Low-energy $K^+N$ scattering revisited and in-medium strange quark condensate

The chiral ward identity connects the in-medium quark condensate to the soft limit value of a correlation function of the pseudoscalar fields evaluated in nuclear medium. For the strange quark condensate, one considers the correlation function of the pseudoscalar fields with strangeness. The correlation function describes in-medium propagation of kaons and it is obtained phenomenologically by kaon-nucleon scattering in the low density approximation. We describe the kaon-nucleon scattering amplitude in chiral perturbation theory and its low energy constants are determined by existent $K^{+}N$ scattering data. Performing analytic continuation of the scattering amplitude obtained by chiral perturbation theory, we can take the soft limit of the scattering amplitude. With this amplitude, we evaluate the in-medium strange quark condensate based on hadron phenomenology.