Nucleon Generalized Parton Distributions from Full Lattice QCD
Ph. Hägler, W. Schroers, J. Bratt, R. G. Edwards, M. Engelhardt, G. T. Fleming, B. Musch, J. W. Negele, K. Orginos, A. V. Pochinsky, D. B. Renner, D. G. Richards
备注：
40 pages, 49 figures; Revised chiral extrapolations in sections A-K, main conclusions unchanged
We present a comprehensive study of the lowest moments of nucleon generalized parton distributions in N_f=2+1 lattice QCD using domain wall valence quarks and improved staggered sea quarks. Our investigation includes helicity dependent and independent generalized parton distributions for pion masses as low as 350 MeV and volumes as large as (3.5 fm)^3, for a lattice spacing of 0.124 fm. We use perturbative renormalization at one-loop level with an improvement based on the non-perturbative renormalization factor for the axial vector current, and only connected diagrams are included in the isosinglet channel.
In these proceedings we discuss recent progress in nucleon structure using lattice QCD simulations at or near the physical value of the pion mass. Main focus will be given in observables such as the nucleon axial charge and the first moments of parton distributions, for both the valence and sea quark contributions, and discuss their implications on the spin content of the nucleon. We will will also report developments on the evaluation of the gluon momentum fraction, which contributes significantly to the nucleon spin.
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.…
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…
In this letter, we investigate the nucleon quasi-parton distribution functions in the chiral quark soliton model. We derive a set of sum-rules depending on the velocity of the nucleon and on the Dirac matrix defining the distribution functions. We present numerical results for the isosinglet unpolarized distribution, in which we find that the anti-quark distribution breaks the positivity condition at nucleon velocities $v\approx 0.99\;(P_N\approx 7.0 M_N)$ and smaller. We found that, for the isosinglet unpolarized case, a large nucleon momentum is required for the quasi-parton distribution to …
We present the $x$-dependent nucleon and pion gluon distribution from lattice QCD using the pseudo-PDF approach, on lattice ensembles with $2+1+1$ flavors of highly improved staggered quarks (HISQ), generated by MILC Collaboration. We use clover fermions for the valence action and momentum smearing to achieve pion boost momentum up to 2.56~GeV on three lattice spacings $a\approx 0.9, 0.12$ and 0.15~fm and three pion masses $M_π\approx 220$, 310 and 690~MeV. We compare our pion and preliminary nucleon gluon results with the determination by global fits.
We present the first lattice calculation of the nucleon isovector unpolarized generalized parton distribution (GPD) at the physical pion mass using a lattice ensemble with 2+1+1 flavors of highly improved staggered quarks (HISQ) generated by MILC Collaboration, with lattice spacing $a\approx 0.09$~fm and volume $64^3\times 96$. We use momentum-smeared sources to improve the signal at nucleon boost momentum $P_z \approx 2.2$ GeV, and report results at nonzero momentum transfers in $[0.2,1.0]\text{ GeV}^2$. Nonperturbative renormalization in RI/MOM scheme is used to obtain the quasi-distribution…
We present the first lattice-QCD calculation of the nucleon isovector unpolarized parton distribution functions (PDFs) at the physical-continuum limit using Large-Momentum Effective Theory (LaMET). The lattice results are calculated using ensembles with multiple sea pion masses with the lightest one around 135~MeV, 3 lattice spacings $a\in[0.06,0.12]$~fm, and multiple volumes with $M_πL$ ranging 3.3 to 5.5. We perform a simultaneous chiral-continuum extrapolation to obtain RI/MOM renormalized nucleon matrix elements with various Wilson-link displacements in the continuum limit at physical pion…
We analyze the moments of the isosinglet generalized parton distributions H, E, H-tilde, E-tilde of the nucleon in one-loop order of heavy-baryon chiral perturbation theory. We discuss in detail the construction of the operators in the effective theory that are required to obtain all corrections to a given order in the chiral power counting. The results will serve to improve the extrapolation of lattice results to the chiral limit.
We present a review of recent applications of nonlocal chiral effective theory to hadron structure studies. Starting from a nonlocal meson--baryon effective chiral Lagrangian, we show how the introduction of a correlation function representing the finite extent of hadrons regularizes the meson loop integrals and introduces momentum dependence in vertex form factors in a gauge invariant manner. We apply the framework to the calculation of nucleon electromagnetic form factors, unpolarized and polarized parton distributions, as well as transverse momentum dependent distributions and generalized p…
Previous Lattice QCD calculations of nucleon transverse momentum-dependent parton distributions (TMDs) focused on the case of transversely polarized nucleons, and thus did not encompass two leading-twist TMDs associated with longitudinal polarization, namely, the helicity TMD and the worm-gear TMD corresponding to transversely polarized quarks in a longitudinally polarized nucleon. Based on a definition of TMDs via hadronic matrix elements of quark bilocal operators containing staple-shaped gauge connections, TMD observables characterizing the aforementioned two TMDs are evaluated, utilizing a…
We evaluate nucleon four-point functions in the framework of lattice QCD in order to extract the first Mellin moment of double parton distributions (DPDs) in the unpolarized proton. In this first study, we employ an nf = 2 + 1 ensemble with pseudoscalar masses of mpi = 355 MeV and mK = 441 MeV. The results are converted to the scale mu = 2 GeV. Our calculation includes all Wick contractions, and for almost all of them a good statistical signal is obtained. We analyze the dependence of the DPD Mellin moments on the quark flavor and the quark polarization. Furthermore, the validity of frequently…
We briefly discuss the current status of lattice QCD simulations and review selective results on nucleon observables focusing on recent developments in the lattice QCD evaluation of the nucleon form factors and radii, parton distribution functions and their moments, and the neutron electric dipole moment. Nucleon charges and moments of parton distribution functions are presented using simulations generated at physical values of the quark masses, while exploratory studies are performed for the parton distribution functions and the neutron electric dipole moment at heavier than physical value of…
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 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.
We provide a first study of Mellin moments of double parton distributions (DPDs) in the nucleon on the lattice, where we consider several combinations of quark flavors and polarizations. These are accessible through two-current correlations, which can be obtained by evaluating four-point functions. In this context we consider all possible Wick contractions, where for almost all of them sufficiently clear signals are obtained. In the present study, we employ an $n_f = 2 + 1$ CLS ensemble on a $96 \times 32^3$ lattice with lattice spacing $a = 0.0856\ \mathrm{fm}$ and the pseudoscalar masses $m_…
Information about double parton distributions (DPDs) can be obtained by calculating four-point functions on the lattice. We continue our study on the first DPD Mellin moment of the unpolarized proton by considering interference effects w.r.t. the quark flavor. In our simulation we employ an $n_f = 2 + 1$ ensemble with inverse coupling $β= 3.4$, and pseudoscalar masses of $m_π= 355~\mathrm{MeV}$ and $m_K = 441~\mathrm{MeV}$. The results are converted to the $\overline{\mathrm{MS}}$-scheme at the scale $μ= 2~\mathrm{GeV}$. We analyze the dependence of the considered Mellin moments on the quark p…
