Low-energy pion-nucleon scattering and the Δ resonance in lattice QCD

Constantia Alexandrou,Gumaro Rendon,Stefan Meinel,Sergey Syritsyn,John W Negele,Srijit Paul,Giannis Koutsou,Giorgio Silvi,Andrew Pochinsky,Luka Leskovec,Marcus Petschlies,Stefan Krieg,R Beck,U Thoma,A Thiel,Y Wunderlich

doi:10.1051/epjconf/202024102006

Abstract

We report on our investigation of low-energy pion-nucleon scattering from lattice QCD with Wilson type fermions. Our focus is on the isospin I = 3/2 channel, which couples to the Delta resonance. We discuss our calculations aiming at the extraction of the Delta resonance mass, width and effective coupling at pion mass 250 MeV, using the Lüscher finite-volume method to extract the phase shift δJ=3/2,l=1.

Highlights

In this proceedings contribution we give an account of our extraction of low-energy pion-nucleon scattering properties in the channel I JP = 3+ 2, which features the Δ resonance, from lattice QCD data at pion mass 250MeV
We report on our investigation of low-energy pion-nucleon scattering from lattice QCD with Wilsontype fermions
Our focus is on the isospin I = 3/2 channel, which couples to the Delta resonance

Summary

Introduction

We will focus on the well-known parametrization in terms of Breit-Wigner parameters with resonance mass mΔ and (energy-dependent) decay width ΓΔ−πN(s) For the latter we will use the parametrization in leading-order effective theory of pions and nucleons, which defines the effective coupling gΔ−πN. The former gives rise to the transition amplitude and cross-section for resonant pion-photoproduction off the nucleon, which can be compared directly to experiment. The pion-nucleon elastic scattering in the Δ channel has been the subject of several lattice QCD calculations Among those are the analysis using the Michael/McNeile method [15, 16], requiring the lattice Hamiltonian to exhibit a Δ-like state perturbatively close and below the pion-nucleon threshold and determining the resonance coupling based on the leading-order effective pion-nucleon interaction. We discuss the first steps of our analysis of pionnucleon scattering in the Δ channel [20] from lattice QCD focusing on the irreps with leading p-wave contribution and neglecting partial wave mixing

Calculation of Lattice Correlation functions

Lattice spectrum determination and Lüscher analysis

Scattering phase shift and resonance parameters

Summary and outlook