Elastic I=3/2 p -wave nucleon-pion scattering amplitude and the Δ(1232) resonance from Nf=2+1 lattice QCD

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 ${m}_{\ensuremath{\pi}}=280\text{ }\text{ }\mathrm{MeV}$ and ${m}_{K}=460\text{ }\text{ }\mathrm{MeV}$. At these quark masses, the $\mathrm{\ensuremath{\Delta}}(1232)$ resonance pole is found close to the $N\ensuremath{-}\ensuremath{\pi}$ threshold and a Breit-Wigner fit to the amplitude gives ${g}_{\mathrm{\ensuremath{\Delta}}N\ensuremath{\pi}}^{\mathrm{BW}}=19.0(4.7)$ in agreement with phenomenologica…