We present our recent high precision calculations (Phys. Rev. D102 (2020) no.5, 054512 and JHEP 04 (2021) 044, JHEP 21 (2020) 004) of the first moment of nucleon isovector polarized, unpolarized and transversity distributions, i.e., momentum fraction, helicity and transversity moment, respectively. We use the standard method for the calculation of these moments (via matrix elements of twist two operators), and carry out a detailed analysis of the sources of systematic uncertainty, in particular of excited state contributions. Our calculations have been performed using two different lattice setups (Clover-on-HISQ and Clover-on-Clover), each with several ensembles. They give consistent results that are in agreement with global fit analyses.
We report a state-of-the-art lattice QCD calculation of the isovector quark transversity distribution of the proton in the continuum and physical mass limit using large-momentum effective theory. The calculation is done at four lattice spacings $a=\{0.098,0.085,0.064,0.049\}$~fm and various pion masses ranging between $220$ and $350$ MeV, with proton momenta up to $2.8$ GeV. The result is non-perturbatively renormalized in the hybrid scheme with self renormalization which treats the infrared physics at large correlation distance properly, and extrapolated to the continuum, physical mass and in…
We investigate the connection of lattice calculations of moments of isovector parton distributions to the physical regime through extrapolations in the quark mass. We consider the one pion loop renormalisation of the nucleon matrix elements of the corresponding operators and thereby develop formulae with which to extrapolate the moments of the unpolarised, helicity and transversity distributions. These formulae are consistent with chiral perturbation theory in the chiral limit and incorporate the correct heavy quark limits. In the polarised cases, the inclusion of intermediate states involving…
We present the first lattice-QCD calculation of the isovector polarized parton distribution functions (both helicity and transversity) using the large-momentum effective field theory (LaMET) approach for direct Bjorken-$x$ dependence. We first review the detailed steps of the procedure in the unpolarized case, then generalize to the helicity and transversity cases. We also derive a new mass-correction formulation for all three cases. We then compare the effects of each finite-momentum correction using lattice data calculated at $M_π\approx 310$ MeV. Finally, we discuss the implications of thes…
High statistics results for the isovector momentum fraction, $\langle x \rangle_{u-d}$, helicity moment, $\langle x \rangle_{Δu-Δd}$, and the transversity moment, $\langle x\rangle_{δu-δd}$, of the nucleon are presented using seven ensembles of gauge configurations generated by the JLab/W&M/LANL/MIT collaborations using $2+1$-flavors of dynamical Wilson-clover quarks. Attention is given to understanding and controlling the contributions of excited states. The final results are obtained using a simultaneous fit in the lattice spacing $a$, pion mass $M_π$ and the finite volume parameter $M_πL$ k…
Nucleon isovector vector- and axialvector-current form factors, the renormalized isovector transversity and scalar charge, and the bare quark momentum and helicity moments of isovector structure functions are reported with improved statistics from two recent RBC+UKQCD 2+1-flavor dynamical domain-wall fermions ensembles: Iwasaki\(\times\)DSDR gauge \(32^3\times64\) at inverse lattice spacing of 1.38 GeV and pion mass of 249 and 172 MeV.
We report a state-of-the-art lattice calculation of the isovector quark transversity distribution of the proton at the physical pion mass. Within the framework of large-momentum effective theory (LaMET), we compute the transversity quasi-distributions using clover valence fermions on 2+1+1-flavor (up/down, strange, charm) HISQ-lattice configurations with boosted proton momenta as large as 3.0~GeV. The relevant lattice matrix elements are nonperturbatively renormalized in regularization-independent momentum-subtraction (RI/MOM) scheme and systematically matched to the physical transversity dist…
We present results on the quark unpolarized, helicity and transversity parton distributions functions of the nucleon. We use the quasi-parton distribution approach within the lattice QCD framework and perform the computation using an ensemble of twisted mass fermions with the strange and charm quark masses tuned to approximately their physical values and light quark masses giving pion mass of 260 MeV. We use hierarchical probing to evaluate the disconnected quark loops. We discuss identification of ground state dominance, the Fourier transform procedure and convergence with the momentum boost.…
In this letter, we report the results for the isovector polarized quark quasi-distribution functions $Δu(x,v) - Δd(x,v)$ in the large $N_c$, calculated within the chiral quark-soliton model. It is shown that the polarized quark quasi-distributions present good convergence to the light-cone PDFs in the limit of the nucleon boost momentum $P_N \to \infty$ (or the velocity $v \to 1$), compared to the case of the unpolarized isosinglet distributions.
