stieler and K.~X.~Su and P.~P.~Su and Y.~J.~Su and G.~X.~Sun and H.~Sun and H.~K.~Sun and J.~F.~Sun and L.~Sun and S.~S.~Sun and T.~Sun and W.~Y.~Sun and X Sun and Y.~J.~Sun and Y.~Z.~Sun and Z.~T.~Sun and Y.~H.~Tan and Y.~X.~Tan and C.~J.~Tang and G.~Y.~Tang and J.~Tang and L.~Y Tao and Q.~T.~Tao and M.~Tat and J.~X.~Teng and V.~Thoren and W.~H.~Tian and Y.~Tian and I.~Uman and B.~Wang and B.~Wang and B.~L.~Wang and C.~W.~Wang and D.~Y.~Wang and F.~Wang and H.~J.~Wang and H.~P.~Wang and K.~Wang and L.~L.~Wang and M.~Wang and Meng Wang and S.~Wang and S.~Wang and T.~Wang and T.~J.~Wang and W.~Wang and W.~H.~Wang and W.~P.~Wang and X.~Wang and X.~F.~Wang and X.~L.~Wang and Y.~Wang and Y.~D.~Wang and Y.~F.~Wang and Y.~H.~Wang and Y.~Q.~Wang and Yaqian Wang and Z.~Wang and Z.~Y.~Wang and Ziyi Wang and D.~Wei and D.~H.~Wei and F.~Weidner and S.~P.~Wen and C.~W.~Wenzel and D.~J.~White and U.~Wiedner and G.~Wilkinson and M.~Wolke and L.~Wollenberg and J.~F.~Wu and L.~H.~Wu and L.~J.~Wu and X.~Wu and X.~H.~Wu and Y.~Wu and Y.~J Wu and Z.~Wu and L.~Xia and T.~Xiang and D.~Xiao and G.~Y.~Xiao and H.~Xiao and S.~Y.~Xiao and Y.~L.~Xiao and Z.~J.~Xiao and C.~Xie and X.~H.~Xie and Y.~Xie and Y.~G.~Xie and Y.~H.~Xie and Z.~P.~Xie and T.~Y.~Xing and C.~F.~Xu and C.~J.~Xu and G.~F.~Xu and H.~Y.~Xu and Q.~J.~Xu and X.~P.~Xu and Y.~C.~Xu and Z.~P.~Xu and F.~Yan and L.~Yan and W.~B.~Yan and W.~C.~Yan and H.~J.~Yang and H.~L.~Yang and H.~X.~Yang and L.~Yang and S.~L.~Yang and Tao Yang and Y.~F.~Yang and Y.~X.~Yang and Yifan Yang and M.~Ye and M.~H.~Ye and J.~H.~Yin and Z.~Y.~You and B.~X.~Yu and C.~X.~Yu and G.~Yu and T.~Yu and X.~D.~Yu and C.~Z.~Yuan and L.~Yuan and S.~C.~Yuan and X.~Q.~Yuan and Y.~Yuan and Z.~Y.~Yuan and C.~X.~Yue and A.~A.~Zafar and F.~R.~Zeng and X.~Zeng and Y.~Zeng and Y.~H.~Zhan and A.~Q.~Zhang and B.~L.~Zhang and B.~X.~Zhang and D.~H.~Zhang and G.~Y.~Zhang and H.~Zhang and H.~H.~Zhang and H.~H.~Zhang and H.~Q.~Zhang and H.~Y.~Zhang and J.~J.~Zhang and J.~L.~Zhang and J.~Q.~Zhang and J.~W.~Zhang and J.~X.~Zhang and J.~Y.~Zhang and J.~Z.~Zhang and Jianyu Zhang and Jiawei Zhang and L.~M.~Zhang and L.~Q.~Zhang and Lei Zhang and P.~Zhang and Q.~Y.~Zhang and Shuihan Zhang and Shulei Zhang and X.~D.~Zhang and X.~M.~Zhang and X.~Y.~Zhang and X.~Y.~Zhang and Y.~Zhang and Y.~T.~Zhang and Y.~H.~Zhang and Yan Zhang and Yao Zhang and Z.~H.~Zhang and Z.~Y.~Zhang and Z.~Y.~Zhang and G.~Zhao and J.~Zhao and J.~Y.~Zhao and J.~Z.~Zhao and Lei Zhao and Ling Zhao and M.~G.~Zhao and S.~J.~Zhao and Y.~B.~Zhao and Y.~X.~Zhao and Z.~G.~Zhao and A.~Zhemchugov and B.~Zheng and J.~P.~Zheng and Y.~H.~Zheng and B.~Zhong and C.~Zhong and X.~Zhong and H.~Zhou and L.~P.~Zhou and X.~Zhou and X.~K.~Zhou and X.~R.~Zhou and X.~Y.~Zhou and Y.~Z.~Zhou and J.~Zhu and K.~Zhu and K.~J.~Zhu and L.~X.~Zhu and S.~H.~Zhu and S.~Q.~Zhu and W.~J.~Zhu and Y.~C.~Zhu and Z.~A.~Zhu and J.~H.~Zou and J.~Zu}, title = {{P}artial wave analysis of the charmed baryon hadronic decay $\{L}ambda_c^+\to\{L}ambda\pi^+\pi^0$}, year = {2022}, eprint = {2209.08464}, doi = {10.1007/JHEP12(2022)033}, note = {arXiv:2209.08464v3} }
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Based on $e^+e^-$ collision samples corresponding to an integrated luminosity of 4.4 $\mbox{fb$^-1$}$ collected with the BESIII detector at center-of-mass energies between $4.6\,\,\mathrm{GeV}$ and $4.7\,\,\mathrm{GeV}$, a partial wave analysis of the charmed baryon hadronic decay $\Lambda_c^+\to\Lambda\pi^+\pi^0$ is performed, and the decays $\Lambda_c^+\to\Lambda\rho(770)^{+}$ and $\Lambda_c^+\to\Sigma(1385)\pi$ are studied for the first time. Making use of the world-average branching fraction $\mathcal{B}(\Lambda_c^+\to\Lambda\pi^+\pi^0)$, their branching fractions are determined to be \begineqnarray* \beginaligned \mathcalB(\Lambda_c^+\to\Lambda\rho(770)^+)=&(4.06\pm0.30\pm0.35\pm0.23)\times10^-2,\\ \mathcalB(\Lambda_c^+\to\Sigma(1385)^+\pi^0)=&(5.86\pm0.49\pm0.52\pm0.35)\times10^-3,\\ \mathcalB(\Lambda_c^+\to\Sigma(1385)^0\pi^+)=&(6.47\pm0.59\pm0.66\pm0.38)\times10^-3,\\ \endaligned \endeqnarray* where the first uncertainties are statistical, the second are systematic, and the third are from the uncertainties of the branching fractions $\mathcal{B}(\Lambda_c^+\to\Lambda\pi^+\pi^0)$ and $\mathcal{B}(\Sigma(1385)\to\Lambda\pi)$. In addition, %according to amplitudes determined from the partial wave analysis, the decay asymmetry parameters are measured to be $\alpha_{\Lambda\rho(770)^+}=-0.763\pm0.053\pm0.045$, $\alpha_{\Sigma(1385)^{+}\pi^0}=-0.917\pm0.069\pm0.056$, and $\alpha_{\Sigma(1385)^{0}\pi^+}=-0.789\pm0.098\pm0.056$.
Lattice QCD and Particle Physics
Andreas S. Kronfeld, Tanmoy Bhattacharya, Thomas Blum, Norman H. Christ, Carleton DeTar, William Detmold, Robert Edwards, Anna Hasenfratz, Huey-Wen Lin, Swagato Mukherjee, Konstantinos Orginos, Richard Brower, Vincenzo Cirigliano, Zohreh Davoudi, Bálint Jóo, Chulwoo Jung, Christoph Lehner, Stefan Meinel, Ethan T. Neil, Peter Petreczky, et al (62)
Jul 18 2022 hep-lat hep-ex hep-ph arXiv:2207.07641v2

@misc{2207.07641, author = {Andreas S.~Kronfeld and Tanmoy Bhattacharya and Thomas Blum and Norman H.~Christ and Carleton DeTar and William Detmold and Robert Edwards and Anna Hasenfratz and Huey-Wen Lin and Swagato Mukherjee and Konstantinos Orginos and Richard Brower and Vincenzo Cirigliano and Zohreh Davoudi and Bálint Jóo and Chulwoo Jung and Christoph Lehner and Stefan Meinel and Ethan T.~Neil and Peter Petreczky and David G.~Richards and Alexei Bazavov and Simon Catterall and Jozef J.~Dudek and Aida X.~El-Khadra and Michael Engelhardt and George T.~Fleming and Joel Giedt and Rajan Gupta and Maxwell T.~Hansen and Taku Izubuchi and Frithjof Karsch and Jack Laiho and Keh-Fei Liu and Aaron S.~Meyer and Enrico Rinaldi and Martin Savage and David Schaich and Phiala E.~Shanahan and Stephen R.~Sharpe and Raza Sufian and Sergey Syritsyn and Ruth S.~Van de Water and Michael L.~Wagman and Evan Weinberg and Oliver Witzel and Christopher Aubin and Peter Boyle and Shailesh Chandrasekharan and Ian C.~Clöet and Martha Constantinou and Kimmy Cushman and Thomas DeGrand and Zoltan Fodor and Sam Foreman and Steven Gottlieb and Daniel Hoying and Yong-Chull Jang and William I.~Jay and Xiao-Yong Jin and Christopher Kelly and Julius Kuti and Henry Lamm and Meifeng Lin and Yin Lin and Andrew T.~Lytle and Paul Mackenzie and Jeffrey Mandula and Yannick Meurice and Christopher Monahan and Colin Morningstar and James C.~Osborn and Sungwoo Park and James N.~Simone and Alexei Strelchenko and Masaaki Tomii and Alejandro Vaquero and Pavlos Vranas and Bigeng Wang and Walter Wilcox and Boram Yoon and Yong Zhao}, title = {{L}attice {QCD} and {P}article {P}hysics}, year = {2022}, eprint = {2207.07641}, note = {arXiv:2207.07641v2} }
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Contribution from the USQCD Collaboration to the Proceedings of the US Community Study on the Future of Particle Physics (Snowmass 2021).
Connected and Disconnected Sea Partons from CT18 Parametrization of PDFs
Tie-Jiun Hou, Mengshi Yan, Jian Liang, Keh-Fei Liu, C.-P. Yuan
Jun 07 2022 hep-ph hep-lat arXiv:2206.02431v3

@misc{2206.02431, author = {Tie-Jiun Hou and Mengshi Yan and Jian Liang and Keh-Fei Liu and C.-P.~Yuan}, title = {{C}onnected and {D}isconnected {S}ea {P}artons from {CT}18 {P}arametrization of {PDF}s}, year = {2022}, eprint = {2206.02431}, note = {arXiv:2206.02431v3} }
PDF
The separation of the connected and disconnected sea partons, which were uncovered in the Euclidean path-integral formulation of the hadronic tensor, is accommodated with an alternative parametrization of the non-perturbative parton distribution functions in the CT18 global analysis. This is achieved with the help of the distinct small $x$ behaviours of these two sea partons and the constraint from the lattice calculation of the ratio of the strange momentum fraction to that of the $\bar u$ or $\bar d$ in the disconnected insertion. The whole dataset of CT18 is used in this CT18CS fit. The impact of the recent SeaQuest data on the $\bar{d}(x)-\bar{u}(x)$ distribution of CT18CS is also discussed. The separate momentum fractions for the valence, the connected sea and disconnected sea of $u$ and $d$, the strange and the gluon partons are presented at $\mu =1.3$ GeV for the first time. They can be compared term-by-term with systematic error controlled lattice calculations.
RI/MOM and RI/SMOM renormalization of quark bilinear operators using overlap fermions
Fangcheng He, Yu-Jiang Bi, Terrence Draper, Keh-Fei Liu, Zhaofeng Liu, Yi-Bo Yang
Apr 21 2022 hep-lat arXiv:2204.09246v3

@misc{2204.09246, author = {Fangcheng He and Yu-Jiang Bi and Terrence Draper and Keh-Fei Liu and Zhaofeng Liu and Yi-Bo Yang}, title = {{RI}/{MOM} and {RI}/{SMOM} renormalization of quark bilinear operators using overlap fermions}, year = {2022}, eprint = {2204.09246}, note = {arXiv:2204.09246v3} }
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We present the vector, scalar and tensor renormalization constants (RCs) using overlap fermions with either regularization independent momentum subtraction (RI/MOM) or symmetric momentum subtraction (RI/SMOM) as the intermediate scheme on the lattice with lattice spacings $a$ from 0.04 fm to 0.12 fm. Our gauge field configurations from the MILC and RBC/UKQCD collaborations include sea quarks using either the domain wall or the HISQ action, respectively. The results show that RI/MOM and RI/SMOM can provide consistent renormalization constants to the $\overline{\textrm{MS}}$ scheme, after proper $a^2p^2$ extrapolations. But at $p\sim 2$\u2009GeV, both RI/MOM and RI/SMOM suffer from nonperturbative effects which cannot be removed by the perturbative matching. The comparison between the results with different sea actions also suggests that the renormalization constant is discernibly sensitive to the lattice spacing but not to the bare gauge coupling in the gauge action.
Muon g-2 with overlap valence fermions
Gen Wang, Terrence Draper, Keh-Fei Liu, Yi-Bo Yang
Apr 05 2022 hep-lat hep-ph arXiv:2204.01280v3

@misc{2204.01280, author = {Gen Wang and Terrence Draper and Keh-Fei Liu and Yi-Bo Yang}, title = {{M}uon g-2 with overlap valence fermions}, year = {2022}, eprint = {2204.01280}, note = {arXiv:2204.01280v3} }
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We present a lattice calculation of the leading order (LO) hadronic vacuum polarization (HVP) contribution to the muon anomalous magnetic moment for the connected light and strange quarks, $a^{\rm W}_{{\rm con}, l/s}$ in the widely used window $t_0=0.4~\mathrm{fm}$, $t_1=1.0~\mathrm{fm}$, $\Delta=0.15~\mathrm{fm}$, and also of $a^{\rm S}_{{\rm con}, l/s}$ in the short distance region. We use overlap fermions on 4 physical-point ensembles. Two 2+1 flavor RBC/UKQCD ensembles use domain wall fermions (DWF) and Iwasaki gauge actions at $a = 0.084$ and 0.114 fm, and two 2+1+1 flavor MILC ensembles use the highly improved staggered quark (HISQ) and Symanzik gauge actions at $a = 0.088$ and 0.121 fm. We have incorporated infinite volume corrections from 3 additional DWF ensembles at ${\rm L}$ = 4.8, 6.4 and 9.6 fm and physical pion mass. For $a^{\rm W}_{{\rm con}, l}$, we find that our results on the two smaller lattice spacings are consistent with those using the unitary setup, but those at the two coarser lattice spacings are slightly different. Eventually, we predict $a^{\rm W}_{{\rm con}, l}=206.7(1.5)(1.0)$ and $a^{\rm W}_{{\rm con}, s}=26.8(0.1)(0.3)$, using linear extrapolation in $a^2$, with systematic uncertainties estimated from the difference of the central values from the RBC/UKQCD and MILC ensembles.
Prospects for precise predictions of $a_\mu$ in the Standard Model
G. Colangelo, M. Davier, A. X. El-Khadra, M. Hoferichter, C. Lehner, L. Lellouch, T. Mibe, B. L. Roberts, T. Teubner, H. Wittig, B. Ananthanarayan, A. Bashir, J. Bijnens, T. Blum, P. Boyle, N. Bray-Ali, I. Caprini, C. M. Carloni Calame, O. Catà, M. Cè, et al (62)
Mar 31 2022 hep-ph hep-ex hep-lat nucl-ex nucl-th arXiv:2203.15810v1

