Nucleon form factors and structure functions with N_f=2+1 dynamical domain wall fermions

TL;DR

This paper presents lattice QCD calculations of nucleon form factors and structure functions using (2+1) dynamical domain-wall fermions, revealing finite-size effects and providing results close to experimental values.

Contribution

First lattice QCD study of nucleon form factors and structure functions with (2+1) dynamical domain-wall fermions at multiple pion masses, analyzing finite-size effects and form factor radii.

Findings

Axial charge g_A shows large finite-size effects at lightest pion mass.

Form factor radii are 20-30% smaller than experimental values.

The ratio of quark momentum to helicity fractions agrees with experiment.

Abstract

We report isovector form factors and low moments of structure functions of nucleon in numerical lattice quantum chromodynamics (QCD) from the on-going calculations by the RIKEN-BNL-Columbia (RBC) and UKQCD Collaborations with (2+1) dynamical flavors of domain-wall fermion (DWF) quarks. We calculate the matrix elements with four light quark masses, corresponding to pion mass values of m_\pi = 330-670 MeV, while the dynamical strange mass is fixed at a value close to physical, on (2.7 fm)^3 spatial volume. We found that our axial charge, g_A, at the lightest mass exhibits a large deviation from the heavier mass results. This deviation seems to be a finite-size effect as the g_A value scales with a single parameter, m_\pi L, the product of pion mass and linear spatial lattice size. The scaling is also seen in earlier 2-flavor dynamical DWF and Wilson quark calculations. Without this lightest point, the three heavier mass results show only very mild mass dependence and linearly extrapolate to g_A=1.16(6). We determined the four form factors, the vector (Dirac), induced tensor (Pauli), axial vector and induced pseudoscalar, at a few finite momentum transfer values as well. At the physical pion mass the form-factors root mean square radii determined from the momentum-transfer dependence %of the form factors are 20-30% smaller than the corresonding experiments. The ratio of the isovector quark momentum to helicity fractions, < x>_{u-d}/< x>_{\Delta u - \Delta d} is in agreement with experiment without much mass dependence including the lightest point. We obtain an estimate, 0.81(2), by a constant fit. Although the individual momentum and helicity fractions are yet to be renormalized, they show encouraging trend toward experiment.