Moments of generalized parton distributions and quark angular momentum of the nucleon

TL;DR

This work computes the first moments of generalized parton distributions (GPDs) for the nucleon on unquenched lattice configurations with two dynamical Wilson quarks, down to $m_\pi \approx 350$ MeV, and uses covariant baryon chiral perturbation theory to extrapolate to the physical point. By relating Mellin moments of GPDs to generalized form factors $A_{n,2k}(t)$, $B_{n,2k}(t)$, and $C_n(t)$, the authors extract quark angular momentum via Ji's sum rule $J^q = \tfrac12 \int_{-1}^1 dx \, x [H(x,\xi,0) + E(x,\xi,0)] = \tfrac12 [A_{20}(0) + B_{20}(0)]$ and quark spin via $s^q = \tfrac12 \tilde{A}_{10}(0)$. The results yield $J^{u}=0.230(8)$, $J^{d}=-0.004(8)$ and, for the isosinglet combination, $J^{u+d}=0.226(13)$ with $s^{u+d}=0.201(24)$ and $L^{u+d}=0.025(27)$, implying the orbital contribution is near zero. These findings rely on dipole fits for $A_{20}$ and on χPT-based extrapolations for $B_{20}$ and related quantities, highlighting the importance of including disconnected diagrams and approaching lighter pion masses in future work.

Abstract

The internal structure of hadrons is important for a variety of topics, including the hadron form factors, proton spin and spin asymmetry in polarized proton scattering. For a systematic study generalized parton distributions (GPDs) encode important information on hadron structure in the entire impact parameter space. We report on a computation of nucleon GPDs based on simulations with two dynamical non-perturbatively improved Wilson quarks with pion masses down to 350MeV. We present results for the total angular momentum of quarks with chiral extrapolation based on covariant baryon chiral perturbation theory.

Figures (5)

• Figure 1: The isoscalar axial form factor $\tilde{A}_{10}(t)$ for $\beta=5.29$, $\kappa=0.13632$ with dipole fit (left) and the forward values with $\chi$PT fit (right). The open star in the right panel represents the latest experimental value of HERMES.
• Figure 2: Generalized form factors in the isovector channel for $\beta=5.29$, $\kappa=0.13632$ with dipole fit for $A_{20}$ and the dipole mass of $A_{20}$. The open star represents the experimental value of $f_2$ tensor meson mass.
• Figure 3: The forward values of $A_{20}$ in the isoscalar (left) and isovector (right) channel with $\chi$PT fits. The open stars represent the phenomenological values from CTEQ6.
• Figure 4: The forward values of $B_{20}$ extrapolated by $\chi$PT in the isoscalar (left) and isovector (right) channel with $\chi$PT fits.
• Figure 5: Total angular momentum of quark in the nucleon with $\chi$PT fit (left) and spin, orbital angular momentum of quarks (right). The open symbols represent the extrapolated values to the physical pion mass.