Using overlap as well as Wilson fermions, we have computed the one-loop renormalization factors of ten non-singlet operators which measure the third moment of quark momentum and helicity distributions (the lowest two having been computed in a previous paper), as well as the lowest three moments of the $g_2$ structure function and the lowest two non-trivial moments of the $h_1$ transversity structure function (plus the tensor charge). These factors are needed to extract physical observables from Monte Carlo simulations of the corresponding matrix elements. An exact chiral symmetry is maintained…
Analyses on possible systematics in some isovector nucleon observables in the RBC+UKQCD 2+1-flavor dynamical domain-wall fermion (DWF) lattice-QCD are presented. The vector charge, axial charge, quark momentum and helicity fractions, and transversity are discussed using mainly the Iwasaki\(\times\)DSDR ensemble at pion mass of 170 MeV. No autocorrelation issue is observed in the vector charge and quark momentum and helicity fractions. Blocked Jack-knife analyses expose significant growth of estimated error for the axial charge with increasing block sizes that are similar to or larger than the …
We present an exploratory study of the gluonic structure of the $ϕ$ meson using lattice QCD (LQCD). This includes the first investigation of gluonic transversity via the leading moment of the twist-two double-helicity-flip gluonic structure function $Δ(x,Q^2)$. This structure function only exists for targets of spin $J\ge1$ and does not mix with quark distributions at leading twist, thereby providing a particularly clean probe of gluonic degrees of freedom. We also explore the gluonic analogue of the Soffer bound which relates the helicity flip and non-flip gluonic distributions, finding it to…
Nucleon spin structure functions have been investigated mainly by longitudinally-polarized ones for finding the origin of the nucleon spin. Other types of spin structure functions are transversely-polarized ones. In particular, quark transversity distributions in the nucleons have very different properties from the longitudinally-polarized quark distribution functions, especially in scaling violation, because they are decoupled from the gluon transversity, due to the fact that they are helicity-flip (chiral-odd) distributions. Such studies are valuable for finding not only the origin of the nu…
We present a state-of-the-art calculation of the isovector quark helicity Bjorken-$x$ distribution in the proton using lattice-QCD ensembles at the physical pion mass. We compute quasi-distributions at proton momenta $P_z \in \{2.2, 2.6, 3.0\}$~GeV on the lattice, and match them systematically to the physical parton distribution using large-momentum effective theory (LaMET). We reach an unprecedented precision through high statistics in simulations, large-momentum proton matrix elements, and control of excited-state contamination. The resulting distribution with combined statistical and system…
We present a complete analysis of the chiral extrapolation of lattice moments of all twist-2 isovector quark distributions, including corrections from N pi and Delta pi loops. Even though the Delta resonance formally gives rise to higher order non-analytic structure, the coefficients of the higher order terms for the helicity and transversity moments are large and cancel much of the curvature generated by the wave function renormalization. The net effect is that, whereas the unpolarized moments exhibit considerable curvature, the polarized moments show little deviation from linearity as the ch…
We report on the first global QCD analysis of the quark transversity distributions in the nucleon from semi-inclusive deep-inelastic scattering (SIDIS), using a new Monte Carlo method based on nested sampling and constraints on the isovector tensor charge $g_T$ from lattice QCD. A simultaneous fit to the available SIDIS Collins asymmetry data is compatible with $g_T$ values extracted from a comprehensive reanalysis of existing lattice simulations, in contrast to previous analyses which found significantly smaller $g_T$ values. The contributions to the nucleon tensor charge from $u$ and $d$ qua…
We present results for the $x$ dependence of the unpolarized, helicity, and transversity isovector quark distributions in the proton using lattice QCD, employing the method of quasi-distributions proposed by Ji in 2013. Compared to a previous calculation by us, the errors are reduced by a factor of about 2.5. Moreover, we present our first results for the polarized sector of the proton, which indicate an asymmetry in the proton sea in favor of the $u$ antiquarks for the case of helicity distributions, and an asymmetry in favor of the $d$ antiquarks for the case of transversity distributions.
