$K^+ N$ elastic scatterings for estimation of in-medium quark condensate with strange quarks

TL;DR

This paper uses chiral perturbation theory to analyze $K^+N$ scattering and estimate the in-medium strange quark condensate, connecting scattering data with fundamental QCD properties in nuclear matter.

Contribution

It constructs and refines kaon-nucleon scattering amplitudes up to next-to-next-to-leading order, including resonance effects, to better estimate the in-medium strange quark condensate.

Findings

Good reproduction of $K^+p$ scattering amplitude by chiral perturbation theory.

Challenges in describing $KN$ amplitude with $I=0$ due to limited data.

Estimated in-medium strange quark condensate via analytic continuation.

Abstract

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 psuedoscalar 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 $P_\mathrm{lab} = 600$ MeV/c for $I=0$ reported in the previous study. The low energy constants are determined by existent $K^+N$ 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.