The Delta-resonance in a finite volume

TL;DR

This paper develops a method to extract Delta-resonance parameters from lattice QCD data by analyzing the volume dependence of energy levels, including detailed calculations up to third order in a small scale expansion.

Contribution

It provides a finite-volume spectrum calculation for the Delta-resonance using infrared regularization and small scale expansion, facilitating parameter extraction from lattice data.

Findings

Feasibility of extracting Delta parameters from volume dependence.

Calculated spectrum up to O(epsilon^3) in small scale expansion.

Supports lattice QCD studies of unstable resonances.

Abstract

We study the extraction of Delta-resonance parameters from lattice data for small quark masses, corresponding to the case of an unstable Delta. To this end, we calculate the spectrum of the correlator of two Delta-fields in a finite Euclidian box up-to-and-including O(epsilon^3) in the small scale expansion using infrared regularization. On the basis of our numerical study, we argue that the extraction of the parameters of the Delta-resonance (in particular, of the mass and the pion-nucleon-delta coupling constant) from the measured volume dependence of the lowest energy levels should be feasible.