We present a calculation of the Mellin moments of the transverse quark spin densities in the nucleon using lattice QCD. The densities are extracted from the unpolarized and transversity generalized form factors extrapolated to the continuum limit using three $N_f=2+1+1$ twisted mass fermion gauge ensembles simulated with physical quark masses and spanning three lattice spacings. The first moment of transversely polarized quarks in an unpolarized nucleon shows an interesting distortion, which can be traced back to the sharp falloff of the transversity generalized form factor $\bar{B}_{Tn0}(t)$.…
Nucleon-structure calculations of isovector vector- and axialvector-current form factors, transversity and scalar charge, and quark momentum and helicity fractions are reported from two recent 2+1-flavor dynamical domain-wall fermions lattice-QCD ensembles generated jointly by the RIKEN-BNL-Columbia and UKQCD Collaborations with Iwasaki $\times$ dislocation-suppressing-determinatn-ratio gauge action at inverse lattice spacing of 1.378(7) GeV and pion mass values of 249.4(3) and 172.3(3) MeV.
We study isovector unpolarized and helicity parton distribution functions (PDF) of the proton within the framework of Large Momentum Effective Theory. We use a gauge ensemble, generated by the MILC Collaboration, with a superfine lattice spacing of $0.042$ fm and a pion mass of $310$ MeV, enabling us to simultaneously reach sub-fermi spatial separations and larger nucleon momenta. We compare the spatial dependence of quasi-PDF matrix elements in different renormalization schemes with the corresponding results of the global fits, obtained using 1-loop perturbative matching. We present determina…
We report on numerical lattice QCD calculations of some of the low moments of the nucleon structure functions. The calculations are carried out with gauge configurations generated by the RBC and UKQCD collaborations with (2+1)-flavors of dynamical domain wall fermions and the Iwasaki gauge action ($β= 2.13$). The inverse lattice spacing is $a^{-1} = 1.73$ GeV, and two spatial volumes of ((2.7{\rm fm})^3) and ((1.8 {\rm fm})^3) are used. The up and down quark masses are varied so the pion mass lies between 0.33 and 0.67 GeV while the strange mass is about 12 % heavier than the physical one. The…
We present the first calculation of the $x$-dependence of the isovector transversity generalized parton distributions (GPDs) for the proton within lattice QCD. We compute the matrix elements with non-local operators containing a Wilson line. The calculation implements the Breit symmetric frame. The proton momenta are chosen as $0.83,\,1.25,\,1.67$ GeV, and the values of the momentum transfer squared are $0.69,\,1.02$ GeV$^2$. These combinations include cases with zero and nonzero skewness. The calculation is performed using one ensemble of two degenerate-mass light, a strange and a charm quark…
We present a numerical lattice quantum chromodynamics calculation of isovector form factors and the first few moments of the isovector structure functions of the nucleon. The calculation employs two degenerate dynamical flavors of domain-wall fermions, resulting in good control of chiral symmetry breaking. Non-perturbative renormalization of the relevant quark currents is performed where necessary. The inverse lattice spacing, $a^{-1}$, is about 1.7 GeV. We use degenerate up and down dynamical quark masses around 1, 3/4 and 1/2 the strange quark mass. The physical volume of the lattice is abou…
We present results on the isovector momentum fraction, $\langle x \rangle_{u-d}$, helicity moment, $\langle x \rangle_{Δu-Δd}$, and the transversity moment, $\langle x \rangle_{δu-δd}$, of the nucleon obtained using nine ensembles of gauge configurations generated by the MILC collaboration using $2+1+1$-flavors of dynamical highly improved staggered quarks (HISQ). The correlation functions are calculated using the Wilson-Clover action and the renormalization of the three operators is carried out nonperturbatively on the lattice in the RI${}^\prime$-MOM scheme. The data have been collected at l…
