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Polarized and unpolarized gluon PDFs: generative machine learning applications for lattice QCD matrix elements at short distance and large momentum
Talal Ahmed Chowdhury, Taku Izubuchi, Methun Kamruzzaman, Nikhil Karthik, Tanjib Khan, Tianbo Liu, Arpon Paul, Jakob Schoenleber, Raza Sabbir Sufian
Sep 27 2024 hep-lat hep-ph nucl-th arXiv:2409.17234v1

@misc{2409.17234, author = {Talal Ahmed Chowdhury and Taku Izubuchi and Methun Kamruzzaman and Nikhil Karthik and Tanjib Khan and Tianbo Liu and Arpon Paul and Jakob Schoenleber and Raza Sabbir Sufian}, title = {{P}olarized and unpolarized gluon {PDF}s: generative machine learning applications for lattice {QCD} matrix elements at short distance and large momentum}, year = {2024}, eprint = {2409.17234}, note = {arXiv:2409.17234v1} }
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Lattice quantum chromodynamics (QCD) calculations share a defining challenge by requiring a small finite range of spatial separation $z$ between quark/gluon bilinears for controllable power corrections in the perturbative QCD factorization, and a large hadron boost $p_z$ for a successful determination of collinear parton distribution functions (PDFs). However, these two requirements make the determination of PDFs from lattice data very challenging. We present the application of generative machine learning algorithms to estimate the polarized and unpolarized gluon correlation functions utilizing short-distance data and extending the correlation up to $zp_z \lesssim 14$, surpassing the current capabilities of lattice QCD calculations. We train physics-informed machine learning algorithms to learn from the short-distance correlation at $z\lesssim 0.36$ fm and take the limit, $p_z \to \infty$, thereby minimizing possible contamination from the higher-twist effects for a successful reconstruction of the polarized gluon PDF. We also expose the bias and problems with underestimating uncertainties associated with the use of model-dependent and overly constrained functional forms, such as $x^\alpha(1-x)^\beta$ and its variants to extract PDFs from the lattice data. We propose the use of generative machine learning algorithms to mitigate these issues and present our determination of the polarized and unpolarized gluon PDFs in the nucleon.
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.
Gluon helicity distribution in the nucleon from lattice QCD and machine learning
Tanjib Khan, Tianbo Liu, Raza Sabbir Sufian
Nov 29 2022 hep-lat hep-ph nucl-th arXiv:2211.15587v4

@misc{2211.15587, author = {Tanjib Khan and Tianbo Liu and Raza Sabbir Sufian}, title = {{G}luon helicity distribution in the nucleon from lattice {QCD} and machine learning}, year = {2022}, eprint = {2211.15587}, note = {arXiv:2211.15587v4} }
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We present the first lattice QCD determination of the light cone gluon helicity correlation parton distribution function (PDF) with numerical evidence toward disfavoring negative gluon polarization in the nucleon. We present a solution for eliminating an inevitable contamination term that dominates the Euclidean correlations and makes determining gluon helicity PDF unfeasible. The proposed synergy between lattice QCD and artificial intelligence offers a superior platform to alleviate the defining challenge of extracting quark and gluon PDFs from the lattice data that are available in a limited domain due to a finite range of accessible hadron momenta. We suggest a systematically improvable method to extract PDFs from the lattice data, independent of inadequate parametrizations. The result of the gluon helicity will improve our understanding of the role of spin in the strong interaction and the nucleon spin structure.
Towards the determination of the gluon helicity distribution in the nucleon from lattice quantum chromodynamics
Colin Egerer, Bálint Joó, Joseph Karpie, Nikhil Karthik, Tanjib Khan, Christopher J. Monahan, Wayne Morris, Kostas Orginos, Anatoly Radyushkin, David G. Richards, Eloy Romero, Raza Sabbir Sufian, Savvas Zafeiropoulos
Jul 19 2022 hep-lat hep-ph nucl-th arXiv:2207.08733v2

