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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.

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.

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.

The non-singlet helicity quark parton distribution functions (PDFs) of the nucleon are determined from lattice QCD, by jointly leveraging pseudo-distributions and the distillation spatial smearing paradigm. A Lorentz decomposition of appropriately isolated space-like matrix elements reveals pseudo-distributions that contain information on the leading-twist helicity PDFs, as well as an invariant amplitude that induces an additional $z^2$ contamination of the leading-twist signal. An analysis of the short-distance behavior of the space-like matrix elements using matching coefficients computed to next-to-leading order (NLO) exposes the desired PDF up to this additional $z^2$ contamination. Due to the non-conservation of the axial current, we elect to isolate the helicity PDFs normalized by the nucleon axial charge at the same scale $\mu^2$. The leading-twist helicity PDFs as well as several sources of systematic error, including higher-twist effects, discretization errors, and the aforementioned $z^2$ contaminating amplitude are jointly determined by characterizing the computed pseudo-distribution in a basis of Jacobi polynomials. The Akaike Information Criterion is exploited to effectively average over distinct model parameterizations and cuts on the pseudo-distribution. Encouraging agreement is observed with recent global analyses of each non-singlet quark helicity PDF, notably a rather small non-singlet anti-quark helicity PDF for all quark momentum fractions.

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, $\nu\lesssim 9$.

Contribution from the USQCD Collaboration to the Proceedings of the US Community Study on the Future of Particle Physics (Snowmass 2021).

We extract pion parton distribution functions (PDFs) in a Monte Carlo global QCD analysis of experimental data together with reduced Ioffe time pseudo-distributions and matrix elements of current-current correlators generated from lattice QCD. By including both experimental and lattice QCD data, our analysis rigorously quantifies both the uncertainties of the pion PDFs and systematic effects intrinsic to the lattice QCD observables. The reduced Ioffe time pseudo-distributions significantly decrease the uncertainties on the PDFs, while the current-current correlators are limited by the systematic effects associated with the lattice. Consistent with recent phenomenological determinations, the behavior of the valence quark distribution of the pion at large momentum fraction is found to be $\sim (1-x)^{ \beta_{\rm eff}}$ with $\beta_{\rm eff} \approx 1.0-1.2$.

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.

The Pomeron Regge trajectory underlies the dynamics dependence of hadronic total cross sections and diffractive reactions at high energies. The physics of the Pomeron is closely related to the gluon distribution function and the gluon gravitational form factor of the target hadron. In this article we examine the scale dependence of the nonperturbative gluon distribution in the nucleon and the pion which was derived in a previous article [Phys. Rev. D 104, 114005 (2021)] in the framework of holographic light-front QCD and the Veneziano model. We argue that the QCD evolution of the gluon distribution function $g(x,\mu)$ to large $\mu^2$ leads to a single scale-dependent Pomeron. The resulting Pomeron trajectory $\alpha_P(t, \mu)$ not only depends on the momentum transfer squared $t$, but also on the physical scale $\mu$ of the amplitude, such as the virtuality $Q^2$ of the interacting photon in inclusive diffractive electroproduction. This can explain not only the $Q^2$ evolution of the proton structure function $F_2(x,Q^2)$ at small $x$, but also the observed energy and $Q^2$ dependence of high energy diffractive processes involving virtual photons up to LHC energies.

We present a determination of the non-singlet transversity parton distribution function (PDF) of the nucleon, normalized with respect to the tensor charge at $\mu^2=2$ GeV$^2$ from lattice quantum chromodynamics. We apply the pseudo-distribution approach, using a gauge ensemble with a lattice spacing of 0.094 fm and the light quark mass tuned to a pion mass of 358 MeV. We extract the transversity PDF from the analysis of the short-distance behavior of the Ioffe-time pseudo-distribution using the leading-twist next-to-leading order (NLO) matching coefficients calculated for transversity. We reconstruct the $x$-dependence of the transversity PDF through an expansion in a basis of Jacobi polynomials in order to reduce the PDF ansatz dependence. Within the limitations imposed by a heavier-than-physical pion mass and a fixed lattice spacing, we present a comparison of our estimate for the valence transversity PDF with the recent global fit results based on single transverse spin asymmetry. We find the intrinsic nucleon sea to be isospin symmetric with respect to transversity.

