Elastic $\pi-N$ scattering in the $I=3/2$ channel

TL;DR

This study performs the first lattice QCD calculation of $/2$ $$ scattering at the physical pion mass, extracting resonance parameters using phase-shift analysis with multiple momentum frames.

Contribution

It is the first to analyze $/2$ $$ scattering at the physical point using lattice QCD with twisted mass fermions and multiple momentum frames.

Findings

Determined $/2$ $$ phase shifts and resonance parameters.

Performed analysis in multiple moving frames and irreducible representations.

Extracted $$ resonance parameters consistent with experimental values.

Abstract

We present our study of $\pi-N$ scattering in the iso-spin $I=3/2$ channel for the first time at the physical point. The calculation is performed using $N_f=2+1+1$ flavors of twisted mass fermions with clover improvement at physical pion mass. We compute energy levels for the rest frame and moving frames up to a total momentum of $|\vec{P}|=\sqrt{3} \,\frac{2\pi}{L}$, and for all the relevant ireducible representations of the lattice symmetry groups. We perform a phase-shift analysis including $s\,(\ell=0)$ and $p\,(\ell=1)$ wave phase shifts assuming a Breit-Wigner form and determine the parameters of the $\Delta$ resonance.