[Paper Review] Some nucleon isovector observables from 2+1-flavor domain-wall QCD at the physical pion mass

Shigemi Ohta|arXiv (Cornell University)|Nov 16, 2015

High-Energy Particle Collisions Research4 citations

TL;DR

This study presents a reanalysis of nucleon isovector observables—such as form factors and quark momentum fractions—using 2+1-flavor domain-wall QCD at the physical pion mass. Despite a minor error in handling timelike boundary conditions affecting ~10% of AMA samples, corrections yielded less than 1% change in all observables, confirming the robustness of prior results and enabling future high-statistics studies with improved computational resources.

ABSTRACT

The current status of the LHP and RBC joint calculations of the nucleon isovector form factors and low moments of structure functions with a 2+1-flavor dynamical domain-wall fermion (DWF) lattice-QCD ensemble at the physical pion mass generated by RBC and UKQCD Collaborations with a momentum cutoff of 1.730(4) GeV and lattice spatial extent of 5.476(12) fm is reported. About ten percent of the statistics reported in Lattice 2014 were found with an incorrect boundary condition in time but correcting for it resulted in less than one-percent difference.

Motivation & Objective

• To reanalyze nucleon isovector form factors and structure functions using a 2+1-flavor dynamical domain-wall fermion lattice-QCD ensemble at the physical pion mass.
• To correct for a previously undetected error in timelike boundary condition handling that affected ~10% of AMA samples.
• To assess the impact of this error on key nucleon observables, particularly the axial and vector charges and form factors.
• To enable future high-statistics calculations by recovering lost computing resources and improving low-mode deflation techniques.
• To address persistent lattice QCD challenges such as underestimation of the axial charge and overestimation of quark momentum fractions.

Proposed method

• Utilized a 2+1-flavor dynamical domain-wall fermion lattice-QCD ensemble with a physical pion mass of 139.2(4) MeV and a spatial extent of 5.476(12) fm.
• Applied the AMA (covariant approximation average) method combined with low-mode deflation to enhance statistical precision.
• Employed multiple source-sink separations (8–12 units) to isolate and remove excited-state contamination in matrix elements.
• Used periodic+antiperiodic boundary conditions in the time direction, with a lattice twice as long as spatial directions.
• Identified and corrected a mishandling of the timelike boundary condition in ~10% of AMA samples, which were displaced by half the lattice extent in all directions.
• Recomputed all observables—including form factors and quark momentum fractions—after correction to assess impact.

Experimental results

Research questions

• RQ1 What is the impact of a minor error in timelike boundary condition handling on nucleon isovector observables in domain-wall QCD?
• RQ2 How does the corrected result compare to the previously reported data for the isovector axial and vector charges?
• RQ3 To what extent does the error affect the extraction of low moments of structure functions, such as quark momentum fraction?
• RQ4 Can the corrected results support future high-statistics studies despite prior computing resource losses?
• RQ5 Does the error significantly alter the extracted values of nucleon form factors, including the pseudoscalar and Pauli form factors?

Key findings

• The correction for the timelike boundary condition error resulted in less than 1% change in all nucleon isovector observables, including the axial charge, vector charge, and form factors.
• The isovector axial-to-vector charge ratio $g_A/g_V$ remained within 1% of its original value after correction, confirming consistency with experimental values.
• The Dirac, Pauli, axial, and pseudoscalar form factors showed negligible shifts post-correction, indicating robustness of the results.
• The quark momentum fraction $\langle x \rangle_{u-d}$ was also affected by less than 1%, confirming the stability of the observable under the error.
• The error was found to be minor, comparable to using slightly non-unitary valence quarks, and did not compromise the validity of prior results.
• Despite the error, the corrected results confirm the need for significantly more statistics to draw physically useful conclusions, especially given persistent underestimation of $g_A$ in lattice QCD.