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

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 $K_0^{\ast }(700)$ (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.

arXiv comment9 pages, 4 figures. Version published in Eur.Phys.J.C

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• Gliding down the QCD transition line, from $N_f=2$ till the onset of conformality
• Precision dispersive approaches versus unitarized Chiral Perturbation Theory for the lightest scalar resonances $\sigma /f_0(500)$ and $\kappa /K_0^{\ast }(700)$