Detailed analysis of excited state systematics in a lattice QCD calculation of $g_A$

TL;DR

This study proposes a cost-effective multi-state analysis method at short to medium time separations in lattice QCD to better control excited state contamination in calculations of the nucleon axial charge, $g_A$, demonstrating improved accuracy over traditional long-time approaches.

Contribution

It introduces a global multi-state analysis strategy that enhances the control of excited state systematic uncertainties in lattice QCD calculations of $g_A$, especially at shorter time separations.

Findings

Excited state contamination reduces to 1% at ~1 fm for Feynman-Hellmann functions.

Standard three-point functions require >2 fm to suppress excited states below 1%.

Global analysis yields stable ground state parameters regardless of model variations.

Abstract

Excited state contamination remains one of the most challenging sources of systematic uncertainty to control in lattice QCD calculations of nucleon matrix elements and form factors: early time separations are contaminated by excited states and late times suffer from an exponentially bad signal-to-noise problem. High-statistics calculations at large time separations $\gtrsim1$ fm are commonly used to combat these issues. In this work, focusing on $g_A$, we explore the alternative strategy of utilizing a large number of relatively low-statistics calculations at short to medium time separations (0.2--1 fm), combined with a multi-state analysis. On an ensemble with a pion mass of approximately 310 MeV and a lattice spacing of approximately 0.09 fm, we find this provides a more robust and economical method of quantifying and controlling the excited state systematic uncertainty. A quantitative separation of various types of excited states enables the identification of the transition matrix elements as the dominant contamination. The excited state contamination of the Feynman-Hellmann correlation function is found to reduce to the 1% level at approximately 1 fm while for the more standard three-point functions, this does not occur until after 2 fm. Critical to our findings is the use of a global minimization, rather than fixing the spectrum from the two-point functions and using them as input to the three-point analysis. We find that the ground state parameters determined in such a global analysis are stable against variations in the excited state model, the number of excited states, and the truncation of early-time or late-time numerical data.