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The nucleon axial charge in full lattice QCD

LHPC collaboration, R. G. Edwards, G. T. Fleming, Ph. Hagler, J. W. Negele, K. Orginos, A. Pochinsky, D. B. Renner, D. G. Richards, W. Schroers

TL;DR

Problem: determine the nucleon axial charge $g_A$ from first principles in full QCD, including chiral and finite-volume effects. Method: a hybrid lattice QCD calculation using domain-wall valence quarks on Asqtad staggered sea quarks, enabling simulations at $m_\pi$ down to $354\ \mathrm{MeV}$ in volumes up to $(3.5\mathrm{fm})^3$, with nonperturbative renormalization via the five-dimensional conserved current and a finite-volume $\chi$PT-based constrained fit. Findings: finite-volume effects are small; the constrained fit yields $g_A(m_\pi=140\mathrm{MeV}) = 1.212 \pm 0.084$, consistent with experiment within $7\%$; results align with other unquenched lattice calculations and demonstrate robust control over systematics. Significance: this work validates lattice QCD approaches to hadron structure and provides a framework for extending to lighter masses and more complete spin-structure studies, including disconnected diagrams.

Abstract

The nucleon axial charge is calculated as a function of the pion mass in full QCD. Using domain wall valence quarks and improved staggered sea quarks, we present the first calculation with pion masses as light as 354 MeV and volumes as large as (3.5 fm)^3. We show that finite volume effects are small for our volumes and that a constrained fit based on finite volume chiral perturbation theory agrees with experiment within 7% statistical errors.

The nucleon axial charge in full lattice QCD

TL;DR

Problem: determine the nucleon axial charge from first principles in full QCD, including chiral and finite-volume effects. Method: a hybrid lattice QCD calculation using domain-wall valence quarks on Asqtad staggered sea quarks, enabling simulations at down to in volumes up to , with nonperturbative renormalization via the five-dimensional conserved current and a finite-volume PT-based constrained fit. Findings: finite-volume effects are small; the constrained fit yields , consistent with experiment within ; results align with other unquenched lattice calculations and demonstrate robust control over systematics. Significance: this work validates lattice QCD approaches to hadron structure and provides a framework for extending to lighter masses and more complete spin-structure studies, including disconnected diagrams.

Abstract

The nucleon axial charge is calculated as a function of the pion mass in full QCD. Using domain wall valence quarks and improved staggered sea quarks, we present the first calculation with pion masses as light as 354 MeV and volumes as large as (3.5 fm)^3. We show that finite volume effects are small for our volumes and that a constrained fit based on finite volume chiral perturbation theory agrees with experiment within 7% statistical errors.

Paper Structure

This paper contains 4 sections, 2 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. Lattice Calculation in the Chiral Regime
  3. Lattice Results
  4. Conclusions

Figures (2)

  • Figure 1: Nucleon axial charge $g_A$ as a function of the pion mass. Lattice data are denoted by squares (smaller volume) and a triangle (larger volume), the lowest smaller volume point is displaced slightly to the right for clarity, and experiment is denoted by the circle. The heavy solid line and shaded error band show the $\chi$PT fit to the finite volume data evaluated in the infinite volume limit, and the lines below it show the behavior of this chiral fit in boxes of finite volume $L^3$, as $L$ is reduced to 3.5, 2.5, and 1.6 fm respectively.
  • Figure 2: Comparison of all full QCD calculations of $g_A$, as described in the text. The solid line and error band denote the infinite volume $\chi$PT fit of Fig. 1 and its continuation to higher masses is indicated by the dotted line.