Quasi-degenerate baryon energy states, the Feynman--Hellmann theorem and transition matrix elements

TL;DR

This paper introduces a Feynman-Hellmann theorem-based method in lattice QCD that simplifies the calculation of matrix elements by using only two-point correlation functions, applicable to both degenerate and quasi-degenerate states.

Contribution

It presents a novel formalism leveraging the Feynman-Hellmann theorem to compute matrix elements in lattice QCD more efficiently, especially for transition states.

Findings

Numerical results for Sigma to Nucleon vector transition matrix element.

Method reduces computational complexity by avoiding three-point functions.

Applicable to both degenerate and quasi-degenerate energy states.

Abstract

The standard method for determining matrix elements in lattice QCD requires the computation of three-point correlation functions. This has the disadvantage of requiring two large time separations: one between the hadron source and operator and the other from the operator to the hadron sink. Here we consider an alternative formalism, based on the Dyson expansion leading to the Feynman-Hellmann theorem, which only requires the computation of two-point correlation functions. Both the cases of degenerate energy levels and quasi-degenerate energy levels which correspond to diagonal and transition matrix elements respectively can be considered in this formalism. As an example numerical results for the Sigma to Nucleon vector transition matrix element are presented.