@misc{2203.15810, author = {G.~Colangelo and M.~Davier and A.~X.~El-Khadra and M.~Hoferichter and C.~Lehner and L.~Lellouch and T.~Mibe and B.~L.~Roberts and T.~Teubner and H.~Wittig and B.~Ananthanarayan and A.~Bashir and J.~Bijnens and T.~Blum and P.~Boyle and N.~Bray-Ali and I.~Caprini and C.~M.~Carloni Calame and O.~Catà and M.~Cè and J.~Charles and N.~H.~Christ and F.~Curciarello and I.~Danilkin and D.~Das and O.~Deineka and M.~Della Morte and A.~Denig and C.~E.~DeTar and C.~A.~Dominguez and G.~Eichmann and C.~S.~Fischer and A.~Gérardin and D.~Giusti and M.~Golterman and Steven Gottlieb and V.~Gülpers and F.~Hagelstein and M.~Hayakawa and N.~Hermansson-Truedsson and B.-L.~Hoid and S.~Holz and T.~Izubuchi and A.~Jüttner and A.~Keshavarzi and M.~Knecht and A.~S.~Kronfeld and B.~Kubis and A.~Kupść and S.~Lahert and K.~F.~Liu and J.~Lüdtke and M.~Lynch and B.~Malaescu and K.~Maltman and W.~Marciano and M.~K.~Marinković and P.~Masjuan and H.~B.~Meyer and S.~E.~Müller and E.~T.~Neil and M.~Passera and M.~Pepe and S.~Peris and A.~A.~Petrov and M.~Procura and K.~Raya and A.~Rebhan and A.~Risch and A.~Rodríguez-Sánchez and P.~Roig and P.~Sánchez-Puertas and S.~Simula and P.~Stoffer and F.~M.~Stokes and R.~Sugar and J.~T.~Tsang and R.~S.~van de Water and A.~Vaquero Avilés-Casco and G.~Venanzoni and G.~M.~von Hippel and Z.~Zhang}, title = {{P}rospects for precise predictions of $a_\mu$ in the {S}tandard {M}odel}, year = {2022}, eprint = {2203.15810}, note = {arXiv:2203.15810v1} }
PDF
We discuss the prospects for improving the precision on the hadronic corrections to the anomalous magnetic moment of the muon, and the plans of the Muon $g-2$ Theory Initiative to update the Standard Model prediction.
Theoretical tools for neutrino scattering: interplay between lattice QCD, EFTs, nuclear physics, phenomenology, and neutrino event generators
L. Alvarez Ruso, A. M. Ankowski, S. Bacca, A. B. Balantekin, J. Carlson, S. Gardiner, R. Gonzalez-Jimenez, R. Gupta, T. J. Hobbs, M. Hoferichter, J. Isaacson, N. Jachowicz, W. I. Jay, T. Katori, F. Kling, A. S. Kronfeld, S. W. Li, H.-W. Lin, K.-F. Liu, A. Lovato, et al (41)
Mar 18 2022 hep-ph hep-ex hep-lat nucl-th physics.comp-ph arXiv:2203.09030v2

@misc{2203.09030, author = {L.~Alvarez Ruso and A.~M.~Ankowski and S.~Bacca and A.~B.~Balantekin and J.~Carlson and S.~Gardiner and R.~Gonzalez-Jimenez and R.~Gupta and T.~J.~Hobbs and M.~Hoferichter and J.~Isaacson and N.~Jachowicz and W.~I.~Jay and T.~Katori and F.~Kling and A.~S.~Kronfeld and S.~W.~Li and H.-W.~Lin and K.-F.~Liu and A.~Lovato and K.~Mahn and J.~Menendez and A.~S.~Meyer and J.~Morfin and S.~Pastore and N.~Rocco and M.~Sajjad Athar and T.~Sato and A.~Schwenk and P.~E.~Shanahan and L.~E.~Strigari and M.~Wagman and X.~Zhang and Y.~Zhao and B.~Acharya and L.~Andreoli and C.~Andreopoulos and J.~L.~Barrow and T.~Bhattacharya and V.~Brdar and Z.~Davoudi and C.~Giusti and Y.~Hayato and A.~N.~Khan and D.~Kim and Y.~F.~Li and M.~Lin and P.~Machado and M.~Martini and K.~Niewczas and P.~Pandey and A.~Papadopoulou and R.~Plestid and M.~Roda and I.~Ruiz Simo and J.~N.~Simone and R.~S.~Sufian and J.~Tena-Vidal and O.~Tomalak and Y.-D.~Tsai and J.~M.~Udias}, title = {{T}heoretical tools for neutrino scattering: interplay between lattice {QCD}, {EFT}s, nuclear physics, phenomenology, and neutrino event generators}, year = {2022}, eprint = {2203.09030}, note = {arXiv:2203.09030v2} }
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Maximizing the discovery potential of increasingly precise neutrino experiments will require an improved theoretical understanding of neutrino-nucleus cross sections over a wide range of energies. Low-energy interactions are needed to reconstruct the energies of astrophysical neutrinos from supernovae bursts and search for new physics using increasingly precise measurement of coherent elastic neutrino scattering. Higher-energy interactions involve a variety of reaction mechanisms including quasi-elastic scattering, resonance production, and deep inelastic scattering that must all be included to reliably predict cross sections for energies relevant to DUNE and other accelerator neutrino experiments. This white paper discusses the theoretical status, challenges, required resources, and path forward for achieving precise predictions of neutrino-nucleus scattering and emphasizes the need for a coordinated theoretical effort involved lattice QCD, nuclear effective theories, phenomenological models of the transition region, and event generators.
Lattice QCD Calculations of Parton Physics
Martha Constantinou, Luigi Del Debbio, Xiangdong Ji, Huey-Wen Lin, Keh-Fei Liu, Christopher Monahan, Kostas Orginos, Peter Petreczky, Jian-Wei Qiu, David Richards, Nobuo Sato, Phiala Shanahan, C.-P. Yuan, Jian-Hui Zhang, Yong Zhao
Feb 16 2022 hep-lat hep-ph arXiv:2202.07193v1

@misc{2202.07193, author = {Martha Constantinou and Luigi Del Debbio and Xiangdong Ji and Huey-Wen Lin and Keh-Fei Liu and Christopher Monahan and Kostas Orginos and Peter Petreczky and Jian-Wei Qiu and David Richards and Nobuo Sato and Phiala Shanahan and C.-P.~Yuan and Jian-Hui Zhang and Yong Zhao}, title = {{L}attice {QCD} {C}alculations of {P}arton {P}hysics}, year = {2022}, eprint = {2202.07193}, note = {arXiv:2202.07193v1} }
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In this document, we summarize the status and challenges of calculating parton physics in lattice QCD for the US Particle Physics Community Planning Exercise (a.k.a. "Snowmass"). While PDF-moments calculations have been very successful and been continuously improved, new methods have been developed to calculate distributions directly in $x$-space. Many recent lattice studies have been focused on calculating isovector PDFs of the pion and nucleon, learning to control systematics associated with excited-state contamination, renormalization and continuum extrapolations, pion-mass and finite-volume effects, etc. Although in some cases, the lattice results are already competitive with experimental data, to reach the level of precision in a wide range of $x$ for unpolarized nucleon PDFs impactful for future collider physics remains a challenge, and may require exascale supercomputing power. The new theoretical methods open the door for calculating other partonic observables which will be the focus of the experimental program in nuclear physics, including generalized parton distributions and transverse-momentum dependent PDFs. A fruitful interplay between experimental data and lattice-QCD calculations will usher in a new era for parton physics and hadron structure.
Status on Lattice Calculations of the Proton Spin Decomposition
Keh-Fei Liu
Dec 17 2021 hep-lat hep-ph arXiv:2112.08416v2

@misc{2112.08416, author = {Keh-Fei Liu}, title = {{S}tatus on {L}attice {C}alculations of the {P}roton {S}pin {D}ecomposition}, year = {2021}, eprint = {2112.08416}, note = {arXiv:2112.08416v2} }
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Lattice calculations of the proton spin components is reviewed. The lattice results of the quark spin from the axial-vector current matrix element at $\sim 0.3- 0.4$ is smaller than those from the constituent quark models. This is largely due to the fact that the vacuum polarization contribution from the disconnected insertion is negative. Its connection with the anomalous Ward identity is clarified and verified numerically. This resolves the contentious issue in the `proton spin crisis'. The glue spin and angular momentum are found to be large and there is notable contribution from the quark orbital angular momentum. Renormalization, mixing and normalization of the quark and glue angular momenta are discussed. With sufficient precision, they can be compared with more precise experimental measurements when the electron-ion collider facility is available.
Glueballs at Physical Pion Mass
Feiyu Chen, Xiangyu Jiang, Ying Chen, Keh-Fei Liu, Wei Sun, Yi-Bo Yang
Nov 24 2021 hep-lat arXiv:2111.11929v1

@misc{2111.11929, author = {Feiyu Chen and Xiangyu Jiang and Ying Chen and Keh-Fei Liu and Wei Sun and Yi-Bo Yang}, title = {{G}lueballs at {P}hysical {P}ion {M}ass}, year = {2021}, eprint = {2111.11929}, note = {arXiv:2111.11929v1} }
PDF
We study glueballs on two $N_f=2+1$ RBC/UKQCD gauge ensembles with physical quark masses at two lattice spacings. The statistical uncertainties of the glueball correlation functions are considerably reduced through the cluster decomposition error reduction (CDER) method. The Bethe-Salpeter wave functions are obtained for the scalar, tensor and pseudoscalar glueballs by using spatially extended glueball operators defined through the gauge potential $A_\mu(x)$ in the Coulomb gauge. These wave functions show similar features of non-relativistic two-gluon systems, and they are used to optimize the signals of the related correlation functions at the early time regions. Consequently, the ground state masses can be extracted precisely. To the extent that the excited state contamination is not important, our calculation gives glueball masses at the physical pion mass for the first time.
Proton momentum and angular momentum decompositions with overlap fermions
Gen Wang, Yi-Bo Yang, Jian Liang, Terrence Draper, Keh-Fei Liu
Nov 19 2021 hep-lat hep-ph arXiv:2111.09329v2

@misc{2111.09329, author = {Gen Wang and Yi-Bo Yang and Jian Liang and Terrence Draper and Keh-Fei Liu}, title = {{P}roton momentum and angular momentum decompositions with overlap fermions}, year = {2021}, eprint = {2111.09329}, doi = {10.1103/PhysRevD.106.014512}, note = {arXiv:2111.09329v2} }
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We present a calculation of the proton momentum and angular momentum decompositions using overlap fermions on a $2+1$-flavor RBC/UKQCD domain-wall lattice at 0.143 fm with a pion mass of 171 MeV which is close to the physical one. A complete determination of the momentum and angular momentum fractions carried by up, down, strange and glue inside the proton has been done with valence pion masses varying from 171 to 391 MeV. We have utilized fast Fourier transform on the stochastic-sandwich method for connected-insertion parts and the cluster-decomposition error reduction technique for disconnected-insertion parts has been used to reduce statistical errors. The full nonperturbative renormalization and mixing between the quark and glue operators are carried out. The final results are normalized with the momentum and angular momentum sum rules and reported at the physical valence pion mass at ${\overline{\rm {MS}}}\, (\mu = 2\ {\rm{GeV}})$. The renormalized momentum fractions for the quarks and glue are $\langle x \rangle^q = 0.491(20)(23)$ and $\langle x \rangle^g = 0.509(20)(23)$, respectively, and the renormalized total angular momentum fractions for quarks and glue are $2 J^q = 0.539(22)(44)$ and $2 J^g = 0.461(22)(44)$, respectively. The quark spin fraction is $\Sigma = 0.405(25)(37)$ from our previous work and the quark orbital angular momentum fraction is deduced from $2 L^q = 2 J^q - \Sigma$ to be $0.134(22)(44)$.
Study of the decay $D^+\to K^*(892)^+ K_S^0$ in $D^+\to K^+ K_S^0 \pi^0$
BESIII Collaboration, M. Ablikim, M. N. Achasov, P. Adlarson, S. Ahmed, M. Albrecht, R. Aliberti, A. Amoroso, M. R. An, Q. An, X. H. Bai, Y. Bai, O. Bakina, R. Baldini Ferroli, I. Balossino, Y. Ban, K. Begzsuren, N. Berger, M. Bertani, D. Bettoni, et al (497)
Apr 20 2021 hep-ex hep-lat hep-ph arXiv:2104.09131v3

