Lanczos algorithm for lattice QCD matrix elements

TL;DR

This paper extends the Lanczos algorithm-based analysis formalism to extract lattice QCD matrix elements from three-point functions, offering faster convergence, reduced statistical fitting, and improved error bounds demonstrated through mock and real data.

Contribution

It introduces a novel extension of the Lanczos formalism for matrix elements, including spurious state filtering and Hermitian subspace restriction, enhancing analysis efficiency and accuracy.

Findings

Faster convergence of matrix element extraction compared to traditional methods

Effective filtering of spurious eigenvalues improves result reliability

Successful application to mock data and nucleon scalar matrix elements

Abstract

Recent work found that an analysis formalism based on the Lanczos algorithm allows energy levels to be extracted from Euclidean correlation functions with faster ground-state convergence than effective masses, convergent estimators for multiple states from a single correlator, and two-sided error bounds. After filtering out spurious eigenvalues and using outlier-robust estimators within a nested bootstrap framework, Lanczos estimators behave more like multi-state fit results than effective masses -- but without involving statistical fitting. We extend this formalism to the determination of matrix elements from three-point correlation functions and provide a physical picture of "spurious state filtering" involving restriction to a Hermitian subspace. We demonstrate similar advantages for matrix elements as for spectroscopy through example applications to noiseless mock-data and (bare) forward matrix elements of the strange scalar current between both ground and excited states with the quantum numbers of the nucleon.