Model prediction for temperature dependence of meson pole masses from lattice QCD results on meson screening masses

TL;DR

This paper develops a temperature-dependent effective model based on lattice QCD data to predict meson pole masses from screening masses, successfully reproducing lattice results and aligning with experimental data for the $ ext{η'}$ meson.

Contribution

The paper introduces a temperature-dependent coupling in the PNJL model, enabling accurate predictions of meson pole masses from screening masses using lattice QCD data.

Findings

Model reproduces lattice QCD screening mass data for mesons.

Predicts meson pole masses consistent with experimental measurements.

Identifies approximate relations between screening and pole masses for scalar and pseudoscalar mesons.

Abstract

We propose a practical effective model by introducing temperature ($T$) dependence to the coupling strengths of four-quark and six-quark Kobayashi-Maskawa-'t Hooft interactions in the 2+1 flavor Polyakov-loop extended Nambu-Jona-Lasinio model. The $T$ dependence is determined from LQCD data on the renormalized chiral condensate around the pseudocritical temperature $T_c^{\chi}$ of chiral crossover and the screening-mass difference between $\pi$ and $a_0$ mesons in $T > 1.1T_c^\chi$ where only the $U(1)_{\rm A}$-symmetry breaking survives. The model well reproduces LQCD data on screening masses $M_{\xi}^{\rm scr}(T)$ for both scalar and pseudoscalar mesons, particularly in $T \ge T_c^{\chi}$. Using this effective model, we predict meson pole masses $M_{\xi}^{\rm pole}(T)$ for scalar and pseudoscalar mesons. For $\eta'$ meson, the prediction is consistent with the experimental value at finite $T$ measured in heavy-ion collisions. We point out that the relation $M_{\xi}^{\rm scr}(T)-M_{\xi}^{\rm pole}(T) \approx M_{\xi'}^{\rm scr}(T)-M_{\xi'}^{\rm pole}(T)$ is pretty good when $\xi$ and $\xi'$ are scalar mesons, and show that the relation $M_{\xi}^{\rm scr}(T)/M_{\xi'}^{\rm scr}(T) \approx M_{\xi}^{\rm pole}(T)/M_{\xi'}^{\rm pole}(T)$ is well satisfied within 20% error when $\xi$ and $\xi'$ are pseudoscalar mesons and also when $\xi$ and $\xi'$ are scalar mesons.