Chiral extrapolation of lattice moments of proton quark distributions

TL;DR

A simple extrapolation formula for the moments of the nonsinglet quark distribution u-d, as a function of quark mass, is proposed, which embodies the general constraints imposed by the chiral symmetry of QCD.

Abstract

We present the resolution of a long-standing discrepancy between the moments of parton distributions calculated from lattice QCD and their experimental values. We propose a simple extrapolation formula for the moments of the nonsinglet quark distribution u-d, as a function of quark mass, which embodies the general constraints imposed by the chiral symmetry of QCD. The inclusion of the leading nonanalytic behavior leads to an excellent description of both the lattice data and the experimental values of the moments.

Figures (1)

• Figure 1: Moments of the $u - d$ quark distribution. The straight (long-dashed) lines are linear fits to the data, while the curves have the correct LNA behavior in the chiral limit. For each moment, the best fit to the lattice data using Eq.(\ref{['eq:fit']}) is shown by the solid curve (with $\mu=550$ MeV), while the inner envelope about this represents the statistical errors in the data. The best fit parameters are: $a_1=0.1427$, $b_1=-0.0624\,{\rm GeV}^{-2}$, $a_2=0.0459$, $b_2=-0.0245\,{\rm GeV}^{-2}$, $a_3=0.0184$, $b_3=-0.00666\,{\rm GeV}^{-2}$, which give a $\chi^2$ per degree of freedom of 0.98, 0.60 and 0.60 for $n=1$, 2 and 3, respectively. The effect of the uncertainty in the parameter $\mu$ is illustrated by the outer lower (upper) short-dashed curves, which correspond to $\mu=450$ (650) MeV. The small squares are the meson cloud model results BOROS, and the dashed curve through them best fits using Eq.(\ref{['eq:fit']}). The star represents the phenomenological values taken from NLO fits PARAMS in the $\overline{\rm MS}$ scheme.