Nucleon Generalized Parton Distributions from Full Lattice QCD

TL;DR

This work presents the first comprehensive full-lattice QCD study of the lowest three moments of unpolarized and polarized nucleon GPDs in the chiral regime, using a $N_f=2+1$ hybrid action with pion masses as low as $m_\pi\approx350$ MeV. It combines domain-wall valence quarks with improved staggered sea, analyzes generalized form factors $A_{20}$, $B_{20}$, $C_{20}$ and their polarized analogs via chiral extrapolations, and employs covariant and heavy-baryon chiral perturbation theory to explore the $(m_\pi,t)$-dependence and extract the quark angular momentum contributions $J^q$ and orbital angular momenta $L^q$. The study reveals a strong, nontrivial correlation between the transverse size of the nucleon and the momentum fraction carried by quarks, and finds that $J^{u+d}$ is about $0.21$–$0.26$ at the physical point with $L^{u+d}$ consistent with zero due to cancellations between spin and orbital components. These results, consistent with phenomenology in many channels, demonstrate the viability of covariant ChPT extrapolations and provide new quantitative insights into the spin and transverse structure of the nucleon from first-principles QCD.

Abstract

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.

Figures (7)

• Figure 1: GPDs as part of a scattering amplitude.
• Figure 2: Connected (a) and disconnected (b) diagrams in unquenched lattice QCD with an operator insertion at $\tau$ and finite momentum transfer $\Delta$.
• Figure 3: Residual quark mass as a function of $L_5$ for the two samples (heavy and light) of $25$ configurations each.
• Figure 4: Dependence of the pion mass on the extent of the fifth dimension $L_5$ for heavy quarks.
• Figure 5: Dependence of the pion mass on the extent of the fifth dimension $L_5$ for light quarks.