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

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.

Comments: 7 pages, 1 figure, presented at the 37th International Symposium on Lattice Field Theory