Thermodynamics of strange baryon system from coupled-channel analysis and missing states

Abstract: We study the thermodynamics of the strange baryon system using an S-matrix formulation of statistical mechanics. For this purpose, we employ an existing coupled-channel study involving $\bar{K} N$, $\pi \Lambda$, and $\pi \Sigma$ interactions in the $S=-1$ sector. A novel method is proposed to extract an effective phase shift due to the interaction, which can subsequently be used to compute various thermal observables via a relativistic virial expansion. As an application of the calculation scheme, we compute the correlation of the net baryon number with strangeness ($\chi_{BS}$) for an interacting hadron gas. We show that the S-matrix approach, which entails a consistent treatment of resonances and naturally incorporates the additional hyperon states which are not listed by the Particle Data Group, leads to an improved description of the lattice data over the Hadron Resonance Gas model.