@misc{2104.09131, author = {BESIII Collaboration and M.~Ablikim and M.~N.~Achasov and P.~Adlarson and S.~Ahmed and M.~Albrecht and R.~Aliberti and A.~Amoroso and M.~R.~An and Q.~An and X.~H.~Bai and Y.~Bai and O.~Bakina and R.~Baldini Ferroli and I.~Balossino and Y.~Ban and K.~Begzsuren and N.~Berger and M.~Bertani and D.~Bettoni and F.~Bianchi and J.~Bloms and A.~Bortone and I.~Boyko and R.~A.~Briere and H.~Cai and X.~Cai and A.~Calcaterra and G.~F.~Cao and N.~Cao and S.~A.~Cetin and J.~F.~Chang and W.~L.~Chang and G.~Chelkov and D.~Y.~Chen and G.~Chen and H.~S.~Chen and M.~L.~Chen and S.~J.~Chen and X.~R.~Chen and Y.~B.~Chen and Z.~J Chen and W.~S.~Cheng and G.~Cibinetto and F.~Cossio and X.~F.~Cui and H.~L.~Dai and X.~C.~Dai and A.~Dbeyssi and R.~E.~de Boer and D.~Dedovich and Z.~Y.~Deng and A.~Denig and I.~Denysenko and M.~Destefanis and F.~De Mori and Y.~Ding and C.~Dong and J.~Dong and L.~Y.~Dong and M.~Y.~Dong and X.~Dong and S.~X.~Du and Y.~L.~Fan and J.~Fang and S.~S.~Fang and Y.~Fang and R.~Farinelli and L.~Fava and F.~Feldbauer and G.~Felici and C.~Q.~Feng and J.~H.~Feng and M.~Fritsch and C.~D.~Fu and Y.~Gao and Y.~Gao and Y.~Gao and Y.~G.~Gao and I.~Garzia and P.~T.~Ge and C.~Geng and E.~M.~Gersabeck and A Gilman and K.~Goetzen and L.~Gong and W.~X.~Gong and W.~Gradl and M.~Greco and L.~M.~Gu and M.~H.~Gu and Y.~T.~Gu and C.~Y Guan and A.~Q.~Guo and L.~B.~Guo and R.~P.~Guo and Y.~P.~Guo and A.~Guskov and T.~T.~Han and W.~Y.~Han and X.~Q.~Hao and F.~A.~Harris and K.~L.~He and F.~H.~Heinsius and C.~H.~Heinz and T.~Held and Y.~K.~Heng and C.~Herold and M.~Himmelreich and T.~Holtmann and G.~Y.~Hou and Y.~R.~Hou and Z.~L.~Hou and H.~M.~Hu and J.~F.~Hu and T.~Hu and Y.~Hu and G.~S.~Huang and L.~Q.~Huang and X.~T.~Huang and Y.~P.~Huang and Z.~Huang and T.~Hussain and N Hüsken and W.~Ikegami Andersson and W.~Imoehl and M.~Irshad and S.~Jaeger and S.~Janchiv and Q.~Ji and Q.~P.~Ji and X.~B.~Ji and X.~L.~Ji and Y.~Y.~Ji and H.~B.~Jiang and X.~S.~Jiang and J.~B.~Jiao and Z.~Jiao and S.~Jin and Y.~Jin and M.~Q.~Jing and T.~Johansson and N.~Kalantar-Nayestanaki and X.~S.~Kang and R.~Kappert and M.~Kavatsyuk and B.~C.~Ke and I.~K.~Keshk and A.~Khoukaz and P.~Kiese and R.~Kiuchi and R.~Kliemt and L.~Koch and O.~B.~Kolcu and B.~Kopf and M.~Kuemmel and M.~Kuessner and A.~Kupsc and M.~G.~Kurth and W.~Kühn and J.~J.~Lane and J.~S.~Lange and P.~Larin and A.~Lavania and L.~Lavezzi and Z.~H.~Lei and H.~Leithoff and M.~Lellmann and T.~Lenz and C.~Li and C.~H.~Li and Cheng Li and D.~M.~Li and F.~Li and G.~Li and H.~Li and H.~Li and H.~B.~Li and H.~J.~Li and J.~L.~Li and J.~Q.~Li and J.~S.~Li and Ke Li and L.~K.~Li and Lei Li and P.~R.~Li and S.~Y.~Li and W.~D.~Li and W.~G.~Li and X.~H.~Li and X.~L.~Li and Xiaoyu Li and Z.~Y.~Li and H.~Liang and H.~Liang and H.~Liang and Y.~F.~Liang and Y.~T.~Liang and G.~R.~Liao and L.~Z.~Liao and J.~Libby and C.~X.~Lin and B.~J.~Liu and C.~X.~Liu and D.~Liu and F.~H.~Liu and Fang Liu and Feng Liu and H.~B.~Liu and H.~M.~Liu and Huanhuan Liu and Huihui Liu and J.~B.~Liu and J.~L.~Liu and J.~Y.~Liu and K.~Liu and K.~Y.~Liu and L.~Liu and M.~H.~Liu and P.~L.~Liu and Q.~Liu and Q.~Liu and S.~B.~Liu and Shuai Liu and T.~Liu and W.~M.~Liu and X.~Liu and Y.~Liu and Y.~B.~Liu and Z.~A.~Liu and Z.~Q.~Liu and X.~C.~Lou and F.~X.~Lu and H.~J.~Lu and J.~D.~Lu and J.~G.~Lu and X.~L.~Lu and Y.~Lu and Y.~P.~Lu and C.~L.~Luo and M.~X.~Luo and P.~W.~Luo and T.~Luo and X.~L.~Luo and X.~R.~Lyu and F.~C.~Ma and H.~L.~Ma and L.~L.~Ma and M.~M.~Ma and Q.~M.~Ma and R.~Q.~Ma and R.~T.~Ma and X.~X.~Ma and X.~Y.~Ma and F.~E.~Maas and M.~Maggiora and S.~Maldaner and S.~Malde and Q.~A.~Malik and A.~Mangoni and Y.~J.~Mao and Z.~P.~Mao and S.~Marcello and Z.~X.~Meng and J.~G.~Messchendorp and G.~Mezzadri and T.~J.~Min and R.~E.~Mitchell and X.~H.~Mo and Y.~J.~Mo and N.~Yu.~Muchnoi and H.~Muramatsu and S.~Nakhoul and Y.~Nefedov and F.~Nerling and I.~B.~Nikolaev and Z.~Ning and S.~Nisar and S.~L.~Olsen and Q.~Ouyang and S.~Pacetti and X.~Pan and Y.~Pan and A.~Pathak and A.~Pathak and P.~Patteri and M.~Pelizaeus and H.~P.~Peng and K.~Peters and J.~Pettersson and J.~L.~Ping and R.~G.~Ping and R.~Poling and V.~Prasad and H.~Qi and H.~R.~Qi and K.~H.~Qi and M.~Qi and T.~Y.~Qi and S.~Qian and W.~B.~Qian and Z.~Qian and C.~F.~Qiao and L.~Q.~Qin and X.~P.~Qin and X.~S.~Qin and Z.~H.~Qin and J.~F.~Qiu and S.~Q.~Qu and K.~H.~Rashid and K.~Ravindran and C.~F.~Redmer and A.~Rivetti and V.~Rodin and M.~Rolo and G.~Rong and Ch.~Rosner and M.~Rump and H.~S.~Sang and A.~Sarantsev and Y.~Schelhaas and C.~Schnier and K.~Schoenning and M.~Scodeggio and D.~C.~Shan and W.~Shan and X.~Y.~Shan and J.~F.~Shangguan and M.~Shao and C.~P.~Shen and H.~F.~Shen and P.~X.~Shen and X.~Y.~Shen and H.~C.~Shi and R.~S.~Shi and X.~Shi and X.~D Shi and J.~J.~Song and W.~M.~Song and Y.~X.~Song and S.~Sosio and S.~Spataro and K.~X.~Su and P.~P.~Su and F.~F.~Sui and G.~X.~Sun and H.~K.~Sun and J.~F.~Sun and L.~Sun and S.~S.~Sun and T.~Sun and W.~Y.~Sun and W.~Y.~Sun and X Sun and Y.~J.~Sun and Y.~K.~Sun and Y.~Z.~Sun and Z.~T.~Sun and Y.~H.~Tan and Y.~X.~Tan and C.~J.~Tang and G.~Y.~Tang and J.~Tang and J.~X.~Teng and V.~Thoren and W.~H.~Tian and Y.~T.~Tian and I.~Uman and B.~Wang and C.~W.~Wang and D.~Y.~Wang and H.~J.~Wang and H.~P.~Wang and K.~Wang and L.~L.~Wang and M.~Wang and M.~Z.~Wang and Meng Wang and W.~Wang and W.~H.~Wang and W.~P.~Wang and X.~Wang and X.~F.~Wang and X.~L.~Wang and Y.~Wang and Y.~Wang and Y.~D.~Wang and Y.~F.~Wang and Y.~Q.~Wang and Y.~Y.~Wang and Z.~Wang and Z.~Y.~Wang and Ziyi Wang and Zongyuan Wang and D.~H.~Wei and F.~Weidner and S.~P.~Wen and D.~J.~White and U.~Wiedner and G.~Wilkinson and M.~Wolke and L.~Wollenberg and J.~F.~Wu and L.~H.~Wu and L.~J.~Wu and X.~Wu and Z.~Wu and L.~Xia and H.~Xiao and S.~Y.~Xiao and Z.~J.~Xiao and X.~H.~Xie and Y.~G.~Xie and Y.~H.~Xie and T.~Y.~Xing and G.~F.~Xu and Q.~J.~Xu and W.~Xu and X.~P.~Xu and Y.~C.~Xu and F.~Yan and L.~Yan and W.~B.~Yan and W.~C.~Yan and Xu Yan and H.~J.~Yang and H.~X.~Yang and L.~Yang and S.~L.~Yang and Y.~X.~Yang and Yifan Yang and Zhi Yang and M.~Ye and M.~H.~Ye and J.~H.~Yin and Z.~Y.~You and B.~X.~Yu and C.~X.~Yu and G.~Yu and J.~S.~Yu and T.~Yu and C.~Z.~Yuan and L.~Yuan and X.~Q.~Yuan and Y.~Yuan and Z.~Y.~Yuan and C.~X.~Yue and A.~A.~Zafar and X.~Zeng Zeng and Y.~Zeng and A.~Q.~Zhang and B.~X.~Zhang and Guangyi Zhang and H.~Zhang and H.~H.~Zhang and H.~H.~Zhang and H.~Y.~Zhang and J.~J.~Zhang and J.~L.~Zhang and J.~Q.~Zhang and J.~W.~Zhang and J.~Y.~Zhang and J.~Z.~Zhang and Jianyu Zhang and Jiawei Zhang and L.~M.~Zhang and L.~Q.~Zhang and Lei Zhang and S.~Zhang and S.~F.~Zhang and Shulei Zhang and X.~D.~Zhang and X.~Y.~Zhang and Y.~Zhang and Y.~T.~Zhang and Y.~H.~Zhang and Yan Zhang and Yao Zhang and Z.~H.~Zhang and Z.~Y.~Zhang and G.~Zhao and J.~Zhao and J.~Y.~Zhao and J.~Z.~Zhao and Lei Zhao and Ling Zhao and M.~G.~Zhao and Q.~Zhao and S.~J.~Zhao and Y.~B.~Zhao and Y.~X.~Zhao and Z.~G.~Zhao and A.~Zhemchugov and B.~Zheng and J.~P.~Zheng and Y.~Zheng and Y.~H.~Zheng and B.~Zhong and C.~Zhong and L.~P.~Zhou and Q.~Zhou and X.~Zhou and X.~K.~Zhou and X.~R.~Zhou and X.~Y.~Zhou and A.~N.~Zhu and J.~Zhu and K.~Zhu and K.~J.~Zhu and S.~H.~Zhu and T.~J.~Zhu and W.~J.~Zhu and W.~J.~Zhu and Y.~C.~Zhu and Z.~A.~Zhu and B.~S.~Zou and J.~H.~Zou}, title = {{S}tudy of the decay ${D}^+\to {K}^*(892)^+ {K}_{S}^0$ in ${D}^+\to {K}^+ {K}_{S}^0 \pi^0$}, year = {2021}, eprint = {2104.09131}, howpublished = {Phys. Rev. D 104, 012006 (2021)}, doi = {10.1103/PhysRevD.104.012006}, note = {arXiv:2104.09131v3} }
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Based on an $e^{+}e^{-}$ collision data sample corresponding to an integrated luminosity of 2.93 $\mathrm{fb}^{-1}$ collected with the BESIII detector at $\sqrt{s}=3.773 \mathrm{GeV}$, the first amplitude analysis of the singly Cabibbo-suppressed decay $D^{+}\to K^+ K_S^0 \pi^0$ is performed. From the amplitude analysis, the $K^*(892)^+ K_S^0$ component is found to be dominant with a fraction of $(57.1\pm2.6\pm4.2)\%$, where the first uncertainty is statistical and the second systematic. In combination with the absolute branching fraction $\mathcal{B}(D^+\to K^+ K_S^0 \pi^0)$ measured by BESIII, we obtain $\mathcal{B}(D^+\to K^*(892)^+ K_S^0)=(8.69\pm0.40\pm0.64\pm0.51)\times10^{-3}$, where the third uncertainty is due to the branching fraction $\mathcal{B}(D^+\to K^+ K_S^0 \pi^0)$. The precision of this result is significantly improved compared to the previous measurement.
Proton Mass Decomposition and Hadron Cosmological Constant
Keh-Fei Liu
Mar 31 2021 hep-ph hep-lat hep-th nucl-th arXiv:2103.15768v3

@misc{2103.15768, author = {Keh-Fei Liu}, title = {{P}roton {M}ass {D}ecomposition and {H}adron {C}osmological {C}onstant}, year = {2021}, eprint = {2103.15768}, note = {arXiv:2103.15768v3} }
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Lattice results on sigma terms and global analysis of parton momentum fractions are used to give the quark and glue fractions of the proton mass and rest energy. The mass decomposition in terms of the trace of the energy-momentum tensor is renormalization group invariant. The decomposition of the rest energy from the Hamiltonian and the gravitational form factors are scheme and scale dependent. The separation of the energy-momentum tensor into the traceless part which is composed of the quark and glue parton momentum fractions and the trace part has the minimum scheme dependence. We identify the glue part of the trace anomaly $\langle H_{\beta}\rangle $ as the vacuum energy from the glue condensate in the vacuum. From the metric term of the gravitational form factors, which is the stress part of the stress-energy-momentum tensor, we find that the trace part of the rest energy, dominated by $\langle H_{\beta}\rangle$, gives a \it constant restoring pressure which balances that from the traceless part of the Hamiltonian to confine the hadron, much like the cosmological constant Einstein introduced for a static universe. From a lattice calculation of $\langle H_{\beta}\rangle$ in the charmonium, we deduce the associated string tension which turns out to be in good agreement with that from a Cornell potential which fits the charmonium spectrum.
Nucleon isovector scalar charge from overlap fermions
Liuming Liu, Ting Chen, Terrence Draper, Jian Liang, Keh-Fei Liu, Gen Wang, Yi-Bo Yang
Mar 25 2021 hep-lat hep-ph arXiv:2103.12933v3

@misc{2103.12933, author = {Liuming Liu and Ting Chen and Terrence Draper and Jian Liang and Keh-Fei Liu and Gen Wang and Yi-Bo Yang}, title = {{N}ucleon isovector scalar charge from overlap fermions}, year = {2021}, eprint = {2103.12933}, howpublished = {Phys. Rev. D 104, 094503(2021)}, doi = {10.1103/PhysRevD.104.094503}, note = {arXiv:2103.12933v3} }
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We calculate the nucleon isovector scalar charge in lattice QCD using overlap fermions on five ensembles of gauge configurations generated by the RBC/UKQCD collaboration using the domain-wall quark action with $2+1$ dynamical flavors. The five ensembles cover five pion masses, $m_\pi \approx$ 139, 171, 302, 337 and 371 MeV, and four lattice spacings, $a \approx $ 0.06, 0.08, 0.11 and 0.14 fm. Three to six valence quark masses are computed on each ensemble to investigate the pion mass dependence. The extrapolation to the physical pion mass, continuum and infinite volume limits is obtained by a global fit of all data to a formula originated from partially quenched chiral perturbation theory. The excited-states contamination is carefully analyzed with 3--5 sink-source separations and multi-state fits. Our final result, in the $\overline{\text{MS}}$ scheme at 2 GeV, is $g_{S}^{u-d}= 0.94 (10)_{stat}(8)_{sys}$, where the first error is the statistical error and the second is the systematic error.
Detecting flavor content of the vacuum using the Dirac operator spectrum
Jian Liang, Andrei Alexandru, Yu-Jiang Bi, Terrence Draper, Keh-Fei Liu, Yi-Bo Yang
Feb 11 2021 hep-lat hep-ph arXiv:2102.05380v3

@misc{2102.05380, author = {Jian Liang and Andrei Alexandru and Yu-Jiang Bi and Terrence Draper and Keh-Fei Liu and Yi-Bo Yang}, title = {{D}etecting flavor content of the vacuum using the {D}irac operator spectrum}, year = {2021}, eprint = {2102.05380}, note = {arXiv:2102.05380v3} }
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We compute the overlap Dirac spectrum on three ensembles generated using 2+1 flavor domain wall fermions. The spectral density is determined up to $\lambda\sim$100 MeV with sub-percentage statistical uncertainty. The three ensembles have different lattice spacings and two of them have quark masses tuned to the physical point. We show that we can resolve the flavor content of the sea quarks and constrain their masses using the Dirac spectral density. We find that the density is close to a constant below $\lambda\le$ 20 MeV (but 10\% higher than that in the 2-flavor chiral limit) as predicted by chiral perturbative theory ($\chi$PT), and then increases linearly due to the strange quark mass. Using the next to leading order $\chi$PT, one can extract the light and strange quark masses with $\sim$20\% uncertainties. Using the non-perturbative RI/MOM renormalization, we obtain the chiral condensates at $\overline{\textrm{MS}}$ 2 GeV as $\Sigma=(260.3(0.7)(1.3)(0.7)(0.8)\ \textrm{MeV})^3$ in the $N_f=2$ (keeping the strange quark mass at the physical point) chiral limit and $\Sigma_0=(232.6(0.9)(1.2)(0.7)(0.8)\ \textrm{MeV})^3$ in the $N_f=3$ chiral limit, where the four uncertainties come from the statistical fluctuation, renormalization constant, continuum extrapolation and lattice spacing determination. Note that $\Sigma/\Sigma_0=1.40(2)(2)$ is much larger than 1 due to the strange quark mass effect.
PDFs and Neutrino-Nucleon Scattering from Hadronic Tensor
Jian Liang, Keh-Fei Liu
Aug 31 2020 hep-lat hep-ph arXiv:2008.12389v1