@misc{2207.08733, author = {Colin Egerer and Bálint Joó and Joseph Karpie and Nikhil Karthik and Tanjib Khan and Christopher J.~Monahan and Wayne Morris and Kostas Orginos and Anatoly Radyushkin and David G.~Richards and Eloy Romero and Raza Sabbir Sufian and Savvas Zafeiropoulos}, title = {{T}owards the determination of the gluon helicity distribution in the nucleon from lattice quantum chromodynamics}, year = {2022}, eprint = {2207.08733}, note = {arXiv:2207.08733v2} }
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We present the first exploratory lattice quantum chromodynamics (QCD) calculation of the polarized gluon Ioffe-time pseudo-distribution in the nucleon. The Ioffe-time pseudo-distribution provides a frame-independent and gauge-invariant framework to determine the gluon helicity in the nucleon from first principles. We employ a high-statistics computation using a $32^3\times 64$ lattice ensemble characterized by a $358$ MeV pion mass and a $0.094$ fm lattice spacing. We establish the pseudo-distribution approach as a feasible method to address the proton spin puzzle with successive improvements in statistical and systematic uncertainties anticipated in the future. Within the statistical precision of our data, we find a good comparison between the lattice determined polarized gluon Ioffe-time distribution and the corresponding expectations from the state-of-the-art global analyses. We find a hint for a nonzero gluon spin contribution to the proton spin from the model-independent extraction of the gluon helicity pseudo-distribution over a range of Ioffe-time, $\nu\lesssim 9$.
Unpolarized gluon distribution in the nucleon from lattice quantum chromodynamics
Tanjib Khan, Raza Sabbir Sufian, Joseph Karpie, Christopher J. Monahan, Colin Egerer, Bálint Joó, Wayne Morris, Kostas Orginos, Anatoly Radyushkin, David G. Richards, Eloy Romero, Savvas Zafeiropoulos
Jul 20 2021 hep-lat hep-ex hep-ph nucl-ex nucl-th arXiv:2107.08960v2

@misc{2107.08960, author = {Tanjib Khan and Raza Sabbir Sufian and Joseph Karpie and Christopher J.~Monahan and Colin Egerer and Bálint Joó and Wayne Morris and Kostas Orginos and Anatoly Radyushkin and David G.~Richards and Eloy Romero and Savvas Zafeiropoulos}, title = {{U}npolarized gluon distribution in the nucleon from lattice quantum chromodynamics}, year = {2021}, eprint = {2107.08960}, note = {arXiv:2107.08960v2} }
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In this study, we present a determination of the unpolarized gluon Ioffe-time distribution in the nucleon from a first principles lattice quantum chromodynamics calculation. We carry out the lattice calculation on a $32^3\times 64$ ensemble with a pion mass of $358$ MeV and lattice spacing of $0.094$ fm. We construct the nucleon interpolating fields using the distillation technique, flow the gauge fields using the gradient flow, and solve the summed generalized eigenvalue problem to determine the glounic matrix elements. Combining these techniques allows us to provide a statistically well-controlled Ioffe-time distribution and unpolarized gluon PDF. We obtain the flow time independent reduced Ioffe-time pseudo-distribution, and calculate the light-cone Ioffe-time distribution and unpolarized gluon distribution function in the $\overline{\rm MS}$ scheme at $\mu = 2$ GeV, neglecting the mixing of the gluon operator with the quark singlet sector. Finally, we compare our results to phenomenological determinations.
The Positive-Parity Baryon Spectrum and the Role of Hybrid Baryons
Tanjib Khan, David Richards, Frank Winter
Oct 08 2020 hep-lat hep-ph nucl-th arXiv:2010.03052v2

@misc{2010.03052, author = {Tanjib Khan and David Richards and Frank Winter}, title = {{T}he {P}ositive-{P}arity {B}aryon {S}pectrum and the {R}ole of {H}ybrid {B}aryons}, year = {2020}, eprint = {2010.03052}, howpublished = {Phys. Rev. D 104, 034503 (2021)}, doi = {10.1103/PhysRevD.104.034503}, note = {arXiv:2010.03052v2} }
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We calculate the low-lying spectra for the positive-parity $\Delta$ and $N$ at two pion masses of 358 and 278 MeV using an isotropic clover action with two degenerate light-quaark and one strange-quark flavors through the application of the generalized variational method within the distillation framework. The spectrum exhibits the general features observed in previous calculations using an anisotropic clover lattice, with a counting of states at least as rich as the quark model. Furthermore, we identify states that are hybrid in nature, where gluonic degrees of freedom play a structural role, indicatinng that such states appear a feature of the excited baryon spectrum, irrespective of the lattice action, or the precise details of the smearing of the lattice interpolating operators used to identify such states.
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: $r_{V}=\frac{V(0)}{A_{1}(0)}=1.695\pm0.083\pm0.051$, $r_{2}=\frac{A_{2}(0)}{A_{1}(0)}=0.845\pm0.056\pm0.039$.