Finite volume effects and quark mass dependence of the N(1535) and N(1650)

TL;DR

This paper investigates how finite volume effects influence the extraction of resonance properties, specifically for N(1535) and N(1650), by extrapolating scattering amplitudes to unphysical quark masses using a unitarized chiral approach.

Contribution

It introduces a method to analyze the quark mass dependence of resonances in finite volumes, accounting for coupled channels and threshold effects, aiding lattice QCD studies.

Findings

Pole movements of N(1535) and N(1650) are complex with changing quark masses.

Strongly coupled thresholds cause avoided level crossings similar to narrow resonances.

Predicted level spectra for typical lattice setups and discussed extraction methods.

Abstract

For resonances decaying in a finite volume, the simple identification of state and eigenvalue is lost. The extraction of the scattering amplitude is a major challenge as we demonstrate by extrapolating the physical S_{11} amplitude of pion-nucleon scattering to the finite volume and unphysical quark masses, using a unitarized chiral framework including all next-to-leading order contact terms. We show that the pole movement of the resonances N(1535)1/2^- and N(1650)1/2^- with varying quark masses is non-trivial. In addition, there are several strongly coupled S-wave thresholds that induce a similar avoided level crossing as narrow resonances. The level spectrum is predicted for two typical lattice setups, and ways to extract the amplitude from upcoming lattice data are discussed.