Detailed analysis of excited-state systematics in a lattice QCD calculation of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>g</mml:mi><mml:mi>A</mml:mi></mml:msub></mml:math>
Jin-Chen He, David Brantley, Chia Cheng Chang, I. L. Chernyshev, Evan Berkowitz, Dean Howarth, Christopher Körber, Aaron S. Meyer, Henry Monge-Camacho, Enrico Rinaldi, Chris Bouchard, M. A. Clark, Arjun Singh Gambhir, Christopher Monahan, Amy Nicholson, Pavlos Vranas, André Walker-Loud
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 $\ensuremath{\gtrsim}1$ 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 multistate 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.