The role of strangeness in chiral and $U(1)_A$ restoration

TL;DR

This paper investigates the role of strangeness in the restoration of chiral and $U(1)_A$ symmetries in QCD, using Ward identities, lattice data, and Unitarized Chiral Perturbation Theory to analyze susceptibilities and meson degenerations.

Contribution

It introduces a novel analysis of scalar and pseudoscalar susceptibilities involving strangeness, highlighting the significance of the $K_0^*(700)$ meson and the $m_l/m_s$ ratio in symmetry restoration.

Findings

$ ext{chi}_S^ ext{kappa}$ peaks above the chiral transition.

Degeneration of $ ext{chi}_S^ ext{kappa}$ with $ ext{chi}_P^K$ near transition.

Strangeness influences $U(1)_A$ restoration and helps reconcile lattice results.

Abstract

We use recently derived Ward identities and lattice data for the light- and strange-quark condensates to reconstruct the scalar and pseudoscalar susceptibilities ($\chi_S^\kappa$, $\chi_P^K$) in the isospin 1/2 channel. We show that $\chi_S^\kappa$ develops a maximum above the QCD chiral transition, after which it degenerates with $\chi_P^K$. We also obtain $\chi_S^\kappa$ within Unitarized Chiral Perturbation Theory (UChPT) at finite temperature, when it is saturated with the $K_0^*(700)$ (or $\kappa$) meson, the dominant lowest-energy state in the isospin 1/2 scalar channel of $\pi K$ scattering. Such UChPT result reproduces the expected peak structure, revealing the importance of thermal interactions, and makes it possible to examine the $\chi_S^\kappa$ dependence on the light- and strange-quark masses. A consistent picture emerges controlled by the $m_l/m_s$ ratio that allows one studying $K-\kappa$ degeneration in the chiral, two-flavor and $SU(3)$ limits. These results provide an alternative sign for $O(4)\times U(1)_A$ restoration that can be explored in lattice simulations and highlight the role of strangeness, which regulated by the strange-quark condensate helps to reconcile the current tension among lattice results regarding $U(1)_A$ restoration.