Symmetry breaking and theπKamplitudes in the unphysical region

Abstract

We apply two different methods of analytic continuation (fixed-$t$ and hyperbolic dispersion relations with discrepancy) to determine the expansion parameters of the $\ensuremath{\pi}K$ amplitudes in the unphysical region near the symmetry point. Part of the available phase-shift data shows inconsistencies with crossing symmetry. The values we obtain for the parameters and for the so-called $\ensuremath{\sigma}$ term are then compared with predictions that we derive from different models of chiral-symmetry breaking.