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 holographic light-front QCD framework provides a unified nonperturbative description of the hadron mass spectrum, form factors and quark distributions. In this article we extend holographic QCD in order to describe the gluonic distribution in both the proton and pion from the coupling of the metric fluctuations induced by the spin-two Pomeron with the energy momentum tensor in anti--de Sitter space, together with constraints imposed by the Veneziano model\colorblue, without additional free parameters. The gluonic and quark distributions are shown to have significantly different effective QCD scales.

We propose an analysis method for the leading-twist operator product expansion based lattice QCD determinations of the valence parton distribution function (PDF). In the first step, we determine the confidence-intervals of the leading-twist $\overline{\mathrm{MS}}$ Wilson coefficients, $C_n(\mu^2 z^2)$, of the equal-time bilocal quark bilinear, given the lattice QCD matrix element of Ioffe-time distribution for a particular hadron $H$ as well as the prior knowledge of the valence PDF, $f(x,\mu)$ of the hadron $H$ determined via global fit from the experimental data. In the next step, we apply the numerically estimated $C_n$ in the lattice QCD determinations of the valence PDFs of other hadrons, and for the zero-skewness generalized parton distribution (GPD) of the same hadron $H$ at non-zero momentum transfers. Our proposal still assumes the dominance of leading-twist terms, but it offers a pragmatic alternative to the usage of perturbative Wilson coefficients and their associated higher-loop uncertainties such as the effect of all-order logarithms at larger sub-Fermi quark-antiquark separations $z$.

We investigate unpolarized and polarized gluon distributions and their applications to the Ioffe-time distributions, which are related to lattice QCD calculations of parton distribution functions. Guided by the counting rules based on the perturbative QCD at large momentum fraction $x$ and the color coherence of gluon couplings at small $x$, we parametrize gluon distributions in the helicity basis. By fitting the unpolarized gluon distribution, the inferred polarized gluon distribution from our parametrization agrees with the one from global analysis. A simultaneous fit to both unpolarized and polarized gluon distributions is also performed to explore the model uncertainty. The agreement with the global analysis supports the $(1-x)$ power suppression of the helicity-antialigned distribution relative to the helicity-aligned distribution. The corresponding Ioffe-time distributions and their asymptotic expansions are calculated from the gluon distributions. Our results of the Ioffe-time distributions can provide guidance to the extrapolation of lattice QCD data to the region lacking precise gluonic matrix elements. Therefore, they can help regulate the ill-posed inverse problem associated with extracting the gluon distributions from discrete data from first-principle calculations, which are available in a limited range of the nucleon momentum and the spatial separation between the gluonic currents. Given various limitations in obtaining lattice QCD data at large Ioffe time, phenomenological approaches can provide important complementary information to extract the gluon distributions in the entire $x$ region. The possibility of investigating higher-twist effects and other systematic uncertainties in the contemporary first-principle calculations of parton distributions from phenomenologically well-determined Ioffe-time distributions in the large Ioffe-time region is also discussed.

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.

We extract the pion valence quark distribution $q^\pi_{\rm v}(x)$ from lattice QCD (LQCD) calculated matrix elements of spacelike correlations of one vector and one axial vector current analyzed in terms of QCD collinear factorization, using a new short-distance matching coefficient calculated to one-loop accuracy. We derive the Ioffe time distribution of the two-current correlations in the physical limit by investigating the finite lattice spacing, volume, quark mass, and higher-twist dependencies in a simultaneous fit of matrix elements computed on four gauge ensembles. We find remarkable consistency between our extracted $q^\pi_{\rm v}(x)$ and that obtained from experimental data across the entire $x$-range. Further, we demonstrate that the one-loop matching coefficient relating the LQCD matrix computed in position space to the $q_{\rm v}^{\pi}(x)$ in momentum space has well-controlled behavior with Ioffe time. This justifies that LQCD calculated current-current correlations are good observables for extracting partonic structures by using QCD factorization, which complements to the global effort to extract partonic structure from experimental data.