@misc{2008.12389, author = {Jian Liang and Keh-Fei Liu}, title = {{PDF}s and {N}eutrino-{N}ucleon {S}cattering from {H}adronic {T}ensor}, year = {2020}, eprint = {2008.12389}, doi = {10.22323/1.363.0046}, note = {arXiv:2008.12389v1} }
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We review the Euclidean path-integral formulation of the nucleon hadronic tensor and classify the gauge invariant and topologically distinct insertions in terms of connected and disconnected insertions and also in terms of leading and higher-twist contributions in the DIS region. Converting the Euclidean hadronic tensor back to the Minkowski space requires solving an inverse problem of the Laplace transform. We have investigated several inverse algorithms and studied the pros and cons of each. We show a result with a relatively large momentum transfer ($Q^2 \sim 4\, {\rm GeV^2}$) to suppress the elastic scattering and reveal the contributions from the resonance and inelastic region of the neutrino-nucleon scattering. For elastic scattering, the hadronic tensor is the the product of the elastic form factors for the two corresponding currents. We checked numerically for the case of two charge vector currents ($V_4$) with the electric form factor calculated from the three-point function and found they agree within errors.
PDF in PDFs from Hadronic Tensor and LaMET
Keh-Fei Liu
Jul 31 2020 hep-ph hep-lat nucl-th arXiv:2007.15075v2

@misc{2007.15075, author = {Keh-Fei Liu}, title = {{PDF} in {PDF}s from {H}adronic {T}ensor and {L}a{MET}}, year = {2020}, eprint = {2007.15075}, note = {arXiv:2007.15075v2} }
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We point out a problem of the phenomenological definition of the valence partons as the difference between the partons and antipartons in the context of the NNLO evolution equations. After demonstrating that the classification of the parton degrees of freedom (PDF) of the parton distribution functions (PDFs) are the same in the QCD path-intergral formulations of the hadronic tensor and the quasi-PDF with LaMET, we resolve the problem by showing that the proper definition of the valence should be in terms of those in the connected insertions only. We also prove that the strange partons appear as the disconnected sea in the nucleon.
Parton distributions and lattice QCD calculations: toward 3D structure
Martha Constantinou, Aurore Courtoy, Markus A. Ebert, Michael Engelhardt, Tommaso Giani, Tim Hobbs, Tie-Jiun Hou, Aleksander Kusina, Krzysztof Kutak, Jian Liang, Huey-Wen Lin, Keh-Fei Liu, Simonetta Liuti, Cédric Mezrag, Pavel Nadolsky, Emanuele R. Nocera, Fred Olness, Jian-Wei Qiu, Marco Radici, Anatoly Radyushkin, et al (7)
Jun 17 2020 hep-ph hep-lat arXiv:2006.08636v2

@misc{2006.08636, author = {Martha Constantinou and Aurore Courtoy and Markus A.~Ebert and Michael Engelhardt and Tommaso Giani and Tim Hobbs and Tie-Jiun Hou and Aleksander Kusina and Krzysztof Kutak and Jian Liang and Huey-Wen Lin and Keh-Fei Liu and Simonetta Liuti and Cédric Mezrag and Pavel Nadolsky and Emanuele R.~Nocera and Fred Olness and Jian-Wei Qiu and Marco Radici and Anatoly Radyushkin and Abha Rajan and Ted Rogers and Juan Rojo and Gerrit Schierholz and C.-P.~Yuan and Jian-Hui Zhang and Rui Zhang}, title = {{P}arton distributions and lattice {QCD} calculations: toward 3{D} structure}, year = {2020}, eprint = {2006.08636}, note = {arXiv:2006.08636v2} }
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The strong force which binds hadrons is described by the theory of Quantum Chromodynamics (QCD). Determining the character and manifestations of QCD is one of the most important and challenging outstanding issues necessary for a comprehensive understanding of the structure of hadrons. Within the context of the QCD parton picture, the Parton Distribution Functions (PDFs) have been remarkably successful in describing a wide variety of processes. However, these PDFs have generally been confined to the description of collinear partons within the hadron. New experiments and facilities provide the opportunity to additionally explore the transverse structure of hadrons which is described by Generalized Parton Distributions (GPDs) and Transverse Momentum Dependent Parton Distribution Functions (TMD PDFs). In our previous review, we compared and contrasted the two main approaches used to determine the collinear PDFs: the first based on perturbative QCD factorization theorems, and the second based on lattice QCD calculations. In the present report, we provide an update of recent progress on the collinear PDFs, and also expand the scope to encompass the generalized PDFs (GPDs and TMD PDFs). We review the current state of the various calculations, and consider what new data might be available in the near future. We also examine how a shared effort can foster dialog between the PDF and Lattice QCD communities, and yield improvements for these generalized PDFs.
Lattice Calculation of Pion Form Factor with Overlap Fermions
Gen Wang, Jian Liang, Terrence Draper, Keh-Fei Liu, Yi-Bo Yang
Jun 11 2020 hep-ph hep-lat arXiv:2006.05431v4

@misc{2006.05431, author = {Gen Wang and Jian Liang and Terrence Draper and Keh-Fei Liu and Yi-Bo Yang}, title = {{L}attice {C}alculation of {P}ion {F}orm {F}actor with {O}verlap {F}ermions}, year = {2020}, eprint = {2006.05431}, note = {arXiv:2006.05431v4} }
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We present a precise calculation of the pion form factor using overlap fermions on seven ensembles of 2+1-flavor domain-wall configurations with pion masses varying from 139 to 340 MeV. Taking advantage of the fast Fourier transform and other techniques to access many combinations of source and sink momenta, we find the pion mean square charge radius to be $\langle {r_\pi^2} \rangle= 0.430(5)(13)\ {\rm{fm^2}}$, which agrees well with the experimental result, and includes the systematic uncertainties from chiral extrapolation, lattice spacing and finite-volume dependence. We also find that $\langle {r_\pi^2} \rangle$ depends on both the valence and sea quark masses strongly and predict the pion form factor up to $Q^2 = 1.0 \ {\rm{GeV^2}}$ which agrees with experiments very well.
Constraints on charm-anticharm asymmetry in the nucleon from lattice QCD
Raza Sabbir Sufian, Tianbo Liu, Andrei Alexandru, Stanley J. Brodsky, Guy F. de Téramond, Hans Günter Dosch, Terrence Draper, Keh-Fei Liu, Yi-Bo Yang
Mar 03 2020 hep-lat hep-ex hep-ph nucl-th arXiv:2003.01078v3

@misc{2003.01078, author = {Raza Sabbir Sufian and Tianbo Liu and Andrei Alexandru and Stanley J.~Brodsky and Guy F.~de Téramond and Hans Günter Dosch and Terrence Draper and Keh-Fei Liu and Yi-Bo Yang}, title = {{C}onstraints on charm-anticharm asymmetry in the nucleon from lattice {QCD}}, year = {2020}, eprint = {2003.01078}, howpublished = {Phys. Lett. B 808 (2020), 135633}, doi = {10.1016/j.physletb.2020.135633}, note = {arXiv:2003.01078v3} }
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We present the first lattice QCD calculation of the charm quark contribution to the nucleon electromagnetic form factors $G^c_{E,M}(Q^2)$ in the momentum transfer range $0\leq Q^2 \leq 1.4$ $\rm GeV^2$. The quark mass dependence, finite lattice spacing and volume corrections are taken into account simultaneously based on the calculation on three gauge ensembles including one at the physical pion mass. The nonzero value of the charm magnetic moment $\mu^c_M=-0.00127(38)_{\rm stat}(5)_{\rm sys}$, as well as the Pauli form factor, reflects a nontrivial role of the charm sea in the nucleon spin structure. The nonzero $G^c_{E}(Q^2)$ indicates the existence of a nonvanishing asymmetric charm-anticharm sea in the nucleon. Performing a nonperturbative analysis based on holographic QCD and the generalized Veneziano model, we study the constraints on the $[c(x)-\bar{c}(x)]$ distribution from the lattice QCD results presented here. Our results provide complementary information and motivation for more detailed studies of physical observables that are sensitive to intrinsic charm and for future global analyses of parton distributions including asymmetric charm-anticharm distribution.
The nucleon isovector tensor charge from lattice QCD using chiral fermions
Derek Horkel, Yujiang Bi, Martha Constantinou, Terrence Draper, Jian Liang, Keh-Fei Liu, Zhaofeng Liu, Yi-Bo Yang
Feb 18 2020 hep-lat arXiv:2002.06699v1

@misc{2002.06699, author = {Derek Horkel and Yujiang Bi and Martha Constantinou and Terrence Draper and Jian Liang and Keh-Fei Liu and Zhaofeng Liu and Yi-Bo Yang}, title = {{T}he nucleon isovector tensor charge from lattice {QCD} using chiral fermions}, year = {2020}, eprint = {2002.06699}, note = {arXiv:2002.06699v1} }
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In this work we present the isovector flavor combination for the nucleon tensor charge extracted from lattice QCD simulations using overlap fermions on $N_f=2+1$ domain-wall configurations. The pion mass dependence is studied using six valence quark masses, each reproducing a value for the pion mass in the valence sector between 147 and 330 MeV. We investigate and eliminate systematic uncertainties due to contamination by excited states, by employing several values for the source-sink separation that span from 1 fm to 1.6 fm. We apply a chiral extrapolation in the valence sector using a quadratic and a logarithmic term to fit the pion mass dependence, which describes well the lattice data. The lattice matrix element is renormalized non-perturbatively, and the final result is $g_T=1.096(30)$ in the $\overline{\rm MS}$ scheme at a renormalization scale of 2 GeV.
Roper State from Overlap Fermions
Mingyang Sun, Ying Chen, Gen Wang, Andrei Alexandru, Shao-Jing Dong, Terrence Draper, Jacob Fallica, Ming Gong, Frank X. Lee, Anyi Li, Jian Liang, Keh-Fei Liu, Nilmani Mathur, Yi-Bo Yang
Nov 11 2019 hep-ph hep-lat nucl-th arXiv:1911.02635v2

@misc{1911.02635, author = {Mingyang Sun and Ying Chen and Gen Wang and Andrei Alexandru and Shao-Jing Dong and Terrence Draper and Jacob Fallica and Ming Gong and Frank X.~Lee and Anyi Li and Jian Liang and Keh-Fei Liu and Nilmani Mathur and Yi-Bo Yang}, title = {{R}oper {S}tate from {O}verlap {F}ermions}, year = {2019}, eprint = {1911.02635}, note = {arXiv:1911.02635v2} }
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The Roper state is extracted with valence overlap fermions on a $2+1$-flavor domain-wall fermion lattice (spacing $a = 0.114$ fm and $m_{\pi} = 330$ MeV) using both the Sequential Empirical Bayes (SEB) method and the variational method. The results are consistent, provided that a large smearing-size interpolation operator is included in the variational calculation to have better overlap with the lowest radial excitation. Similar calculations carried out for an anisotropic clover lattice with similar parameters find the Roper $\approx 280$ MeV higher than that of the overlap fermion. The fact that the prediction of the Roper state by overlap fermions is consistently lower than those of clover fermions, chirally improved fermions, and twisted-mass fermions over a wide range of pion masses has been dubbed a "Roper puzzle." To understand the origin of this difference, we study the hairpin $Z$-diagram in the isovector scalar meson ($a_0$) correlator in the quenched approximation. Comparing the $a_0$ correlators for clover and overlap fermions, at a pion mass of 290 MeV, we find that the spectral weight of the ghost state with clover fermions is smaller than that of the overlap at $a = 0.12$ fm and $0.09$ fm, whereas the whole $a_0$ correlators of clover and overlap at $a = 0.06$ fm coincide within errors. This suggests that chiral symmetry is restored for clover at $a \le 0.06$ fm and that the Roper should come down at and below this $a$. We conclude that this work supports a resolution of the "Roper puzzle" due to $Z$-graph type chiral dynamics. This entails coupling to higher components in the Fock space (e.g. $N\pi$, $N\pi\pi$ states) to induce the effective flavor-spin interaction between quarks as prescribed in the chiral quark model, resulting in the parity-reversal pattern as observed in the experimental excited states of $N, \Delta$ and $\Lambda$.
Towards the nucleon hadronic tensor from lattice QCD
Jian Liang, Terrence Draper, Keh-Fei Liu, Alexander Rothkopf, Yi-Bo Yang
Jun 14 2019 hep-ph hep-lat arXiv:1906.05312v1

@misc{1906.05312, author = {Jian Liang and Terrence Draper and Keh-Fei Liu and Alexander Rothkopf and Yi-Bo Yang}, title = {{T}owards the nucleon hadronic tensor from lattice {QCD}}, year = {2019}, eprint = {1906.05312}, note = {arXiv:1906.05312v1} }
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We present the first calculation of the hadronic tensor on the lattice for the nucleon. The hadronic tensor can be used to extract the structure functions in deep inelastic scatterings and also provide information for the neutrino-nucleon scattering which is crucial to the neutrino-nucleus scattering experiments at low energies. The most challenging part in the calculation is to solve an inverse problem. We have implemented and tested three algorithms using mock data, showing that the Bayesian Reconstruction method has the best resolution in extracting peak structures while the Backus-Gilbert and Maximum Entropy methods are somewhat more stable for the flat spectral function. Numerical results are presented for both the elastic case (clover fermions on domain wall configuration with $m_\pi\sim$ 370 MeV and $a\sim$ 0.06 fm) and a case (anisotropic clover lattice with $m_\pi\sim$ 380 MeV and $a_t\sim$ 0.035 fm) with large momentum transfer. For the former case, the reconstructed Minkowski hadronic tensor gives precisely the vector charge which proves the feasibility of the approach. While for the latter case, the nucleon resonances and possibly shallow inelastic scattering contributions around $\nu=1$ GeV are clearly observed but no information is obtained for higher excited states with $\nu>2$ GeV. A check of the effective masses of $\rho$ meson with different lattice setups indicates that, in order to reach higher energy transfers, using lattices with smaller lattice spacings is essential.
Lattice QCD and Neutrino-Nucleus Scattering
Andreas S. Kronfeld, David G. Richards, William Detmold, Rajan Gupta, Huey-Wen Lin, Keh-Fei Liu, Aaron S. Meyer, Raza Sufian, Sergey Syritsin
Apr 23 2019 hep-lat hep-ex hep-ph nucl-ex nucl-th arXiv:1904.09931v1

@misc{1904.09931, author = {Andreas S.~Kronfeld and David G.~Richards and William Detmold and Rajan Gupta and Huey-Wen Lin and Keh-Fei Liu and Aaron S.~Meyer and Raza Sufian and Sergey Syritsin}, title = {{L}attice {QCD} and {N}eutrino-{N}ucleus {S}cattering}, year = {2019}, eprint = {1904.09931}, note = {arXiv:1904.09931v1} }
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This document is one of a series of whitepapers from the USQCD collaboration. Here, we discuss opportunities for lattice QCD in neutrino-oscillation physics, which inevitably entails nucleon and nuclear structure. In addition to discussing pertinent lattice-QCD calculations of nucleon and nuclear matrix elements, the interplay with models of nuclei is discussed. This program of lattice- QCD calculations is relevant to current and upcoming neutrino experiments, becoming increasingly important on the timescale of LBNF/DUNE and HyperK.
Ratio of strange to $u/d$ momentum fraction in disconnected insertions
Jian Liang, Mingyang Sun, Yi-Bo Yang, Terrence Draper, Keh-Fei Liu
Jan 23 2019 hep-ph hep-lat arXiv:1901.07526v2

