Detailed analysis of excited state systematics in a lattice QCD calculation of \(g_A\)

• Published in: arXiv.org 2022-06
• Main Authors: He, Jinchen, Brantley, David A, Chia Cheng Chang, Chernyshev, Ivan, Berkowitz, Evan, Howarth, Dean, Körber, Christopher, Meyer, Aaron S, Monge-Camacho, Henry, Rinaldi, Enrico, Bouchard, Chris, Clark, M A, Arjun Singh Gambhir, Monahan, Christopher J, Nicholson, Amy, Vranas, Pavlos, Walker-Loud, André
• Format: Article
• Language: English
• Subjects: Contamination; Excitation; Form factors; Pions; Quantum chromodynamics; Robustness (mathematics); Uncertainty
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2104.05226

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.