K + N Elastic Scatterings for Estimation of the In-Medium Quark Condensate with Strange Quarks

We revisit the low-energy K+N elastic scatterings in the context of the in-medium quark condensate with strange quarks. The chiral ward identity connects the in-medium quark condensate to the soft limit value of the pseudoscalar correlation function evaluated in nuclear matter. The in-medium correlation function of the pseudoscalar fields with strangeness describes in-medium kaon propagation and is obtained by kaon-nucleon scattering amplitudes in the low-density approximation. We construct the kaon-nucleon scattering amplitudes in chiral perturbation theory up to the next-to-leading order and add some terms of the next-to-next-to-leading order with the strange quark mass to improve expansion of the strange quark sector. We also consider the effect of a possible broad resonance state around P-lab = 600 MeV/c for I = 0 reported in the previous study. The low-energy constants are determined by existing K+N scattering data. We obtain good reproduction of the K(+)p scattering amplitude by chiral perturbation theory, while the description of the KN amplitude with I = 0 is not so satisfactory due to the lack of low-energy data. Performing analytic continuation of the scattering amplitudes obtained by chiral perturbation theory to the soft limit, we estimate the in-medium strange quark condensate.