@misc{1901.07526, author = {Jian Liang and Mingyang Sun and Yi-Bo Yang and Terrence Draper and Keh-Fei Liu}, title = {{R}atio of strange to $u/d$ momentum fraction in disconnected insertions}, year = {2019}, eprint = {1901.07526}, doi = {10.1103/PhysRevD.102.034514}, note = {arXiv:1901.07526v2} }
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The ratio of the strange quark momentum fraction $\langle x\rangle_{s+\bar{s}}$ to that of light quark $u$ or $d$ in disconnected insertions (DI) is calculated on the lattice with overlap fermions on four domain wall fermion ensembles. These ensembles cover three lattice spacings, three volumes and several pion masses including the physical one, from which a global fitting is carried out. A complete nonperturbative renormalization and the mixing between the quark and glue operators are taken into account. We find the ratio to be $\langle x\rangle_{s+\bar{s}}/\langle x\rangle_{u+\bar{u}} ({\rm DI})=0.795(79)(77)$ at $\mu = 2$ GeV in the $\overline{{\rm MS}}$ scheme. This ratio can be used as a constraint to better determine the strange parton distribution especially in the small $x$ region in the global fittings of PDFs when the connected and disconnected sea are fitted and evolved separately, demonstrating a new way that connects lattice calculations with global analyses.
Coupling to Multihadron States with Chiral Fermions
Jacob Fallica, Keh-Fei Liu, Jian Liang, Gen Wang, Yi-Bo Yang
Dec 07 2018 hep-lat arXiv:1812.02252v1

@misc{1812.02252, author = {Jacob Fallica and Keh-Fei Liu and Jian Liang and Gen Wang and Yi-Bo Yang}, title = {{C}oupling to {M}ultihadron {S}tates with {C}hiral {F}ermions}, year = {2018}, eprint = {1812.02252}, note = {arXiv:1812.02252v1} }
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Chiral symmerty is presumed to be a crucial component in the strong interaction and QCD, but its role in spectroscopy, especially for baryons, has not been fully explored. Compounding this, chiral fermions are uncommon in lattice calculations due to their expensive nature. We calculate $\eta\pi$, $K\pi$ and $N\pi$ states with $q\bar{q}$ and $qqq$ interpolation fields at $a=0.114\,\mathrm{fm}$ on a $48^3\times 96$ mixed-action lattice at the physical pion mass, with domain-wall sea quarks and overlap valence quarks. We study the spectral weights of these states as a function of the valence pion mass, which ranges from $m_{\pi}=115-665\,\mathrm{MeV}$, to be compared with the results from non-chiral clover valence quarks on the same domain-wall lattice in order to examine their non-chiral effects, which are expected to decrease with the lattice spacing.
Pion Form Factor with Overlap Fermion
Gen Wang, Jian Liang, Terrence Draper, Keh-Fei Liu, Yi-Bo Yang
Oct 31 2018 hep-lat arXiv:1810.12824v1

@misc{1810.12824, author = {Gen Wang and Jian Liang and Terrence Draper and Keh-Fei Liu and Yi-Bo Yang}, title = {{P}ion {F}orm {F}actor with {O}verlap {F}ermion}, year = {2018}, eprint = {1810.12824}, note = {arXiv:1810.12824v1} }
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We present a calculation of the pion form factor using overlap fermions on 2+1-flavor domain-wall configurations on a $24^3\times 64$ lattice with $a=0.11 \, {\rm{fm}}$ and on a $32^3 \times 64$ lattice with $a=0.143 \, {\rm{fm}}$ generated by the RBC/UKQCD collaboration. Using the multi-mass algorithm, a simulation has been done with various valence quark masses with a range of space-like $Q^2$ from 0.0 to 0.6 ${\rm{GeV^2}}$.
Observation of $D^+ \to f_0(500) e^+\nu_e$ and Improved Measurements of $D \to\rho e^+\nu_e$
M. Ablikim, M. N. Achasov, S. Ahmed, M. Albrecht, M. Alekseev, A. Amoroso, F. F. An, Q. An, Y. Bai, O. Bakina, R. Baldini Ferroli, Y. Ban, K. Begzsuren, D. W. Bennett, J. V. Bennett, N. Berger, M. Bertani, D. Bettoni, F. Bianchi, E. Boger, et al (443)
Sep 19 2018 hep-ex hep-lat arXiv:1809.06496v2

@misc{1809.06496, author = {M.~Ablikim and M.~N.~Achasov and S.~Ahmed and M.~Albrecht and M.~Alekseev and A.~Amoroso and F.~F.~An and Q.~An and Y.~Bai and O.~Bakina and R.~Baldini Ferroli and Y.~Ban and K.~Begzsuren and D.~W.~Bennett and J.~V.~Bennett and N.~Berger and M.~Bertani and D.~Bettoni and F.~Bianchi and E.~Boger and I.~Boyko and R.~A.~Briere and H.~Cai and X.~Cai and A.~Calcaterra and G.~F.~Cao and S.~A.~Cetin and J.~Chai and J.~F.~Chang and W.~L.~Chang and G.~Chelkov and G.~Chen and H.~S.~Chen and J.~C.~Chen and M.~L.~Chen and P.~L.~Chen and S.~J.~Chen and X.~R.~Chen and Y.~B.~Chen and W.~Cheng and X.~K.~Chu and G.~Cibinetto and F.~Cossio and H.~L.~Dai and J.~P.~Dai and A.~Dbeyssi and D.~Dedovich and Z.~Y.~Deng and A.~Denig and I.~Denysenko and M.~Destefanis and F.~De Mori and Y.~Ding and C.~Dong and J.~Dong and L.~Y.~Dong and M.~Y.~Dong and Z.~L.~Dou and S.~X.~Du and P.~F.~Duan and J.~Fang and S.~S.~Fang and Y.~Fang and R.~Farinelli and L.~Fava and S.~Fegan and F.~Feldbauer and G.~Felici and C.~Q.~Feng and E.~Fioravanti and M.~Fritsch and C.~D.~Fu and Q.~Gao and X.~L.~Gao and Y.~Gao and Y.~G.~Gao and Z.~Gao and B.~Garillon and I.~Garzia and A.~Gilman and K.~Goetzen and L.~Gong and W.~X.~Gong and W.~Gradl and M.~Greco and L.~M.~Gu and M.~H.~Gu and Y.~T.~Gu and A.~Q.~Guo and L.~B.~Guo and R.~P.~Guo and Y.~P.~Guo and A.~Guskov and Z.~Haddadi and S.~Han and X.~Q.~Hao and F.~A.~Harris and K.~L.~He and X.~Q.~He and F.~H.~Heinsius and T.~Held and Y.~K.~Heng and Z.~L.~Hou and H.~M.~Hu and J.~F.~Hu and T.~Hu and Y.~Hu and G.~S.~Huang and J.~S.~Huang and X.~T.~Huang and X.~Z.~Huang and Z.~L.~Huang and T.~Hussain and W.~Ikegami Andersson and M.~Irshad and Q.~Ji and Q.~P.~Ji and X.~B.~Ji and X.~L.~Ji and X.~S.~Jiang and X.~Y.~Jiang and J.~B.~Jiao and Z.~Jiao and D.~P.~Jin and S.~Jin and Y.~Jin and T.~Johansson and A.~Julin and N.~Kalantar-Nayestanaki and X.~S.~Kang and M.~Kavatsyuk and B.~C.~Ke and I.~K.~Keshk and T.~Khan and A.~Khoukaz and P.~Kiese and R.~Kiuchi and R.~Kliemt and L.~Koch and O.~B.~Kolcu and B.~Kopf and M.~Kornicer and M.~Kuemmel and M.~Kuessner and A.~Kupsc and M.~Kurth and W.~Kühn and J.~S.~Lange and P.~Larin and L.~Lavezzi and S.~Leiber and H.~Leithoff and C.~Li and Cheng Li and D.~M.~Li and F.~Li and F.~Y.~Li and G.~Li and H.~B.~Li and H.~J.~Li and J.~C.~Li and J.~W.~Li and K.~J.~Li and Kang Li and Ke Li and Lei Li and P.~L.~Li and P.~R.~Li and Q.~Y.~Li and T.~Li and W.~D.~Li and W.~G.~Li and X.~L.~Li and X.~N.~Li and X.~Q.~Li and Z.~B.~Li and H.~Liang and Y.~F.~Liang and Y.~T.~Liang and G.~R.~Liao and L.~Z.~Liao and J.~Libby and C.~X.~Lin and D.~X.~Lin and B.~Liu and B.~J.~Liu and C.~X.~Liu and D.~Liu and D.~Y.~Liu and F.~H.~Liu and Fang Liu and Feng Liu and H.~B.~Liu and H.~L Liu and H.~M.~Liu and Huanhuan Liu and Huihui Liu and J.~B.~Liu and J.~Y.~Liu and K.~Y.~Liu and Ke Liu and L.~D.~Liu and Q.~Liu and S.~B.~Liu and X.~Liu and Y.~B.~Liu and Z.~A.~Liu and Zhiqing Liu and Y.~F.~Long and X.~C.~Lou and H.~J.~Lu and J.~G.~Lu and Y.~Lu and Y.~P.~Lu and C.~L.~Luo and M.~X.~Luo and T.~Luo and X.~L.~Luo and S.~Lusso and X.~R.~Lyu and F.~C.~Ma and H.~L.~Ma and L.~L.~Ma and M.~M.~Ma and Q.~M.~Ma and X.~N.~Ma and X.~Y.~Ma and Y.~M.~Ma and F.~E.~Maas and M.~Maggiora and S.~Maldaner and Q.~A.~Malik and A.~Mangoni and Y.~J.~Mao and Z.~P.~Mao and S.~Marcello and Z.~X.~Meng and J.~G.~Messchendorp and G.~Mezzadri and J.~Min and T.~J.~Min and R.~E.~Mitchell and X.~H.~Mo and Y.~J.~Mo and C.~Morales Morales and N.~Yu.~Muchnoi and H.~Muramatsu and A.~Mustafa and S.~Nakhoul and Y.~Nefedov and F.~Nerling and I.~B.~Nikolaev and Z.~Ning and S.~Nisar and S.~L.~Niu and X.~Y.~Niu and S.~L.~Olsen and Q.~Ouyang and S.~Pacetti and Y.~Pan and M.~Papenbrock and P.~Patteri and M.~Pelizaeus and J.~Pellegrino and H.~P.~Peng and Z.~Y.~Peng and K.~Peters and J.~Pettersson and J.~L.~Ping and R.~G.~Ping and A.~Pitka and R.~Poling and V.~Prasad and H.~R.~Qi and M.~Qi and T.~Y.~Qi and S.~Qian and C.~F.~Qiao and N.~Qin and X.~S.~Qin and Z.~H.~Qin and J.~F.~Qiu and S.~Q.~Qu and K.~H.~Rashid and C.~F.~Redmer and M.~Richter and M.~Ripka and A.~Rivetti and M.~Rolo and G.~Rong and Ch.~Rosner and A.~Sarantsev and M.~Savrié and K.~Schoenning and W.~Shan and X.~Y.~Shan and M.~Shao and C.~P.~Shen and P.~X.~Shen and X.~Y.~Shen and H.~Y.~Sheng and X.~Shi and J.~J.~Song and W.~M.~Song and X.~Y.~Song and S.~Sosio and C.~Sowa and S.~Spataro and G.~X.~Sun and J.~F.~Sun and L.~Sun and S.~S.~Sun and X.~H.~Sun and Y.~J.~Sun and Y.~K Sun and Y.~Z.~Sun and Z.~J.~Sun and Z.~T.~Sun and Y.~T Tan and C.~J.~Tang and G.~Y.~Tang and X.~Tang and M.~Tiemens and B.~Tsednee and I.~Uman and B.~Wang and B.~L.~Wang and C.~W.~Wang and D.~Wang and D.~Y.~Wang and Dan Wang and K.~Wang and L.~L.~Wang and L.~S.~Wang and M.~Wang and Meng Wang and P.~Wang and P.~L.~Wang and W.~P.~Wang and X.~F.~Wang and Y.~Wang and Y.~F.~Wang and Z.~Wang and Z.~G.~Wang and Z.~Y.~Wang and Zongyuan Wang and T.~Weber and D.~H.~Wei and P.~Weidenkaff and S.~P.~Wen and U.~Wiedner and M.~Wolke and L.~H.~Wu and L.~J.~Wu and Z.~Wu and L.~Xia and X.~Xia and Y.~Xia and D.~Xiao and Y.~J.~Xiao and Z.~J.~Xiao and Y.~G.~Xie and Y.~H.~Xie and X.~A.~Xiong and Q.~L.~Xiu and G.~F.~Xu and J.~J.~Xu and L.~Xu and Q.~J.~Xu and X.~P.~Xu and F.~Yan and L.~Yan and W.~B.~Yan and W.~C.~Yan and Y.~H.~Yan and H.~J.~Yang and H.~X.~Yang and L.~Yang and R.~X.~Yang and S.~L.~Yang and Y.~H.~Yang and Y.~X.~Yang and Yifan Yang and Z.~Q.~Yang and M.~Ye and M.~H.~Ye and J.~H.~Yin and Z.~Y.~You and B.~X.~Yu and C.~X.~Yu and J.~S.~Yu and J.~S.~Yu and C.~Z.~Yuan and Y.~Yuan and A.~Yuncu and A.~A.~Zafar and Y.~Zeng and B.~X.~Zhang and B.~Y.~Zhang and C.~C.~Zhang and D.~H.~Zhang and H.~H.~Zhang and H.~Y.~Zhang and J.~Zhang and J.~L.~Zhang and J.~Q.~Zhang and J.~W.~Zhang and J.~Y.~Zhang and J.~Z.~Zhang and K.~Zhang and L.~Zhang and S.~F.~Zhang and T.~J.~Zhang and X.~Y.~Zhang and Y.~Zhang and Y.~H.~Zhang and Y.~T.~Zhang and Yang Zhang and Yao Zhang and Yu Zhang and Z.~H.~Zhang and Z.~P.~Zhang and Z.~Y.~Zhang and G.~Zhao and J.~W.~Zhao and J.~Y.~Zhao and J.~Z.~Zhao and Lei Zhao and Ling Zhao and M.~G.~Zhao and Q.~Zhao and S.~J.~Zhao and T.~C.~Zhao and Y.~B.~Zhao and Z.~G.~Zhao and A.~Zhemchugov and B.~Zheng and J.~P.~Zheng and W.~J.~Zheng and Y.~H.~Zheng and B.~Zhong and L.~Zhou and Q.~Zhou and X.~Zhou and X.~K.~Zhou and X.~R.~Zhou and X.~Y.~Zhou and Xiaoyu Zhou and Xu Zhou and A.~N.~Zhu and J.~Zhu and J.~Zhu and K.~Zhu and K.~J.~Zhu and S.~Zhu and S.~H.~Zhu and X.~L.~Zhu and Y.~C.~Zhu and Y.~S.~Zhu and Z.~A.~Zhu and J.~Zhuang and B.~S.~Zou and J.~H.~Zou}, title = {{O}bservation of ${D}^+ \to f_0(500) e^+\nu_e$ and {I}mproved {M}easurements of ${D} \to\rho e^+\nu_e$}, year = {2018}, eprint = {1809.06496}, howpublished = {M. Ablikim et al. (BESIII Collaboration), Phys. Rev. Lett. 122, 062001 (2019)}, doi = {10.1103/PhysRevLett.122.062001}, note = {arXiv:1809.06496v2} }
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Using a data sample corresponding to an integrated luminosity of 2.93~fb$^{-1}$ recorded by the BESIII detector at a center-of-mass energy of $3.773$ GeV, we present an analysis of the decays $\bar{D}^0\to\pi^+\pi^0 e^-\bar{\nu}_e$ and $D^+\to\pi^-\pi^+ e^+\nu_e$. By performing a partial wave analysis, the $\pi^+\pi^-$ $S$-wave contribution to $D^+\to\pi^-\pi^+ e^+\nu_e$ is observed to be $(25.7\pm1.6\pm1.1)$% with a statistical significance greater than 10$\sigma$, besides the dominant $P$-wave contribution. This is the first observation of the $S$-wave contribution. We measure the branching fractions $\mathcal{B}(D^{0} \to \rho^- e^+ \nu_e) = (1.445\pm 0.058 \pm 0.039) \times10^{-3}$, $\mathcal{B}(D^{+} \to \rho^0 e^+ \nu_e) = (1.860\pm 0.070 \pm 0.061) \times10^{-3}$, and $\mathcal{B}(D^{+} \to f_0(500) e^+ \nu_e, f_0(500)\to\pi^+\pi^-) = (6.30\pm 0.43 \pm 0.32) \times10^{-4}$. An upper limit of $\mathcal{B}(D^{+} \to f_0(980) e^+ \nu_e, f_0(980)\to\pi^+\pi^-) < 2.8 \times10^{-5}$ is set at the 90% confidence level. We also obtain the hadronic form factor ratios of $D\to \rho e^+\nu_e$ at $q^{2}=0$ assuming the single-pole dominance parameterization: $r_{V}=\frac{V(0)}{A_{1}(0)}=1.695\pm0.083\pm0.051$, $r_{2}=\frac{A_{2}(0)}{A_{1}(0)}=0.845\pm0.056\pm0.039$.
Weak Neutral Current Axial Form Factor Using $(\bar{\nu})\nu$-Nucleon Scattering and Lattice QCD Inputs
Raza Sabbir Sufian, Keh-Fei Liu, David G. Richards
Sep 12 2018 hep-ph hep-lat nucl-ex nucl-th arXiv:1809.03509v3

