$K_1/K^{*}$ enhancement in heavy-ion collisions and the restoration of chiral symmetry

We extend the recent study of $K_1/K^{*}$ enhancement as a signature of chiral symmetry restoration in heavy ion collisions at the CERN Large Hadron Collider via the kinetic approach to include the effects due to nonunity hadron fugacities during the evolution of produced hadronic matter and the temperature-dependent $K_1$ mass. Although including nonunity pion and kaon fugacities reduces slightly the $K_1/K^{*}$ enhancement found in previous study due to chiral symmetry restoration, adding temperature-dependent $K_1$ mass leads to a substantial further reduction of the $K_1/K^{*}$ enhancement. However, the final $K_1/K^{*}$ ratio still shows a factor of 2.4 and 1.3 enhancement, respectively, in peripheral and midcentral collisions compared to the case without chiral symmetry restoration, confirming its use as a good signature for chiral symmetry restoration in the hot dense matter produced in relativistic heavy ion collisions.

Figure 1

Temperature dependence of $K_1$ mass. Solid line is from the QCD sum rule calculations of Ref. [5], while dotted line is the one assumed in Ref. [8] with $T_C=156$ MeV.

Figure 2

Isospin averaged cross sections for $K_1\pi \to K\pi$ (a), $K_1\pi \to K^{*}\rho$ (b), $K_1\rho \to K\rho$ (c), and $K_1\rho \to K^{*}\pi$ (d) as functions of center-of-mass energy $\sqrt{s}$ with $\sqrt{s_0}$ denoting the threshold of a reaction and temperature.

Figure 3

Temperature dependence of thermal averaged cross sections $\langle \sigma v\rangle$ for the reactions $K_1\pi \to K\pi$ (dotted line), $K_1\pi \to K^{*}\rho$ (solid line), $K_1\rho \to K\rho$ (dash-dash-dot-dotted line), $K_1\rho \to K^{*}\pi$ (dash-dot-dotted line), and thermal averaged decay widths $\langle \mathrm{\Gamma }\rangle$ of $K_1\to K\rho$ (dash-dash-dotted line) and $K_1\to K^{*}\pi$ (dash-dotted line).

Figure 4

Temperature dependence of pion (solid line), kaon (dotted line), and nucleon (dash-dotted line) fugacities as well as the volume ratio of hadronic matter (solid line in the inset).

Figure 5

The yield ratio $K_1/K^{*}$ in $\mathrm{Pb}+\mathrm{Pb}$ collisions at $\sqrt{s_{NN}}=5.02$ TeV at three centralities of 0–5%, 40–50%, and 70–80% for various scenarios.