The elastic $I=3\mathrm{/}2$ $p$-wave nucleon-pion scattering amplitude and the $\mathrm{\Delta }(1232)$ resonance from $N_{\mathrm{f}}=2+1$ 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 $I=3\mathrm{/}2$, $p$-wave nucleon-pion amplitude on a single ensemble of $N_{\mathrm{f}}=2+1$ Wilson-clover fermions with $m_{\pi }=280\mathrm{M}\mathrm{e}\mathrm{V}$ and $m_K=460\mathrm{M}\mathrm{e}\mathrm{V}$. At these quark masses, the $\mathrm{\Delta }(1232)$ resonance pole is found close to the $N-\pi$ threshold and a Breit-Wigner fit to the amplitude gives $g^{$\mathrm{B}\mathrm{W}$}_{\Delta N\pi}=19.0(4.7)$ in agreement with phenomenological determinations.