We present a calculation of the pion valence quark distribution extracted using the formalism of reduced Ioffe time pseudo-distributions or more commonly known as pseudo-PDFs. Our calculation is carried out on two different 2+1 flavor QCD ensembles using the isotropic-clover fermion action, with lattice dimensions $24^3\times 64$ and $32^3\times 96$ at the lattice spacing of $a=0.127$ fm, and with the quark mass equivalent to a pion mass of $m_\pi \simeq 415$ MeV. We incorporate several combinations of smeared-point and smeared-smeared pion source-sink interpolation fields in obtaining the lattice QCD matrix elements using the summation method. After one-loop perturbative matching and combining the pseudo-distributions from these two ensembles, we extract the pion valence quark distribution using a phenomenological functional form motivated by the global fits of parton distribution functions. We also calculate the lowest four moments of the pion quark distribution through the "OPE without OPE". We present a qualitative comparison between our lattice QCD extraction of the pion valence quark distribution with that obtained from global fits and previous lattice QCD calculations.

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.

We present the first exploratory lattice QCD calculation of the pion valence quark distribution extracted from spatially separated current-current correlations in coordinate space. We show that an antisymmetric combination of vector and axial-vector currents provides direct information on the pion valence quark distribution. Using the collinear factorization approach, we calculate the perturbative tree-level kernel for this current combination and extract the pion valence distribution. The main goal of this article is to demonstrate the efficacy of this general lattice QCD approach in the reliable extraction of parton distributions. With controllable power corrections and a good understanding of the lattice systematics, this method has the potential to serve as a complementary to the many efforts to extract parton distributions in global analyses from experimentally measured cross sections. We perform our calculation on an ensemble of 2+1 flavor QCD using the isotropic-clover fermion action, with lattice dimensions $32^3\times 96$ at a lattice spacing \mbox$a=0.127$ fm and the quark mass equivalent to a pion mass $m_\pi \simeq 416$ MeV.

We demonstrate that a nonzero strangeness contribution to the spacelike electromagnetic form factor of the nucleon is evidence for a strange-antistrange asymmetry in the nucleon's light-front wave function, thus implying different nonperturbative contributions to the strange and antistrange quark distribution functions. A recent lattice QCD calculation of the nucleon strange quark form factor predicts that the strange quark distribution is more centralized in coordinate space than the antistrange quark distribution, and thus the strange quark distribution is more spread out in light-front momentum space. We show that the lattice prediction implies that the difference between the strange and antistrange parton distribution functions, $s(x)-\bar{s}(x)$, is negative at small-$x$ and positive at large-$x$. We also evaluate the strange quark form factor and $s(x)-\bar{s}(x)$ using a baryon-meson fluctuation model and a novel nonperturbative model based on light-front holographic QCD. This procedure leads to a Veneziano-like expression of the form factor, which depends exclusively on the twist of the hadron and the properties of the Regge trajectory of the vector meson which couples to the quark current in the hadron. The holographic structure of the model allows us to introduce unambiguously quark masses in the form factors and quark distributions preserving the hard scattering counting rule at large-$Q^2$ and the inclusive counting rule at large-$x$. Quark masses modify the Regge intercept which governs the small-$x$ behavior of quark distributions, therefore modifying their small-$x$ singular behavior. Both nonperturbative approaches provide descriptions of the strange-antistrange asymmetry and intrinsic strangeness in the nucleon consistent with the lattice QCD result.

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.

The structure of generalized parton distributions is determined from light-front holographic QCD up to a universal reparametrization function $w(x)$ which incorporates Regge behavior at small $x$ and inclusive counting rules at $x \to 1$. A simple ansatz for $w(x)$ which fulfills these physics constraints with a single-parameter results in precise descriptions of both the nucleon and the pion quark distribution functions in comparison with global fits. The analytic structure of the amplitudes leads to a connection with the Veneziano model and hence to a nontrivial connection with Regge theory and the hadron spectrum.

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$^2$.

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.