We show the first results for parton distribution functions within the proton at the physical pion mass, employing the method of quasi-distributions. In particular, we present the matrix elements for the iso-vector combination of the unpolarized, helicity and transversity quasi-distributions, obtained with $N_f=2$ twisted mass clover-improved fermions and a proton boosted with momentum $|\vec{p}|=0.83\mbox{ GeV}$. The momentum smearing technique has been applied to improve the overlap with the proton boosted state. Moreover, we present the renormalized helicity matrix elements in the RI$'$ sch…
Proton isovector helicity PDF at NNLO and the twist-3 moment $\tilde{d}_2$ from lattice QCD at physical quark masses
Brookhaven National Laboratory（布鲁克海文国家实验室）；Kent State University（肯特州立大学）；Central China Normal University（华中师范大学）；Massachusetts Institute of Technology（麻省理工学院）；Argonne National Laboratory（阿贡国家实验室）
Generalized parton distributions (GPDs) are among the most fundamental quantities for describing the internal structure of hadrons. In this work, we present results on isovector GPDs of the proton obtained within lattice Quantum Chromodynamics. We use the quasi-distribution formalism and perform the calculations on an ensemble of $N_f = 2 + 1 + 1$ twisted mass fermions, with pion mass $M_π=260$~MeV and lattice spacing $a\simeq 0.093$~fm. Results are presented for unpolarized, helicity, and transversity GPDs at zero and nonzero skewness with controlled statistical uncertainties. Comparisons wit…
Momentum and spatial distributions of quarks and gluons inside hadrons are typically encoded in the so-called generalized parton distributions (GPDs). GPDs are multi-dimensional quantities that are very challenging to extract, both experimentally and within lattice QCD. We present the first lattice results on the $x$-dependence of isovector unpolarized, helicity and transversity GPDs of the proton, obtained from lattice QCD using an ensemble of $N_f=2+1+1$ maximally twisted mass fermions, with pion mass $M_π=260$ MeV and lattice spacing $a\simeq 0.093$ fm. Our calculations use the quasi-distri…
Moments of light cone quark density, helicity, and transversity distributions are calculated in unquenched lattice QCD at $β= 5.5$ and $β= 5.3$ using Wilson fermions on $ 16^3 \times 32 $ lattices. These results are combined with earlier calculations at $β= 5.6$ using SESAM configurations to study the continuum limit.
We report isovector form factors and low moments of isovector structure functions of nucleon from the coarse RIKEN-BNL-Columbia (RBC) and UKQCD joint dynamical (2+1)-flavor domain-wall fermions (DWF) ensembles. The lattice cut off is estimated at (a^{-1}=1.7) GeV. The lattice volume is as large as 2.7 fm across. We carefully optimize the nucleon source/sink separation in time to about 1.4 fm. Unexpectedly large finite-size effect in the axial charge is found. The effect scales with a single variable, the product (m_πL) of the pion mass (m_π) and lattice spatial linear extent (L), and sets in a…
We employ chiral perturbation theory to calculate the nucleon-pion-state contribution to the 3-point correlation functions measured in lattice QCD to compute various moments of parton distribution functions (quark momentum fraction, helicity and transversity moment). We estimate the impact of the nucleon-pion-state contribution on the plateau method for lattice simulations with a physical pion mass. The nucleon-pion-state contribution results in an overestimation of all three moments. The overestimation is at the 5-20% level for source-sink separations of about 1.5 fm.
