A coupled-channel system with anomalous thresholds and unitarity

TL;DR

This paper investigates the effects of anomalous thresholds in a coupled-channel system with charm and light mesons, using chiral Lagrangian and lattice QCD data to analyze phase shifts as pion mass varies.

Contribution

It introduces a detailed analysis of anomalous thresholds in a coupled-channel system with charm mesons, illustrating their impact through pion mass variation using chiral Lagrangian and lattice QCD inputs.

Findings

Anomalous thresholds significantly affect phase shifts near 145 MeV pion mass.

No anomalous thresholds are observed at 150 MeV pion mass.

Variation in pion mass can induce dramatic changes in scattering behavior.

Abstract

We consider the isospin one-half example system, with $D \,\pi , D\,\eta, D_s \bar K, D^* \pi , D^*\eta, D^*\bar K$ coupled channels in the $J^P = 1^-$ partial wave, chosen such that various phenomena that come with the opening of an anomalous threshold can be illustrated in a step-wise procedure by a suitable variation of up, down and strange quark masses. We use a set of LEC in the chiral Lagrangian that were adjusted to a large set of Lattice QCD results. The six phase shifts and inelasticity parameters are presented for various choices of the pion mass. For a pion mass of 150 MeV there are no anomalous thresholds encountered. The small change from 150 MeV to 145 MeV pion mass causes a dramatic impact of the anomalous threshold on the phase shifts.