Moments of nucleon generalized parton distributions from lattice QCD

TL;DR

This study computes the lower moments of nucleon generalized parton distributions using two-flavor twisted-mass lattice QCD across three lattice spacings and two volumes, with pion masses from 260 to 470 MeV. It non-perturbatively renormalizes the one-derivative vector and axial-vector operators and performs continuum and chiral extrapolations to connect lattice results to phenomenology, including Ji's sum rule for quark angular momentum. The results show small finite-volume and discretization effects for isovector quantities, and the chiral-extrapolated isovector moments tend to lie higher than experimental values, while the isoscalar spin decomposition indicates a sizable u-quark spin and a negligible d-quark spin when disconnected contributions are neglected. Overall, the work demonstrates consistency with other discretizations and provides a framework for refining nucleon spin studies by incorporating disconnected diagrams and improving chiral dynamics. The findings highlight both the progress and the remaining challenges in linking lattice GPD moments to the physical nucleon structure.

Abstract

We present results on the lower moments of the nucleon generalized parton distri butions within lattice QCD using two dynamical flavors of degenerate twisted mass fermions. Our simulations are performed on lattices with three different values of the lattice spacings, namely $a=0.089$ fm, $a=0.070$ fm and $a=0.056$ fm, allowing the investigation of cut-off effects. The volume dependence is examined using simulations on two lattices of spatial length $L=2.1$ fm and $L=2.8$ fm. The simulations span pion masses in the range of 260-470 MeV. Our results are renormalized non-perturbatively and the values are given in the $\bar{\rm MS}$ scheme at a scale $ μ=2$ GeV. They are chirally extrapolated to the physical point in order to compare with experiment. The consequences of these results on the spin carried by the quarks in the nucleon are investigated.

Figures (15)

• Figure 1: "Handbag" diagram.
• Figure 2: Connected nucleon three-point function.
• Figure 3: Ratios for the one derivative vector (left) and axial vector (right) operator for a few exemplary choices of the momentum. The solid lines with the bands indicate the fitted plateau values with their jackknife errors. From top to bottom the momentum takes values $\vec{p}=(0,0,0); (0,1,0), (1,0,0)$ and $(1,1,0)$.
• Figure 4: $\langle x\rangle_{u-d}$ and $\frac{3}{2}\langle x\rangle_{\Delta u-\Delta d}$ using twisted mass fermions (this work), $N_F=2$ clover fermions Pleiter:2011gw (preliminary), hybrid Bratt:2010jn and DWF Aoki:2010xg.
• Figure 5: Left panel: The isovector GFFs $A_{20}$ and $B_{20}$ for pion mass $\sim 300$ MeV for a lattice of spatial length $L=2.1$ fm and $L=2.8$ fm. Right panel: The axial-vector GFFs $\tilde{A}_{20}$ and $\tilde{B}_{20}$ for $L=2.1$ fm and $L=2.8$ fm.