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

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 $g_{\Delta N\pi }^{\mathrm{BW}}=19.0(4.7)$ in agreement with phenomenological determinations.

Comments: 7 pages, 2 figures. Agrees with published version, one additional phase shift point and clarification of different coupling conventions