Moments of Isovector Quark Distributions in Lattice QCD

TL;DR

This paper develops chiral extrapolation formulae for lattice QCD calculations of isovector quark distribution moments, incorporating pion loop effects and $ riangle$ isobar states, aligning with phenomenology and chiral symmetry.

Contribution

It introduces novel chiral extrapolation formulae for lattice moments of unpolarised, helicity, and transversity distributions, including $ riangle$ isobar effects, consistent with chiral and heavy quark limits.

Findings

Extrapolated moments agree with phenomenological values.

First chiral-consistent extrapolation of isovector transversity moments.

Inclusion of $ riangle$ isobar states is crucial for accurate results.

Abstract

We investigate the connection of lattice calculations of moments of isovector parton distributions to the physical regime through extrapolations in the quark mass. We consider the one pion loop renormalisation of the nucleon matrix elements of the corresponding operators and thereby develop formulae with which to extrapolate the moments of the unpolarised, helicity and transversity distributions. These formulae are consistent with chiral perturbation theory in the chiral limit and incorporate the correct heavy quark limits. In the polarised cases, the inclusion of intermediate states involving the $\Delta$ isobar is found to be very important. The results of our extrapolations are in general agreement with the phenomenological values of these moments where they are known, and for the first time we perform an extrapolation of the low moments of the isovector transversity distribution which is consistent with chiral symmetry.