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Excited state contamination remains one of the most challenging sources ofsystematic uncertainty to control in lattice QCD calculations of nucleon matrixelements and form factors: early time separations are contaminated by excitedstates and late times suffer from an exponentially bad signal-to-noise problem.High-statistics calculations at large time separations $\gtrsim1$ fm arecommonly used to combat these issues. In this work, focusing on $g_A$, weexplore the alternative strategy of utilizing a large number of relativelylow-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 ofapproximately 310 MeV and a lattice spacing of approximately 0.09 fm, we findthis provides a more robust and economical method of quantifying andcontrolling the excited state systematic uncertainty. A quantitative separationof various types of excited states enables the identification of the transitionmatrix elements as the dominant contamination. The excited state contaminationof the Feynman-Hellmann correlation function is found to reduce to the 1% levelat approximately 1 fm while for the more standard three-point functions, thisdoes not occur until after 2 fm. Critical to our findings is the use of aglobal minimization, rather than fixing the spectrum from the two-pointfunctions and using them as input to the three-point analysis. We find that theground state parameters determined in such a global analysis are stable againstvariations in the excited state model, the number of excited states, and thetruncation of early-time or late-time numerical data.

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