We determine the nucleon neutral weak electromagnetic form factors $G^{Z,p(n)}_{E,M}$ by combining results from light-front holographic QCD and lattice QCD calculations. We deduce nucleon electromagnetic form factors from light-front holographic QCD which provides a good parametrization of the experimental data of the nucleon electromagnetic form factors in the entire momentum transfer range and isolate the strange quark electromagnetic form factors $G^{s}_{E,M}$ using lattice QCD. From these calculations, we obtain precise estimates of the neutral weak form factors in the momentum transfer range of $0\,\text{GeV}^2\leq Q^2 \leq 0.5 \,\text{GeV}^2 $. From the lattice QCD calculation, we present $Q^2$-dependence of the strange quark form factors. We also deduce the neutral weak Dirac and Pauli form factors $F_{1,2}^{Z,p(n)}$ of the proton and the neutron.

We present a comprehensive analysis of the spacelike nucleon electromagnetic form factors and their flavor decomposition within the framework of light-front holographic QCD. We show that the inclusion of the higher Fock components $\ket {qqqq\bar{q}}$ has a significant effect on the spin-flip elastic Pauli form factor and almost zero effect on the spin-conserving Dirac form factor. We present light-front holographic QCD results for the proton and neutron form factors at any momentum transfer range, including asymptotic predictions, and show that our results agree with the available experimental data with high accuracy. In order to correctly describe the Pauli form factor we need an admixture of a five quark state of about 30$\%$ in the proton and about 40$\%$ in the neutron. We also extract the nucleon charge and magnetic radii and perform a flavor decomposition of the nucleon electromagnetic form factors. The free parameters needed to describe the experimental nucleon form factors are very few: two parameters for the probabilities of higher Fock states for the spin-flip form factor and a phenomenological parameter $r$, required to account for possible SU(6) spin-flavor symmetry breaking effects in the neutron, whereas the Pauli form factors are normalized to the experimental values of the anomalous magnetic moments. The covariant spin structure for the Dirac and Pauli nucleon form factors prescribed by AdS$_5$ semiclassical gravity incorporates the correct twist scaling behavior from hard scattering and also leads to vector dominance at low energy.

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.

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 $\langle r_s^2\rangle_E = -0.0043 (16)(14)\,$ $\text{fm}^2$.

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).

We investigate the origin and behavior of oscillations observed in the hadron correlators constructed from the domain wall fermion (DWF) for different parameters involved in lattice QCD simulations. This oscillatory behavior at early time slices hinders the extraction of excited states in hadron spectroscopy. Furthermore, the deviation from exponential decay may have a significant impact on fermion loop calculations performed on the lattice. We present results for several well-known implementations of the DWF actions. We extend the study of Shamir DWF action to include Boriçi and Möbius DWF actions by analyzing the poles of 4D quark propagator. For each action considered, we find an unphysical mode when analyzing the pole structure of the free DWF propagator for a finite extent of the $5^{\text{th}}$ dimension $L_s$, and we show that this mode is responsible for the oscillatory behavior observed in hadron correlators. We have performed numerical checks on these results and have found that the presence of oscillatory behavior is sensitive to the DWF parameters $a_5$, $b_5$, $c_5$ and DW height $M$. To minimize oscillations, our results suggest that one should choose $M a_5<1$ for the Shamir and Boriçi DWFs, and $M(b_5-c_5)<1$ for Möbius DWF when $M>1$. For each calculation considered, the Borçi DWF displayed the smallest magnitude of oscillation when compared to the Shamir and Möbius DWF actions using the same input parameters.

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.

We carried out a calculation of the Roper state with the Sequential Empirical Bayesian (SEB) method with overlap valence fermion on 2+1-flavor domain-wall fermion configurations on the 24^3 x 64 lattice with a^-1 = 1.73 GeV. The light sea quark mass corresponds to a pion mass of 330 MeV. The mass of the Roper, chirally extrapolated to the physical pion mass, is 1404(112) MeV which is consistent with the experimental value at 1440 MeV. When compared to the Roper state calculation with variational method for Clover and twisted mass fermions, it is found that the Roper states from SEB with overlap fermion are systematically lower by 400 - 800 MeV for all the quark masses ranging from light to the strange mass region. We study the origin of the difference by exploring the size of the interpolation field in relation to the radial wavefunction of the Roper and also the dynamical influence of the higher Fock space.