Lattice QCD Benchmark of Proton Helicity and Flavor-Dependent Unpolarized Transverse Momentum-Dependent Parton Distribution Functions at Physical Quark Masses
We present results from a lattice QCD study of nucleon matrix elements at vanishing momentum transfer for local and twist-2 isovector operator insertions. Computations are performed on gauge ensembles with non-perturbatively improved $N_f=2+1$ Wilson fermions, covering four values of the lattice spacing and pion masses down to $M_π\approx200$MeV. Several source-sink separations (typically ~1.0fm to ~1.5fm) allow us to assess excited-state contamination. Results on individual ensembles are obtained from simultaneous two-state fits across all observables and all available source-sink separations…
We compute various (generalized) isovector charges of the octet baryons. These include $g_A$, $g_T$ and $g_S$ as well as the unpolarized, polarized and transversity parton distribution function (PDF) momentum fractions $\langle x\rangle_{u^+-d^+}$, $\langle x\rangle_{Δu^--Δd^-}$ and $\langle x\rangle_{δu^+-δ^+}$. The simulations are carried out on a subset of the (isospin symmetric) $N_f=2+1$ flavour Coordinated Lattice Simulations (CLS) gauge ensembles with lattice spacings ranging from $a\approx 0.086\,$fm down to $a\approx 0.050\,$fm. First results on the breaking of flavour symmetry and th…
Moments of unpolarized, helicity, and transversity distributions, electromagnetic form factors, and generalized form factors of the nucleon are presented from a preliminary analysis of lattice results using pion masses down to 359 MeV. The twist two matrix elements are calculated using a mixed action of domain wall valence quarks and asqtad staggered sea quarks and are renormalized perturbatively. Several observables are extrapolated to the physical limit using chiral perturbation theory. Results are compared with experimental moments of quark distributions and electromagnetic form factors and…
The generalized parton distributions (GPDs) offer a window on three-dimensional imaging of the nucleon, providing understanding of how the fundamental properties of the nucleon, such as its mass and spin, arise from the underlying quark and gluon degrees of freedom. In this work, we present the first lattice calculation of the nucleon isovector helicity GPD at physical pion mass, using an $a \approx 0.09$ fm lattice ensemble with 2+1+1 flavors of highly improved staggered quarks generated by MILC Collaboration. We perform the GPD calculation in Breit frame using averaged nucleon boost momentum…
Moments of the generalized parton distributions of the nucleon, calculated with a mixed action of domain wall valence quarks and asqtad staggered sea quarks, are presented for pion masses extending down to 359 MeV. Results for the moments of the unpolarized, helicity, and transversity distributions are given and compared to the available experimental measurements. Additionally, a selection of the generalized form factors are shown and the implications for the spin decomposition and transverse structure of the nucleon are discussed. Particular emphasis is placed on understanding systematic erro…
We report isovector form factors and low moments of structure functions of nucleon in numerical lattice quantum chromodynamics (QCD) from the on-going calculations by the RIKEN-BNL-Columbia (RBC) and UKQCD Collaborations with (2+1) dynamical flavors of domain-wall fermion (DWF) quarks. We calculate the matrix elements with four light quark masses, corresponding to pion mass values of m_π= 330-670 MeV, while the dynamical strange mass is fixed at a value close to physical, on (2.7 fm)^3 spatial volume. We found that our axial charge, g_A, at the lightest mass exhibits a large deviation from the…
We present the first calculation of the $x$-dependence of the proton generalized parton distributions (GPDs) within lattice QCD. Results are obtained for the isovector unpolarized and helicity GPDs. We compute the appropriate matrix elements of fast-moving protons coupled to non-local operators containing a Wilson line. We present results for proton momenta $0.83,\,1.25,\,1.67$ GeV, and momentum transfer squared $0.69,\,1.38$ GeV$^2$. These combinations include cases with zero and nonzero skewness. The calculation is performed using one ensemble of two degenerate mass light, a strange and a ch…
