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 $M_πL$ keeping leading order corrections. The data show no significant dependence on the lattice spacing and some evidence for finite-volume corrections. The main variation is with $M_π$, whose magnitude depends on the mass gap of the first excited state used in the analysis. Our final results, in the $\overline{\rm MS}$ scheme at 2 GeV, are $\langle x \rangle_{u-d} = 0.160(16)(20)$, $\langle x \rangle_{Δu-Δd} = 0.192(13)(20)$ and $\langle x \rangle_{δu-δd} = 0.215(17)(20)$, where the first error is the overall analysis uncertainty assuming excited-state contributions have been removed, and the second is an additional systematic uncertainty due to possible residual excited-state contributions. These results are consistent with other recent lattice calculations and phenomenological global fit values.
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 set…
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…
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 present results on the nucleon tensor form factors and first moment of the transversity distribution using maximally twisted mass fermions. We analyze two Nf=2+1+1 ensembles having pion masses of 213 MeV and 373 MeV with lattice spacing a=0.064 fm and a=0.082 fm, respectively. First results using an Nf=2 ensemble of twisted mass fermions with a clover term at a physical pion mass and lattice spacing a=0.094 fm are also presented. The renormalization function for the local tensor form factors is evaluated non-perturbatively with a perturbative subtraction of O(a^2)-terms, while for the first…
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.…
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…
We present a determination of the non-singlet transversity parton distribution function (PDF) of the nucleon, normalized with respect to the tensor charge at $μ^2=2$ 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 recon…
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 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 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 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 $\bar{B}_{Tn0}(t)$.…
The transversity and the tensor charge of the nucleon, currently under active investigation experimentally and theoretically, are fundamental quantities in hadron physics as well as for our comprehension of the nucleon structure. Some tension between the values of the tensor charge, as computed on the basis of phenomenological extractions and lattice QCD calculations, has been observed. In this letter, by means of an explicit example, we study the role of assumptions, usually adopted in phenomenological parametrizations, and we show that, by relaxing some of them, such a tension could be eased…
We show how generalized quark distributions in the nucleon describe the density of polarized quarks in the impact parameter plane, both for longitudinal and transverse polarization of the quark and the nucleon. This density representation entails positivity bounds including chiral-odd distributions, which tighten the known bounds in the chiral-even sector. Using the quark equations of motion, we derive relations between the moments of chiral-odd generalized parton distributions of twist two and twist three. We exhibit the analogy between polarized quark distributions in impact parameter space …
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.
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.
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 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.
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 present the first direct calculation of the transversity parton distribution function within the nucleon from lattice QCD. The calculation is performed using simulations with the light quark mass fixed to its physical value and at one value of the lattice spacing. Novel elements of the calculations are non-perturbative renormalization and extraction of a formula for the matching to light-cone PDFs. Final results are presented in the $\overline{\rm MS}$ scheme at a scale of $\sqrt{2}$ GeV.
This talk presents results from the QCDSF-UKQCD collaboration for moments of leading twist generalized parton distributions in two-flavor lattice QCD based on O(a) improved Wilson Fermions. We study helicity independent and helicity flip GPDs with a focus on densities of quarks in the transverse plane.
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.
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 …
A complete description of the nucleon structure in terms of generalized parton distributions (GPDs) at twist 2 level requires the measurement/computation of the eight functions H, E, \tilde H, \tilde E, H_T, E_T, \tilde H_T and \tilde E_T, all depending on the three variables x, ξand t. In this talk, we present and discuss our first steps in the framework of lattice QCD towards this enormous task. Dynamical lattice QCD results for the lowest three Mellin moments of the helicity dependent and independent GPDs are shown in terms of their corresponding generalized form factors. Implications for t…
We show that the total gluon helicity $ΔG$ in a polarized nucleon can be calculated on a Euclidean lattice through a universality class of QCD operators that describe the helicity or polarization of the onshell gluon radiation. We in particular find some operators whose matrix elements in a nucleon of momentum $P^z$ are directly related to $ΔG$ with only power-law $(1/P^z)^n (n\ge 2)$ corrections.
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…
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 …
