I=3/2 nucleon-pion scattering and the Delta(1232) resonance on 2+1 flavor CLS ensembles using the stochastic LapH method

TL;DR

This study computes nucleon-pion scattering phase shifts and Delta(1232) resonance parameters using lattice QCD with 2+1 flavors, revealing how resonance mass varies with pion mass and employing the stochastic LapH method for improved calculations.

Contribution

The paper presents the first lattice QCD determination of the Delta(1232) resonance parameters on 2+1 flavor ensembles using the stochastic LapH method, including partial wave mixing analysis.

Findings

Resonance mass increases as pion mass decreases.

Resonance approaches the Nπ threshold at lighter quark masses.

Agreement with experimental resonance behavior.

Abstract

Calculations of the elastic $I=\frac{3}{2}$ nucleon-pion scattering phase shifts on two lattice QCD ensembles with $m_\pi=200\mathrm{MeV}$ and $280\mathrm{MeV}$ are presented. The ensembles both employ $N_\mathrm{f} = 2+1$ Wilson clover fermions. We determine the $\Delta(1232)$ resonance parameters from a finite volume scattering analysis. In one study the single partial wave simplification is employed to compute the $p$-wave amplitude while in the other we treat the partial wave mixing between $s$- and $p$-wave contributions. Fitting our data to a Breit-Wigner resonance model we find $m_\Delta/m_\pi = 7.13(9)$ and $4.75(5)$ on the two ensembles respectively, showing that for a lighter quark mass the resonance mass moves from near the $N\pi$ threshold to near the $N\pi\pi$ threshold, in agreement with experiment.