We report the first-ever calculation of the isovector flavor combination of the chiral-odd twist-3 parton distribution $h_L(x)$ for the proton from lattice QCD. We employ gauge configurations with two degenerate light, a strange and a charm quark ($N_f=2+1+1$) of maximally twisted mass fermions with a clover improvement. The lattice has a spatial extent of 3 fm and lattice spacing of 0.093 fm. The values of the quark masses lead to a pion mass of $260$ MeV. We use a source-sink time separation of 1.12 fm to control contamination from excited states. Our calculation is based on the quasi-distri…
The large-momentum effective theory (LaMET) framework has been widely used to determine the Bjorken-$x$ dependence of parton distribution functions (PDFs) in lattice-QCD hadron-structure calculations. In this proceeding, I highlighted selected recent lattice-QCD results on parton distributions from MSULat group. We use clover valence fermions on ensembles generated by MILC Collaboration with lattice spacing $a \approx 0.06$, 0.09, and 0.12 fm, with $M_πL \approx 4$, and with pion masses including 135, 220 and 310 MeV and $N_f=2+1+1$ flavors of highly improved staggered dynamical quarks. Result…
We present a calculation of the Mellin moments of the nucleon transverse quark spin densities extracted from the unpolarized and transversity generalized form factors. We use three $N_F=2+1+1$ ensembles of twisted mass fermions with quark masses tuned to their physical values and lattice spacings $a\sim 0.08$~fm, $a\sim 0.07$~fm and $a\sim 0.06$~fm and extrapolate the form factors to the continuum limit. Besides isovector densities we also include results for the tensor charge for each quark flavor using the ensemble with $a\sim 0.08$~fm for which we include the disconnected contributions.
We present results for the flavor non-singlet u-d parton distribution functions within the nucleon using the quasi-PDF approach. The lattice calculation is performed by employing the twisted mass formulation and two gauge ensembles, having $N_f = 2$ and $N_f = 2 + 1 + 1$ dynamical fermions with masses tuned to their physical value. For the $N_f = 2$ physical point ensemble, the unpolarized, helicity and transversity distributions are computed for three values of the nucleon momentum, namely [6, 8, 10]$π/L$ corresponding to [0.83,1.11,1.38] GeV. Upon renormalization, we find that, as the nucleo…
Multi-particle states with additional pions are expected to be a non-negligible source of excited-state contamination in lattice simulations at the physical point. It is shown that baryon chiral perturbation theory can be employed to calculate the contamination due to two-particle nucleon-pion states in various nucleon observables. Leading order results are presented for the nucleon axial, tensor and scalar charge and three Mellin moments of parton distribution functions (quark momentum fraction, helicity and transversity moment). Taking into account phenomenological results for the charges an…
In order to advance lattice calculations of moments of unpolarized, helicity, and transversity distributions, electromagnetic form factors, and generalized form factors of the nucleon to a new level of precision, this work investigates several key aspects of precision lattice calculations. We calculate the number of configurations required for constant statistical errors as a function of pion mass, describe the coherent sink method to help achieve these statistics, examine the statistical correlations between separate measurements, study correlations in the behavior of form factors at differen…
In these proceedings, we summarize the main results from the first-ever calculations of the chiral-even and chiral-odd twist-3 parton distributions, $g_T(x)$ and $h_L(x)$, of the proton from lattice QCD. We use an $N_f=2+1+1$ ensemble of maximally twisted mass fermions with a clover improvement. The lattice has a spatial extent of 3~fm, the lattice spacing is 0.093~fm, and the pion mass is $260$~MeV. The matrix elements are obtained with a source-sink time separation of 1.12~fm to control contamination from excited states. The calculation is based on the quasi-PDF approach and employs three va…
In this work we continue our effort to explore a recent proposal, which allows light-cone distributions to be extracted from purely spatial correlations, being thus accessible to lattice methods. In order to test the feasibility of this method, we present our latest results from a twisted mass lattice calculation of the flavor non-singlet momentum, helicity and transversity distributions of the nucleon. Furthermore, we apply a newly proposed momentum improved smearing, which has the potential to reach higher nucleon momenta as required for a safe matching procedure to the physical distribution…