@misc{1809.03509, author = {Raza Sabbir Sufian and Keh-Fei Liu and David G.~Richards}, title = {{W}eak {N}eutral {C}urrent {A}xial {F}orm {F}actor {U}sing $(\bar{\nu})\nu$-{N}ucleon {S}cattering and {L}attice {QCD} {I}nputs}, year = {2018}, eprint = {1809.03509}, howpublished = {JHEP 2001 (2020) 136}, doi = {10.1007/JHEP01(2020)136}, note = {arXiv:1809.03509v3} }
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We present a determination of the neutral current weak axial charge $G^Z_A(0)=-0.654(3)_{\rm stat}(5)_{\rm sys}$ using the strange quark axial charge $G^s_A(0)$ calculated with lattice QCD. We then perform a phenomenological analysis, where we combine the strange quark electromagnetic form factor from lattice QCD with (anti)neutrino-nucleon scattering differential cross section from MiniBooNE experiments in a momentum transfer region $0.24\lesssim Q^2 \lesssim 0.71$ GeV$^2$ to determine the neutral current weak axial form factor $G^Z_A(Q^2)$ in the range of $0\lesssim Q^2\leq 1$ GeV$^2$. This yields a phenomenological value of $G^Z_A(0)=-0.687(89)_{\rm stat}(40)_{\rm sys}$. The value of $G^Z_A(0)$ constrained by the lattice QCD calculation of $G^s_A(0)$, when compared to its phenomenological determination, provides a significant improvement in precision and accuracy and can be used to provide a constraint on the fit to $G^Z_A(Q^2)$ for $Q^2>0$. This constrained fit leads to an unambiguous determination of (anti)neutrino-nucleon neutral current elastic scattering differential cross section near $Q^2=0$ and can play an important role in numerically isolating nuclear effects in this region. We show a consistent description of $G^Z_A(Q^2)$ obtained from the (anti)neutrino-nucleon scattering cross section data requires a nonzero contribution of the strange quark electromagnetic form factor. We demonstrate the robustness of our analysis by providing a post-diction of the BNL E734 experimental data.
Proton Mass Decomposition from the QCD Energy Momentum Tensor
Yi-Bo Yang, Jian Liang, Yu-Jiang Bi, Ying Chen, Terrence Draper, Keh-Fei Liu, Zhaofeng Liu
Aug 28 2018 hep-lat hep-ph nucl-th arXiv:1808.08677v2

@misc{1808.08677, author = {Yi-Bo Yang and Jian Liang and Yu-Jiang Bi and Ying Chen and Terrence Draper and Keh-Fei Liu and Zhaofeng Liu}, title = {{P}roton {M}ass {D}ecomposition from the {QCD} {E}nergy {M}omentum {T}ensor}, year = {2018}, eprint = {1808.08677}, note = {arXiv:1808.08677v2} }
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We report results on the proton mass decomposition and also on related quark and glue momentum fractions. The results are based on overlap valence fermions on four ensembles of $N_f = 2+1$ DWF configurations with three lattice spacings and three volumes, and several pion masses including the physical pion mass. With fully non-perturbative renormalization (and universal normalization on both quark and gluon), we find that the quark energy and glue field energy contribute 33(4)(4)\% and 37(5)(4)\% respectively in the $\overline{MS}$ scheme at $\mu = 2$ GeV. A quarter of the trace anomaly gives a 23(1)(1)\% contribution to the proton mass based on the sum rule, given 9(2)(1)\% contribution from the $u, d,$ and $s$ quark scalar condensates. The $u,d,s$ and glue momentum fractions in the $\overline{MS}$ scheme are in good agreement with global analyses at $\mu = 2$ GeV.
Gluon Quasi-PDF From Lattice QCD
Zhou-You Fan, Yi-Bo Yang, Adam Anthony, Huey-Wen Lin, Keh-Fei Liu
Aug 08 2018 hep-lat hep-ph nucl-th arXiv:1808.02077v3

@misc{1808.02077, author = {Zhou-You Fan and Yi-Bo Yang and Adam Anthony and Huey-Wen Lin and Keh-Fei Liu}, title = {{G}luon {Q}uasi-{PDF} {F}rom {L}attice {QCD}}, year = {2018}, eprint = {1808.02077}, note = {arXiv:1808.02077v3} }
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We present the first attempt to access the $x$-dependence of the gluon unpolarized parton distribution function (PDF), based on lattice simulations using the large-momentum effective theory (LaMET) approach. The lattice calculation is carried out with pion masses of 340 and 678 MeV on a 2+1-flavor DWF configuration with lattice spacing $a=0.111$~fm, for the gluon quasi-PDF matrix element with the nucleon momentum up to 0.93 GeV. Taking the normalization from similar matrix elements in the rest frame of the nucleon and pion, our results for these matrix elements are consistent with the Fourier transform of the global fit CT14 and PDF4LHC15 NNLO of the gluon PDF, within statistical uncertainty and the systematic one up to power corrections, perturbative ${\cal O}(\alpha_s)$ matching and the mixing from the quark PDFs.
Quark spins and Anomalous Ward Identity
Jian Liang, Yi-Bo Yang, Terrence Draper, Ming Gong, Keh-Fei Liu
Jun 25 2018 hep-ph hep-lat arXiv:1806.08366v2

@misc{1806.08366, author = {Jian Liang and Yi-Bo Yang and Terrence Draper and Ming Gong and Keh-Fei Liu}, title = {{Q}uark spins and {A}nomalous {W}ard {I}dentity}, year = {2018}, eprint = {1806.08366}, howpublished = {Phys. Rev. D 98, 074505 (2018)}, doi = {10.1103/PhysRevD.98.074505}, note = {arXiv:1806.08366v2} }
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We calculate the intrinsic quark spin contribution to the total proton spin using overlap valence quarks on three ensembles of $2+1$-flavor RBC/UKQCD domain-wall configurations with different lattice spacings. The lowest pion mass of the ensembles is around 171 MeV which is close to the physical point. With overlap fermions and topological charge derived from the overlap operator, we verify the anomalous Ward identity between nucleon states with momentum transfer. Both the connected and disconnected insertions of the axial-vector current are calculated. For the disconnected-insertion part, the cluster-decomposition error reduction (CDER) technique is utilized for the lattice with the largest volume and the error can be reduced by $10\%\sim40\%$. Nonperturbative renormalization is carried out and the final results are all reported in the $\overline{{\rm MS}}$ scheme at 2 GeV. We determine the total quark spin contribution to the nucleon spin to be $\Delta\Sigma=0.401(25)(37)$, which is consistent with the recent global fitting result of experimental data. The isovector axial coupling we obtain in this study is $g_A^3=1.256(16)(30)$, which agrees well with the experimental value of 1.2723(23).
Nonperturbatively-renormalized glue momentum fraction at physical pion mass from Lattice QCD
Yi-Bo Yang, Ming Gong, Jian Liang, Huey-Wen Lin, Keh-Fei Liu, Dimitra Pefkou, Phiala Shanahan
May 03 2018 hep-lat hep-ph nucl-th arXiv:1805.00531v3

@misc{1805.00531, author = {Yi-Bo Yang and Ming Gong and Jian Liang and Huey-Wen Lin and Keh-Fei Liu and Dimitra Pefkou and Phiala Shanahan}, title = {{N}onperturbatively-renormalized glue momentum fraction at physical pion mass from {L}attice {QCD}}, year = {2018}, eprint = {1805.00531}, note = {arXiv:1805.00531v3} }
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We present the first nonperturbatively-renormalized determination of the glue momentum fraction $\langle x \rangle_g$ in the nucleon, based on lattice-QCD simulations at physical pion mass using the cluster-decomposition error reduction (CDER) technique. We provide the first practical strategy to renormalize the glue energy-momentum tensor (EMT) nonperturbatively in the RI/MOM scheme, and convert the results to the $\overline{\textrm{MS}}$ scheme with 1-loop matching. The simulation results show that the CDER technique can reduce the statistical uncertainty of its renormalization constant by a factor of ${\cal O}$(300) in calculations using typical state-of-the-art lattice volume, and the nonperturbatively-renormalized $\langle x \rangle_g$ is shown to be independent of the lattice definitions of the glue EMT up to discretization errors. We determine the renormalized $\langle x \rangle_g^{\overline{\textrm{MS}}}(2\textrm{ GeV})$ to be 0.47(4)(11) at physical pion mass, which is consistent with the experimentally-determined value.
Comment on `Nucleon Structure Functions from Operator Product Expansion on the Lattice'
Keh-Fei Liu
Nov 29 2017 hep-ph hep-lat nucl-th arXiv:1711.09956v2

@misc{1711.09956, author = {Keh-Fei Liu}, title = {{C}omment on `{N}ucleon {S}tructure {F}unctions from {O}perator {P}roduct {E}xpansion on the {L}attice'}, year = {2017}, eprint = {1711.09956}, note = {arXiv:1711.09956v2} }
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It is suggested in the paper by A.J. Chambers \it et al. (Phys. Rev. Lett. 118, 242001 (2017), arXiv:1703.01153) that the time-ordered current-curent correlator in the nucleon calculated on the lattice is to be identified as the forward Compton amplitude so that it is related to the sum of the even moments of the structure function as in the Minkowski space in the continuum. We point out two problems with this identification. First of all, the current-current correlator defined in the Euclidean space is not analytic everywhere on the rest of the complex $\nu$ or $\omega$ plane, besides the cuts on the real axis. As such, there is no dispersion relation to relate it to its imaginary part and hence the moments of the structure function. On the lattice, there is an additional difficulty in that the higher dimensional local operators from the operator production expansion (OPE) of the current-current product can mix with lower dimensional higher-twist operators which leads to divergences in the powers of inverse lattice spacing. This mixing needs to be removed before their matrix elements can be identified as the moments of the structure function.
Parton distributions and lattice QCD calculations: a community white paper
Huey-Wen Lin, Emanuele R. Nocera, Fred Olness, Kostas Orginos, Juan Rojo, Alberto Accardi, Constantia Alexandrou, Alessandro Bacchetta, Giuseppe Bozzi, Jiunn-Wei Chen, Sara Collins, Amanda Cooper-Sarkar, Martha Constantinou, Luigi Del Debbio, Michael Engelhardt, Jeremy Green, Rajan Gupta, Lucian A. Harland-Lang, Tomomi Ishikawa, Aleksander Kusina, et al (12)
Nov 22 2017 hep-ph hep-lat arXiv:1711.07916v3

@misc{1711.07916, author = {Huey-Wen Lin and Emanuele R.~Nocera and Fred Olness and Kostas Orginos and Juan Rojo and Alberto Accardi and Constantia Alexandrou and Alessandro Bacchetta and Giuseppe Bozzi and Jiunn-Wei Chen and Sara Collins and Amanda Cooper-Sarkar and Martha Constantinou and Luigi Del Debbio and Michael Engelhardt and Jeremy Green and Rajan Gupta and Lucian A.~Harland-Lang and Tomomi Ishikawa and Aleksander Kusina and Keh-Fei Liu and Simonetta Liuti and Christopher Monahan and Pavel Nadolsky and Jian-Wei Qiu and Ingo Schienbein and Gerrit Schierholz and Robert S.~Thorne and Werner Vogelsang and Hartmut Wittig and C.-P.~Yuan and James Zanotti}, title = {{P}arton distributions and lattice {QCD} calculations: a community white paper}, year = {2017}, eprint = {1711.07916}, note = {arXiv:1711.07916v3} }
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In the framework of quantum chromodynamics (QCD), parton distribution functions (PDFs) quantify how the momentum and spin of a hadron are divided among its quark and gluon constituents. Two main approaches exist to determine PDFs. The first approach, based on QCD factorization theorems, realizes a QCD analysis of a suitable set of hard-scattering measurements, often using a variety of hadronic observables. The second approach, based on first-principle operator definitions of PDFs, uses lattice QCD to compute directly some PDF-related quantities, such as their moments. Motivated by recent progress in both approaches, in this document we present an overview of lattice-QCD and global-analysis techniques used to determine unpolarized and polarized proton PDFs and their moments. We provide benchmark numbers to validate present and future lattice-QCD calculations and we illustrate how they could be used to reduce the PDF uncertainties in current unpolarized and polarized global analyses. This document represents a first step towards establishing a common language between the two communities, to foster dialogue and to further improve our knowledge of PDFs.
Lattice calculation of hadronic tensor of the nucleon
Jian Liang, Keh-Fei Liu, Yi-Bo Yang
Nov 01 2017 hep-lat arXiv:1710.11145v1

@misc{1710.11145, author = {Jian Liang and Keh-Fei Liu and Yi-Bo Yang}, title = {{L}attice calculation of hadronic tensor of the nucleon}, year = {2017}, eprint = {1710.11145}, note = {arXiv:1710.11145v1} }
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We report an attempt to calculate the deep inelastic scattering structure functions from the hadronic tensor calculated on the lattice. We used the Backus-Gilbert reconstruction method to address the inverse Laplace transformation for the analytic continuation from the Euclidean to the Minkowski space.
Proton mass decomposition
Yi-Bo Yang, Ying Chen, Terrence Draper, Jian Liang, Keh-Fei Liu
Oct 26 2017 hep-lat hep-ph nucl-th arXiv:1710.09011v1

