The mass of the Delta resonance in a finite volume: fourth-order calculation

TL;DR

This paper presents a fourth-order chiral effective field theory calculation of the Delta resonance's self-energy in a finite volume, providing a detailed parameterization of the energy spectrum relevant for lattice QCD studies.

Contribution

It offers a novel fourth-order calculation of the Delta resonance in finite volume, including explicit parameterization of the energy spectrum with respect to quark mass and box size.

Findings

Finite-volume corrections are significant at small quark masses.

The energy spectrum can be explicitly parameterized in terms of quark mass and box size.

The approach improves understanding of resonance behavior in lattice simulations.

Abstract

We calculate the self-energy of the Delta (1232) resonance in a finite volume, using chiral effective field theory with explicit spin-3/2 fields. The calculations are performed up-to-and-including fourth order in the small scale expansion and yield an explicit parameterization of the energy spectrum of the interacting pion-nucleon pair in a finite box in terms of both the quark mass and the box size L. It is shown that finite-volume corrections can be sizeable at small quark masses.