We present one-loop results for the forward twist-two matrix elements relevant to the unpolarised, helicity and transversity baryon structure functions, in partially-quenched (N_f=2 and N_f=2+1) heavy baryon chiral perturbation theory. The full-QCD limit can be straightforwardly obtained from these results and we also consider SU(2|2) quenched QCD. Our calculations are performed in finite volume as well as in infinite volume. We discuss features of lattice simulations and investigate finite volume effects in detail. We find that volume effects are not negligible, typically around 5--10% in cur…
Multi-particle states with additional pions are expected to be a non-negligible source of the excited-state contamination in lattice simulations at the physical point. It is shown that baryon chiral perturbation theory (ChPT) can be employed to calculate the contamination due to two-particle nucleon-pion states in various nucleon observables. Results to leading order are presented for the nucleon axial, tensor and scalar charge and three Mellin moments of parton distribution functions: the average quark momentum fraction, the helicity and the transversity moment. Taking into account experiment…
We provide an analysis of the x-dependence of the bare unpolarized, helicity and transversity iso-vector parton distribution functions (PDFs) from lattice calculations employing (maximally) twisted mass fermions. The x-dependence of the calculated PDFs resembles the one of the phenomenological parameterizations, a feature that makes this approach very promising. Furthermore, we apply momentum smearing for the relevant matrix elements to compute the lattice PDFs and find a large improvement factor when compared to conventional Gaussian smearing. This allows us to extend the lattice computation …
A review of recent nucleon structure calculations within lattice QCD is presented. The nucleon excited states, the axial charge, the isovector momentum fraction and helicity distribution are discussed, assessing the methods applied for their study, including approaches to evaluate the disconnected contributions. Results on the spin carried by the quarks in the nucleon are also presented.
We present a quenched lattice QCD calculation of the first few moments of the polarized and un-polarized structure functions of the nucleon. Our calculations are done using domain wall fermions and the DBW2 gauge action with inverse lattice spacing ~1.3GeV, physical volume approximatelly (2.4 fm)^3, and light quark masses down to about 1/4 the strange quark mass. Values of the individual moments are found to be significantly larger than experiment, as in past lattice calculations, but interestingly the chiral symmetry of domain wall fermions allows for a precise determination of the ratio of t…
We present the first direct lattice calculation of the isovector sea-quark parton distributions using the formalism developed recently by one of the authors. We use $N_f=2+1+1$ HISQ lattice gauge ensembles (generated by MILC Collaboration) and clover valence fermions with pion mass 310 MeV. We are able to obtain the qualitative features of the nucleon sea flavor structure even at this large pion mass: We observe violation of the Gottfried sum rule, indicating $\overline{d}(x) > \overline{u}(x)$; the helicity distribution obeys $Δ\overline{u}(x) > Δ\overline{d}(x)$, which is consistent with the…
We report lattice-volume independence of low moments of nucleon structure functions from the coarse RIKEN-BNL-Columbia (RBC) and UKQCD joint dynamical (2+1)-flavor domain-wall fermions (DWF) ensembles at the lattice cut off of (a^{-1}\sim1.7) GeV. The isovector quark momentum fraction, (< x >_{u-d}), and helicity fraction, (< x >_{Δu - Δd}), both fully non-perturbatively renormalized are studied on two spatial volumes of ((\sim {\rm 2.7 fm})^3) and ((\sim {\rm 1.8 fm})^3). Their naturally renormalized ratio, (< x >_{u-d}/< x >_{Δu - Δd}), is not affected by any finite-size effect. It does not …
We present results on the nucleon scalar, axial and tensor charges as well as on the momentum fraction, and the helicity and transversity moments. The pion momentum fraction is also presented. The computation of these key observables is carried out using lattice QCD simulations at a physical value of the pion mass. The evaluation is based on gauge configurations generated with two degenerate sea quarks of twisted mass fermions with a clover term. We investigate excited states contributions with the nucleon quantum numbers by analyzing three sink-source time separations. We find that, for the s…
