On the computation of hadron-to-hadron transition matrix elements in lattice QCD

TL;DR

This paper presents a method using the Generalized Eigenvalue Problem (GEVP) to accurately compute hadron-to-hadron transition matrix elements in lattice QCD, improving convergence and applicability to excited states.

Contribution

The paper introduces GEVP-based estimators for transition matrix elements that converge rapidly and are effective for both ground and excited states in lattice QCD calculations.

Findings

GEVP estimators show rapid convergence with Euclidean time.

Method works well for B*B pi-coupling in quenched approximation.

Compared favorably to standard ratio and summed ratio methods.

Abstract

We discuss the accurate determination of matrix elements < f| h_w | i > where neither |i> nor |f> is the vacuum state and h_w is some operator. Using solutions of the Generalized Eigenvalue Problem (GEVP) we construct estimators for matrix elements which converge rapidly as a function of the Euclidean time separations involved. |i> and |f> may be either the ground state in a given hadron channel or an excited state. Apart from a model calculation, the estimators are demonstrated to work well for the computation of the B*B pi-coupling in the quenched approximation. They are also compared to a standard ratio as well as to the "summed ratio method" of [1,2,3]. In the model, we also illustrate the ordinary use of the GEVP for energy levels.