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

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.