@misc{1710.09011, author = {Yi-Bo Yang and Ying Chen and Terrence Draper and Jian Liang and Keh-Fei Liu}, title = {{P}roton mass decomposition}, year = {2017}, eprint = {1710.09011}, note = {arXiv:1710.09011v1} }
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We report the results on the proton mass decomposition and also on the related quark and glue momentum fractions. The results are based on overlap valence fermions on four ensembles of $N_f = 2+1$ DWF configurations with three lattice spacings and volumes, and several pion masses including the physical pion mass. With 1-loop perturbative calculation and proper normalization of the glue operator, we find that the $u, d,$ and $s$ quark masses contribute 9(2)\% to the proton mass. The quark energy and glue field energy contribute 31(5)\% and 37(5)\% respectively in the $\overline{MS}$ scheme at $\mu = 2$ GeV. The trace anomaly gives the remaining 23(1)\% contribution. The $u,d,s$ and glue momentum fractions in the $\overline{MS}$ scheme are consistent with the global analysis at $\mu = 2$ GeV.
RI/MOM and RI/SMOM renormalization of overlap quark bilinears on domain wall fermion configurations
Yujiang Bi, Hao Cai, Ying Chen, Ming Gong, Keh-Fei Liu, Zhaofeng Liu, Yi-Bo Yang
Oct 25 2017 hep-lat arXiv:1710.08678v2

@misc{1710.08678, author = {Yujiang Bi and Hao Cai and Ying Chen and Ming Gong and Keh-Fei Liu and Zhaofeng Liu and Yi-Bo Yang}, title = {{RI}/{MOM} and {RI}/{SMOM} renormalization of overlap quark bilinears on domain wall fermion configurations}, year = {2017}, eprint = {1710.08678}, note = {arXiv:1710.08678v2} }
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Renormalization constants (RCs) of overlap quark bilinear operators on 2+1-flavor domain wall fermion configurations are calculated by using the RI/MOM and RI/SMOM schemes. The scale independent RC for the axial vector current is computed by using a Ward identity. Then the RCs for the quark field and the vector, tensor, scalar and pseudoscalar operators are calculated in both the RI/MOM and RI/SMOM schemes. The RCs are converted to the $\overline{\rm MS}$ scheme and we compare the numerical results from using the two intermediate schemes. The lattice size is $48^3\times96$ and the inverse spacing $1/a = 1.730(4) {\rm~GeV}$.
Variance Reduction and Cluster Decomposition
Keh-Fei Liu, Jian Liang, Yi-Bo Yang
May 19 2017 hep-lat cond-mat.stat-mech hep-ph nucl-th physics.comp-ph arXiv:1705.06358v3

@misc{1705.06358, author = {Keh-Fei Liu and Jian Liang and Yi-Bo Yang}, title = {{V}ariance {R}eduction and {C}luster {D}ecomposition}, year = {2017}, eprint = {1705.06358}, howpublished = {Phys. Rev. D 97, 034507 (2018)}, doi = {10.1103/PhysRevD.97.034507}, note = {arXiv:1705.06358v3} }
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It is a common problem in lattice QCD calculation of the mass of the hadron with an annihilation channel that the signal falls off in time while the noise remains constant. In addition, the disconnected insertion calculation of the three-point function and the calculation of the neutron electric dipole moment with the $\theta$ term suffer from a noise problem due to the $\sqrt{V}$ fluctuation. We identify these problems to have the same origin and the $\sqrt{V}$ problem can be overcome by utilizing the cluster decomposition principle. We demonstrate this by considering the calculations of the glueball mass, the strangeness content in the nucleon, and the CP violation angle in the nucleon due to the $\theta$ term. It is found that for lattices with physical sizes of 4.5 - 5.5 fm, the statistical errors of these quantities can be reduced by a factor of 3 to 4. The systematic errors can be estimated from the Akaike information criterion. For the strangeness content, we find that the systematic error is of the same size as that of the statistical one when the cluster decomposition principle is utilized. This results in a 2 to 3 times reduction in the overall error.
Sea Quarks Contribution to the Nucleon Magnetic Moment and Charge Radius at the Physical Point
Raza Sabbir Sufian, Yi-Bo Yang, Jian Liang, Terrence Draper, Keh-Fei Liu
May 18 2017 hep-lat hep-ph nucl-th arXiv:1705.05849v3

@misc{1705.05849, author = {Raza Sabbir Sufian and Yi-Bo Yang and Jian Liang and Terrence Draper and Keh-Fei Liu}, title = {{S}ea {Q}uarks {C}ontribution to the {N}ucleon {M}agnetic {M}oment and {C}harge {R}adius at the {P}hysical {P}oint}, year = {2017}, eprint = {1705.05849}, howpublished = {Phys. Rev. D 96, 114504 (2017)}, doi = {10.1103/PhysRevD.96.093007}, note = {arXiv:1705.05849v3} }
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We report a comprehensive analysis of the light and strange disconnected-sea quarks contribution to the nucleon magnetic moment, charge radius, and the electric and magnetic form factors. The lattice QCD calculation includes ensembles across several lattice volumes and lattice spacings with one of the ensembles at the physical pion mass. We adopt a model-independent extrapolation of the nucleon magnetic moment and the charge radius. We have performed a simultaneous chiral, infinite volume, and continuum extrapolation in a global fit to calculate results in the continuum limit. We find that the combined light and strange disconnected-sea quarks contribution to the nucleon magnetic moment is $\mu_M\,(\text{DI})=-0.022(11)(09)\,\mu_N$ and to the nucleon mean square charge radius is $\langle r^2\rangle_E\,\text{(DI)}=-0.019(05)(05)$ fm$^2$ which is about $1/3$ of the difference between the $\langle r_p^2\rangle_E$ of electron-proton scattering and that of muonic atom and so cannot be ignored in obtaining the proton charge radius in the lattice QCD calculation. The most important outcome of this lattice QCD calculation is that while the combined light-sea and strange quarks contribution to the nucleon magnetic moment is small at about $1\%$, a negative $2.5(9)\%$ contribution to the proton mean square charge radius and a relatively larger positive $16.3(6.1)\%$ contribution to the neutron mean square charge radius come from the sea quarks in the nucleon. For the first time, by performing global fits, we also give predictions of the light and strange disconnected-sea quarks contributions to the nucleon electric and magnetic form factors at the physical point and in the continuum and infinite volume limits in the momentum transfer range of $0\leq Q^2\leq 0.5$ GeV$^2$.
Evolution Equations for Connected and Disconnected Sea Parton Distributions
Keh-Fei Liu
Mar 16 2017 hep-ph hep-lat nucl-th arXiv:1703.04690v3

@misc{1703.04690, author = {Keh-Fei Liu}, title = {{E}volution {E}quations for {C}onnected and {D}isconnected {S}ea {P}arton {D}istributions}, year = {2017}, eprint = {1703.04690}, howpublished = {Phys. Rev. D 96, 033001 (2017)}, doi = {10.1103/PhysRevD.96.033001}, note = {arXiv:1703.04690v3} }
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It has been revealed from the path-integral formulation of the hadronic tensor that there are connected sea and disconnected sea partons. The former is responsible for the Gottfried sum rule violation primarily and evolves the same way as the valence. Therefore, the DGLAP evolution equations can be extended to accommodate them separately. We discuss its consequences and implications vis-a-vis lattice calculations.
Nucleon Matrix Elements at Physical Pion Mass and Cost Comparison
Keh-Fei Liu, Jian Liang, Yi-Bo Yang
Feb 16 2017 hep-lat hep-ph arXiv:1702.04384v1

@misc{1702.04384, author = {Keh-Fei Liu and Jian Liang and Yi-Bo Yang}, title = {{N}ucleon {M}atrix {E}lements at {P}hysical {P}ion {M}ass and {C}ost {C}omparison}, year = {2017}, eprint = {1702.04384}, note = {arXiv:1702.04384v1} }
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We report a lattice calculation of nucleon forward matrix elements on a $48^3 \times 96$ lattice at the physical pion mass and a spatial size of 5.5 fm. The $2+1$ flavor dynamical fermion configurations are generated with domain-wall fermions (DWF) and the overlap fermions are adopted for the valence quarks. The isovector $g_A^3$ and $g_S^3$, and the connected insertion part of $g_S^0$ are reported for three source-sink separations. With local current, we obtain $g_A^3 = 1.18(4)$ from a two-state fit. For the quark momentum fraction $\langle x \rangle_{u-d}$, we have included smaller lattices (i.e. $24^3 \times 64$ and $32^3 \times 64$ lattice with pion mass at 330 and 290 MeV respectively) for a fit which includes partially quenched cases as well as finite volume and continuum corrections. A global fit with perturbative renormalization gives $\langle x \rangle_{u-d} (\overline{MS},\, \mu = 2\, {\rm GeV}) = 0.170(14)$. We made a cost comparison of calculating the nucleon matrix elements with those from the twisted mass fermion on similar sized lattice at the physical pion point and the domain-wall fermion calculation on the same DWF lattice. We also compare cost with the clover fermion calculation on similar sized lattice at about the same quark mass. The comparison shows that with several improvements, such as many-to-all correlator with grid source and low-mode substitution in the connected insertion and low-mode average in the quark loop can make the overlap as efficient as the twisted-mass and clover fermions in calculating the three-point functions. It is more efficient than the DWF. When the multi-mass feature is invoked, the overlap can be more efficient in reaching the same precision than the single mass comparison made so far.
Lattice Calculation of Nucleon Isovector Axial Charge with Improved Currents
Jian Liang, Yi-Bo Yang, Keh-Fei Liu, Andrei Alexandru, Terrence Draper, Raza Sabbir Sufian
Dec 15 2016 hep-lat hep-ph arXiv:1612.04388v2

@misc{1612.04388, author = {Jian Liang and Yi-Bo Yang and Keh-Fei Liu and Andrei Alexandru and Terrence Draper and Raza Sabbir Sufian}, title = {{L}attice {C}alculation of {N}ucleon {I}sovector {A}xial {C}harge with {I}mproved {C}urrents}, year = {2016}, eprint = {1612.04388}, howpublished = {Phys. Rev. D 96, 034519 (2017)}, doi = {10.1103/PhysRevD.96.034519}, note = {arXiv:1612.04388v2} }
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We employ dimension-4 operators to improve the local vector and axial-vector currents and calculate the nucleon isovector axial coupling $g^3_A$ with overlap valence on $2+1$-flavor Domain Wall Fermion sea. Using the equality of $g^3_A$ from the spatial and temporal components of the axial-vector current as a normalization condition, we find that $g_A^3$ is increased by a few percent towards the experimental value. The excited-state contamination has been taken into account with three time separations between the source and sink. The improved axial charges $g_A^{3}(24I)=1.22(4)$ and $g_A^{3}(32I)=1.21(3)$ are obtained on a $24^3\times 64$ lattice at pion mass of 330 MeV and a $32^3\times 64$ lattice at pion mass 300 MeV are increased by $3.4\%$ and $1.7\%$ from their unimproved values, respectively. We have also used clover fermion on the same DWF configurations and find the same behavior for the local axial charge as that of the overlap fermion.
The 1-loop correction of the QCD energy momentum tensor with the overlap fermion and HYP smeared Iwasaki gluon
Yi-Bo Yang, Michael Glatzmaier, Keh-Fei Liu, Yong Zhao
Dec 12 2016 nucl-th hep-lat hep-ph arXiv:1612.02855v1

@misc{1612.02855, author = {Yi-Bo Yang and Michael Glatzmaier and Keh-Fei Liu and Yong Zhao}, title = {{T}he 1-loop correction of the {QCD} energy momentum tensor with the overlap fermion and {HYP} smeared {I}wasaki gluon}, year = {2016}, eprint = {1612.02855}, note = {arXiv:1612.02855v1} }
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We present the 1-loop renormalization of the energy momentum tensor using the overlap fermion and a HYP-smeared Iwasaki gauge action. We also calculate the 1-loop matching coefficient that convert the lattice simulation results renormalized in the RI/MOM scheme to the $\overline{\textrm{MS}}$ scheme. The dependence of the renormalization on the gauge action and the number of HYP smearing steps are also investigated.
Glue spin and helicity in proton from lattice QCD
Yi-Bo Yang, Raza Sabbir Sufian, Andrei Alexandru, Terrence Draper, Michael J. Glatzmaier, Keh-Fei Liu, Yong Zhao
Sep 21 2016 hep-ph hep-lat nucl-th arXiv:1609.05937v3

@misc{1609.05937, author = {Yi-Bo Yang and Raza Sabbir Sufian and Andrei Alexandru and Terrence Draper and Michael J.~Glatzmaier and Keh-Fei Liu and Yong Zhao}, title = {{G}lue spin and helicity in proton from lattice {QCD}}, year = {2016}, eprint = {1609.05937}, note = {arXiv:1609.05937v3} }
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We report the first lattice QCD calculation of the glue spin in the nucleon. The lattice calculation is carried out with valence overlap fermions on 2+1 flavor DWF gauge configurations on four lattice spacings and four volumes including an ensemble with physical values for the quark masses. The glue spin $S_{G}$ in the Coulomb gauge in the $\overline{\text{MS}}$ scheme is obtained with the 1-loop perturbative matching. We find the results fairly insensitive to lattice spacing and quark masses. We also find that the proton momentum dependence of $S_G$ in the range $0\leq |\vec{p}| < 1.5$ GeV is very mild, and we determine it in the large momentum limit to be $S_{G}=0.251(47)(16)$ at the physical pion mass in the $\overline{\text{MS}}$ scheme at $\mu^2=10$ GeV$^2$. If the matching procedure in large momentum effective theory is neglected, $S_G$ is equal to the glue helicity measured in high-energy scattering experiments.
Baryons and Chiral Symmetry
Keh-Fei Liu
Sep 12 2016 hep-ph hep-lat nucl-th arXiv:1609.02572v1

@misc{1609.02572, author = {Keh-Fei Liu}, title = {{B}aryons and {C}hiral {S}ymmetry}, year = {2016}, eprint = {1609.02572}, note = {arXiv:1609.02572v1} }
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The relevance of chiral symmetry in baryons is highlighted in three examples in the nucleon spectroscopy and structure. The first one is the importance of chiral dynamics in understanding the Roper resonance. The second one is the role of chiral symmetry in the lattice calculation of $\pi N \sigma$ term and strangeness. The third one is the role of chiral $U(1)$ anomaly in the anomalous Ward identity in evaluating the quark spin and the quark orbital angular momentum. Finally, the chiral effective theory for baryons is discussed.
Strange Quark Magnetic Moment of the Nucleon at Physical Point
Raza Sabbir Sufian, Yi-Bo Yang, Andrei Alexandru, Terrence Draper, Keh-Fei Liu, Jian Liang
Jun 24 2016 hep-ph hep-lat nucl-th arXiv:1606.07075v3

