Matrix elements of unstable states
V. Bernard, D. Hoja, U.-G. Mei{\ss}ner, A. Rusetsky
TL;DR
This paper develops a systematic framework using non-relativistic effective Lagrangians for calculating resonance matrix elements in lattice QCD, including a generalized L"uscher-Lellouch formula and analytic continuation methods.
Contribution
It introduces a novel systematic approach for resonance matrix element calculations in lattice QCD, extending existing formulas and analyzing the infinite-volume limit.
Findings
Derived a generalized L"uscher-Lellouch formula for resonances
Outlined procedures for analytic continuation into the complex energy plane
Investigated the infinite-volume limit of resonance matrix elements
Abstract
Using the language of non-relativistic effective Lagrangians, we formulate a systematic framework for the calculation of resonance matrix elements in lattice QCD. The generalization of the L\"uscher-Lellouch formula for these matrix elements is derived. We further discuss in detail the procedure of the analytic continuation of the resonance matrix elements into the complex energy plane and investigate the infinite-volume limit.
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