Elastic Nucleon-Pion scattering amplitudes in the $\Delta$ channel at physical pion mass from Lattice QCD

TL;DR

This paper uses lattice QCD to study pion-nucleon elastic scattering at physical quark masses, focusing on the $ ext{Delta}$ resonance in the $J^P=3/2^+$ channel, providing insights into resonance properties and scattering lengths.

Contribution

It presents a novel lattice QCD analysis of pion-nucleon scattering in the $ ext{Delta}$ channel at physical quark masses, including finite volume effects and partial wave mixing.

Findings

Estimated the $ ext{Delta}$ resonance pole position.

Determined the $S$-wave isospin-3/2 scattering length.

Analyzed scattering amplitudes in multiple frames.

Abstract

We present an investigation of pion-nucleon elastic scattering in the $I\,(J^P) = \frac{3}{2}\,(\frac{3}{2}^+)$ channel using lattice QCD with degenerate up and down, strange and charm quarks with masses tuned to their physical values. We use an ensemble of twisted mass fermions with box size $L = 5.1\,\mathrm{fm}$ and lattice spacing $a = 0.08\,\mathrm{fm}$ and we consider the $\pi N$ system in rest and moving frames up to total momentum $\vec{P}^2 = 3\,(2\pi/L)^2$ = 0.17 GeV$^2$. We take into account the finite volume symmetries and $S$- and $P$-wave mixing, and use the L\"uscher formalism to simultaneously constrain the $J = 1/2,\,\ell = 0$ and $J = 3/2,\,\ell = 1$ scattering amplitudes. We estimate the $\Delta$ resonance pole in the $P$-wave channel as well as the $S$-wave isospin-3/2 scattering length.