@misc{1606.07075, author = {Raza Sabbir Sufian and Yi-Bo Yang and Andrei Alexandru and Terrence Draper and Keh-Fei Liu and Jian Liang}, title = {{S}trange {Q}uark {M}agnetic {M}oment of the {N}ucleon at {P}hysical {P}oint}, year = {2016}, eprint = {1606.07075}, howpublished = {Phys. Rev. Lett. 118, 042001 (2017)}, doi = {10.1103/PhysRevLett.118.042001}, note = {arXiv:1606.07075v3} }
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We report a lattice QCD calculation of the strange quark contribution to the nucleon's magnetic moment and charge radius. This analysis presents the first direct determination of strange electromagnetic form factors including at the physical pion mass. We perform a model-independent extraction of the strange magnetic moment and the strange charge radius from the electromagnetic form factors in the momentum transfer range of $0.051 \,\text{GeV}^2 \lesssim Q^2 \lesssim 1.31 \,\text{GeV}^2 $. The finite lattice spacing and finite volume corrections are included in a global fit with $24$ valence quark masses on four lattices with different lattice spacings, different volumes, and four sea quark masses including one at the physical pion mass. We obtain the strange magnetic moment $G^s_M(0) = - 0.064(14)(09)\, \mu_N$. The four-sigma precision in statistics is achieved partly due to low-mode averaging of the quark loop and low-mode substitution to improve the statistics of the nucleon propagator. We also obtain the strange charge radius $\langle r_s^2\rangle_E = -0.0043 (16)(14)\,$ $\text{fm}^2$.
Parton Distribution Function from the Hadronic Tensor on the Lattice
Keh-Fei Liu
Mar 25 2016 hep-ph hep-lat nucl-th arXiv:1603.07352v1

@misc{1603.07352, author = {Keh-Fei Liu}, title = {{P}arton {D}istribution {F}unction from the {H}adronic {T}ensor on the {L}attice}, year = {2016}, eprint = {1603.07352}, note = {arXiv:1603.07352v1} }
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The path-integral formulation of the hadronic tensor W_\mu\nu of deep inelastic scattering is reviewed. It is shown that there are 3 gauge invariant and topologically distinct contributions. The separation of the connected sea partons from those of the disconnected sea can be achieved with a combination of the global fit of the parton distribution function (PDF), the semi-inclusive DIS data on the strange PDF and the lattice calculation of the ratio of the strange to $u/d$ momentum fraction in the disconnected insertion. We shall discuss numerical issues associated with lattice calculation of the hadronic tensor involving a four-point function, such as large hadron momenta and improved maximum entropy method to obtain the spectral density from the hadronic tensor in Euclidean time. We also draw a comparison between the large momentum approach to the parton distribution function (PDF) and the hadronic tensor approach.
Glue Spin of the Proton
Yi-Bo Yang, Raza Sabbir Sufian, Andrei Alexandru, Terrence Draper, Michael J. Glatzmaier, Keh-Fei Liu
Mar 18 2016 hep-ph hep-lat arXiv:1603.05256v2

@misc{1603.05256, author = {Yi-Bo Yang and Raza Sabbir Sufian and Andrei Alexandru and Terrence Draper and Michael J.~Glatzmaier and Keh-Fei Liu}, title = {{G}lue {S}pin of the {P}roton}, year = {2016}, eprint = {1603.05256}, note = {arXiv:1603.05256v2} }
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We report the progress on the lattice QCD calculation of the glue spin contribution to proton spin. This calculation is carried out with valence overlap fermion on 2+1 flavor DWF gauge configurations at two lattice spacings with the momentum of the frame in the kinematic range $0\leq p^2 \leq 2$ GeV$^2$. A mild frame dependence is observed. The matching and mixing with large-momentum effective field theory are in progress. The unrenormalized result at $p^2=4$ GeV$^2$ with $O(a^2)$ correction gives $S_G$ = 0.13(3).
$\pi$N and strangeness sigma terms at the physical point with chiral fermions
Yi-Bo Yang, Andrei Alexandru, Terrence Draper, Jian Liang, Keh-Fei Liu
Dec 01 2015 hep-lat hep-ph arXiv:1511.09089v3

@misc{1511.09089, author = {Yi-Bo Yang and Andrei Alexandru and Terrence Draper and Jian Liang and Keh-Fei Liu}, title = {$\pi${N} and strangeness sigma terms at the physical point with chiral fermions}, year = {2015}, eprint = {1511.09089}, note = {arXiv:1511.09089v3} }
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Lattice QCD calculations with chiral fermions of the $\pi$N sigma term $\sigma_{\pi N}$ and strangeness sigma term $\sigma_{sN}$ including chiral interpolation with continuum and volume corrections are provided in this work, with the excited-state contaminations subtracted properly. We calculate the scalar matrix element for the light/strange quark directly and find $\sigma_{\pi N}=45.9(7.4)(2.8)$ MeV, with the disconnected insertion part contributing 20(12)(4)\%, and $\sigma_{sN}=40.2(11.7)(3.5)$ MeV, which is somewhat smaller than $\sigma_{\pi N}$. The ratio of the strange/light scalar matrix elements is $y$ = 0.09(3)(1).
Strange and Charm Quark Spins from Anomalous Ward Identity
Ming Gong, Yi-Bo Yang, Jian Liang, Andrei Alexandru, Terrence Draper, Keh-Fei Liu
Nov 13 2015 hep-ph hep-lat arXiv:1511.03671v2

@misc{1511.03671, author = {Ming Gong and Yi-Bo Yang and Jian Liang and Andrei Alexandru and Terrence Draper and Keh-Fei Liu}, title = {{S}trange and {C}harm {Q}uark {S}pins from {A}nomalous {W}ard {I}dentity}, year = {2015}, eprint = {1511.03671}, note = {arXiv:1511.03671v2} }
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We present a calculation of the strange and charm quark contributions to the nucleon spin from the anomalous Ward identity (AWI). It is performed with overlap valence quarks on 2+1-flavor domain-wall fermion gauge configurations on a $24^3 \times 64$ lattice with the light sea mass at $m_{\pi} = 330$ MeV. To satisfy the AWI, the overlap fermion for the pseudoscalar density and the overlap Dirac operator for the topological density, which do not have multiplicative renormalization, are used to normalize the form factor of the local axial-vector current at finite $q^2$. For the charm quark, we find that the negative pseudoscalar term almost cancels the positive topological term. For the strange quark, the pseudoscalar term is less negative than that of the charm. By imposing the AWI, the strange $g_A(q^2)$ at $q^2 =0$ is obtained by a global fit of the pseudoscalar and the topological form factors, together with $g_A(q^2)$ and the induced pseudoscalar form factor $h_A(q^2)$ at finite $q^2$. The chiral extrapolation to the physical pion mass gives $\Delta s + \Delta {\bar{s}} = -0.0403(44)(78)$.
Stochastic method with low mode substitution for nucleon isovector matrix elements
Yi-Bo Yang, Andrei Alexandru, Terrence Draper, Ming Gong, Keh-Fei Liu
Sep 16 2015 hep-lat hep-ph arXiv:1509.04616v3

@misc{1509.04616, author = {Yi-Bo Yang and Andrei Alexandru and Terrence Draper and Ming Gong and Keh-Fei Liu}, title = {{S}tochastic method with low mode substitution for nucleon isovector matrix elements}, year = {2015}, eprint = {1509.04616}, note = {arXiv:1509.04616v3} }
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We introduce a stochastic sandwich method with low-mode substitution to evaluate the connected three-point functions. The isovector matrix elements of the nucleon for the axial-vector coupling $g_A^3$, scalar couplings $g_S^3$ and the quark momentum fraction $\langle x\rangle_{u -d}$ are calculated with overlap fermion on 2+1 flavor domain-wall configurations on a $24^3 \times 64$ lattice at $m_{\pi} = 330$ MeV with lattice spacing $a = 0.114$ fm.
The Parton Orbital Angular Momentum: Status and Prospects
Keh-Fei Liu, Cedric Lorce
Aug 06 2015 hep-ph hep-lat nucl-th arXiv:1508.00911v1

@misc{1508.00911, author = {Keh-Fei Liu and Cedric Lorce}, title = {{T}he {P}arton {O}rbital {A}ngular {M}omentum: {S}tatus and {P}rospects}, year = {2015}, eprint = {1508.00911}, note = {arXiv:1508.00911v1} }
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Theoretical progress on the formulation and classification of the quark and gluon orbital angular momenta (OAM) is reviewed. Their relation to parton distributions and open questions and puzzles are discussed. We give a status report on the lattice calculation of the parton kinetic and canonical OAM and point out several strategies to calculate the quark and gluon canonical OAM on the lattice.
Orbital Angular Momentum and Generalized Transverse Momentum Distribution
Yong Zhao, Keh-Fei Liu, Yibo Yang
Jul 01 2015 hep-ph hep-lat nucl-th arXiv:1506.08832v1

@misc{1506.08832, author = {Yong Zhao and Keh-Fei Liu and Yibo Yang}, title = {{O}rbital {A}ngular {M}omentum and {G}eneralized {T}ransverse {M}omentum {D}istribution}, year = {2015}, eprint = {1506.08832}, note = {arXiv:1506.08832v1} }
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We show that, when boosted to the infinite momentum frame, the quark and gluon orbital angular momentum operators defined in the nucleon spin sum rule of X. S. Chen et al. are the same as those derived from generalized transverse momentum distributions. This completes the connection between the infinite momentum limit of each term in that sum rule and experimentally measurable observables. We also show that these orbital angular momentum operators can be defined locally, and discuss the strategies of calculating them in lattice QCD.
Quark and Glue Components of the Proton Spin from Lattice Calculation
Keh-Fei Liu
Apr 27 2015 hep-ph hep-lat nucl-th arXiv:1504.06601v2

@misc{1504.06601, author = {Keh-Fei Liu}, title = {{Q}uark and {G}lue {C}omponents of the {P}roton {S}pin from {L}attice {C}alculation}, year = {2015}, eprint = {1504.06601}, note = {arXiv:1504.06601v2} }
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The status of lattice calculations of the quark spin, the quark orbital angular momentum, the glue angular momentum and glue spin in the nucleon is summarized. The quark spin calculation is recently carried out from the anomalous Ward identity with chiral fermions and is found to be small mainly due to the large negative anomaly term which is believed to be the source of the `proton spin crisis'. We also present the first calculation of the glue spin at finite nucleon momenta.
Quark Spin in Proton from Anomalous Ward Indentity
Yi-Bo Yang, Ming Gong, Keh-Fei Liu, Mingyang Sun
Apr 17 2015 hep-ph hep-lat arXiv:1504.04052v1

@misc{1504.04052, author = {Yi-Bo Yang and Ming Gong and Keh-Fei Liu and Mingyang Sun}, title = {{Q}uark {S}pin in {P}roton from {A}nomalous {W}ard {I}ndentity}, year = {2015}, eprint = {1504.04052}, howpublished = {PoS(LATTICE2014)138}, note = {arXiv:1504.04052v1} }
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We report a quark spin calculation from the anomalous Ward identity with overlap fermions on 2+1 flavor dynamical fermion configurations with light sea quark masses. Such a formulation decomposes the divergence of the flavor-singlet axial-vector current into a quark pseudoscalar term and a triangle anomaly term, flavor by flavor. A large negative contribution from the anomaly term is observed and it is canceled within errors by the contribution from the pseudoscalar term in the disconnected insertion in the heavy quark region. On the other hand, net negative contributions are obtained for the light and strange quarks in the disconnected insertion, since their quark pseudoscalar terms are smaller than that of the heavy quark. Our results are obtained from the 2+1 flavor domain wall fermion configurations on the 24^3*64 lattice with a-1 = 1.78(5) GeV and the light sea quark at m_\pi = 330 MeV. We use the overlap fermion for the valence and the quark loop so that the renormalization constants Z_m and Z_P cancel in the pseudoscalar operator 2mP. In addition, the overlap Dirac operator is used to calculate the local topological charge in the anomaly so that there is no renormalization for the anomaly term either. In this study, we find the total quark spin to be small mainlyly due to the large negative anomaly term which could be the source for the 'proton spin crisis'.
Revisiting Scalar Glueballs
Hai-Yang Cheng, Chun-Khiang Chua, Keh-Fei Liu
Mar 25 2015 hep-ph hep-ex hep-lat nucl-th arXiv:1503.06827v3

@misc{1503.06827, author = {Hai-Yang Cheng and Chun-Khiang Chua and Keh-Fei Liu}, title = {{R}evisiting {S}calar {G}lueballs}, year = {2015}, eprint = {1503.06827}, note = {arXiv:1503.06827v3} }
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It is commonly believed that the lowest-lying scalar glueball lies somewhere in the isosinglet scalar mesons $f_0(1370), f_0(1500)$ and $f_0(1710)$ denoted generically by $f_{0}$. In this work we consider lattice calculations and experimental data to infer the glue and $q\bar q$ components of $f_0$. These include the calculations of the scalar glueball masses in quenched and unquenched lattice QCD, measurements of the radiative decays $J/\psi\to\gamma f_{0}$, the ratio of $f_{0}$ decays to $\pi\pi$ and $K\bar K$, the ratio of $J/\psi$ decays to $f_0(1710)\omega$ and $f_0(1710)\phi$, the $f_0$ contributions to $B_s\to J/\psi\pi^+\pi^-$, and the near mass degeneracy of $a_0(1450)$ and $K_0^*(1430)$. All analyses suggest the prominent glueball nature of $f_0(1710)$ and the flavor octet structure of $f_0(1500)$.
Strange quark momentum fraction from overlap fermion
Mingyang Sun, Yi-Bo Yang, Keh-Fei Liu, Ming Gong
Feb 20 2015 hep-lat hep-ph arXiv:1502.05482v3

@misc{1502.05482, author = {Mingyang Sun and Yi-Bo Yang and Keh-Fei Liu and Ming Gong}, title = {{S}trange quark momentum fraction from overlap fermion}, year = {2015}, eprint = {1502.05482}, note = {arXiv:1502.05482v3} }
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We present a calculation of $< x >_s$ for the strange quark in the nucleon. We also report the ratio of the strange $< x >$ to that of $u/d$ in the disconnected insertion which will be useful in constraining the global fit of parton distribution functions at small $x$. We adopt overlap fermion action on $2 + 1$ flavor domain-wall fermion configurations on the $24^3 \times 64$ lattice with a light sea quark mass which corresponds to $m_{\pi}=330$ MeV. Smeared grid $Z_3$ sources are deployed to calculate the nucleon propagator with low-mode substitution. Even-odd grid sources and time-dilution technique with stochastic noises are used to calculate the high mode contribution to the quark loop. Low mode averaging (LMA) for the quark loop is applied to reduce the statistical error of the disconnected insertion calculation. We find the ratio $< x >_s/< x >_{u/d}^{\mathrm{DI}}= 0.78(3)$ in this study.
Glue Spin $S_G$ in The Longitudinally Polarized Nucleon
Raza Sabbir Sufian, Michael J. Glatzmaier, Yi-Bo Yang, Keh-Fei Liu, Mingyang Sun
Dec 24 2014 hep-lat hep-ph arXiv:1412.7168v2

@misc{1412.7168, author = {Raza Sabbir Sufian and Michael J.~Glatzmaier and Yi-Bo Yang and Keh-Fei Liu and Mingyang Sun}, title = {{G}lue {S}pin ${S}_{G}$ in {T}he {L}ongitudinally {P}olarized {N}ucleon}, year = {2014}, eprint = {1412.7168}, note = {arXiv:1412.7168v2} }
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We present a lattice QCD calculation of the glue spin $S_G$ in the nucleon for the first time. It was recently shown that the first moment of the glue helicity distribution could be obtained through the cross-product of the the electric field $\vec{E}$ and the physical gauge field $\vec{A}_{phys}$ with the non-Abelian Coulomb gauge condition, i.e. $\int d^3 x\, \,\vec{E}(x) \times \vec{A}_{phys}(x)$ in the infinite momentum frame. We use the gauge field tensor from the overlap Dirac operator to check the frame dependence and calculate glue spin with several momenta. The calculation is carried out with valence overlap fermion on 2+1 flavor DWF gauge configurations on the $24^3 \times 64$ lattice with $a^{-1}=1.77$ GeV with the light sea quark mass corresponding to a pion mass of 330 MeV.