The elastic $I=3/2$ $p$-wave nucleon-pion scattering amplitude and the $\Delta(1232)$ resonance from $N_{\mathrm{f}}=2+1$ lattice QCD

TL;DR

This paper reports the first direct lattice QCD calculation of the nucleon-pion scattering amplitude in the $I=3/2$, $p$-wave channel, determining the $
(1232)$ resonance parameters with results consistent with phenomenology.

Contribution

It provides the first direct lattice QCD determination of meson-baryon resonance parameters from scattering amplitudes, specifically for the $
(1232)$ resonance.

Findings

Resonance pole close to the $N-
$ threshold.

Breit-Wigner fit yields $g^{BW}_{
N
ext{pi}}=19.0(4.7)$.

Results agree with phenomenological determinations.

Abstract

We present the first direct determination of meson-baryon resonance parameters from a scattering amplitude calculated using lattice QCD. In particular, we calculate the elastic $I=3/2$, $p$-wave nucleon-pion amplitude on a single ensemble of $N_{\mathrm{f}}=2+1$ Wilson-clover fermions with $m_{\pi}=280\mathrm{MeV}$ and $m_{K}=460\mathrm{MeV}$. At these quark masses, the $\Delta(1232)$ resonance pole is found close to the $N-\pi$ threshold and a Breit-Wigner fit to the amplitude gives $g^{\mathrm{BW}}_{\Delta N\pi}=19.0(4.7)$ in agreement with phenomenological determinations.