A coupled-channel system with anomalous thresholds and unitarity

Abstract

We consider the isospin one-half example system, with $D\pi ,D\eta ,D_s\bar{K},D^{\ast }\pi ,D^{\ast }\eta ,D^{\ast }\bar{K}$ 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.

Comments: 11 pages, 4 figures