Temperature Dependence of the Masses of Various Meson States: A Comparative Study in SU(3) and SU(4) extended Linear-Sigma Model

TL;DR

The paper addresses how meson masses and the chiral transition evolve with temperature in QCD-like matter, emphasizing the role of charm by comparing SU(3) and SU(4) extensions of the extended Linear Sigma Model (eLSM). It employs a mean-field, Polyakov-loop-extended formalism to compute in-medium masses from second derivatives of the grand potential, with parameters fitted to experimental meson data. The key finding is that SU(4) better reproduces observed masses, and that while individual meson masses show state-specific temperature dependence, they dissolve in a similar temperature window, with quarkonium largely unaffected by temperature; the U(1)_A anomaly and the F(T) factor modulate the pseudo-critical temperature differently between SU(3) and SU(4). These results have implications for interpreting hadron-quark transitions in heavy-ion collisions and for refining effective QCD models with heavy flavors.

Abstract

In the extended Linear-Sigma Model (eLSM), the chiral phase structure of meson states, including pseudoscalars ($J^{pc}=0^{-+}$), scalars ($J^{pc}=0^{++}$), vectors ($J^{pc}=1^{--}$), and axial-vectors ($J^{pc}=1^{++}$), is investigated with the mean-field approximation. A systematic comparison between SU(3) and SU(4) configurations is provided. It has been found that the estimations of meson masses derived from SU(4) eLSM are more congruent with experimental values than those derived from SU(3) eLSM. Consequently, we conclude that an increase in quark degrees of freedom significantly enhances the accuracy of meson mass simulations. We investigate the effect of temperature on the masses of various meson states calculated in the SU(3) and SU(4) eLSM. After establishing all the fitting parameters, the temperature dependence of meson masses shows that although various meson states exhibit unique patterns in their mass changes with temperature, they all seem to share a similar range of dissolution temperatures. This means that the critical temperature that marks the phase transition from hadrons to quarks appears to vary slightly depending on the meson states. In this regard, we find that the quarkonium states, formed by a quark and its antiquark, are largely unaffected by variations in the temperature.

Figures (5)

• Figure 1: The quark condensates for SU(3) (left panel) and SU(4) (right panel) for $c=0$, $c \neq 0$ with (dashed lines) and without factor $F(T) = (1-T^2/T_0^2)$ (solid lines).
• Figure 2: Scalar mesons for SU(3) (left panel) and SU(4) (right panel). Meson masses are plotted both for $c=0$ (solid lines), $c \neq 0$ (dashed lines) cases without involving the factor $F(T) = (1-T^2/T_0^2)$.
• Figure 3: Masses of pseudo-scalar mesons for SU(3) (left panel) and SU(4) (right panel) cases. Meson masses are plotted for $c=0$ (solid lines) and $c \neq 0$ (dashed line). Meson masses presented for the case without the factor $F(T) = (1-T^2/T_0^2)$.
• Figure 4: Vector and axial-vector mesons for SU(3) (left panel) and SU(4) (right panel). Meson masses are plotted both for $c=0$ (solid lines), $c \neq 0$ (dashed lines) cases without involving the factor $F(T) = (1-T^2/T_0^2)$.
• Figure 5: Left panel: scalar and pseudo-scalar mesons with open charm and quarkonia. Right panel: vector and axial-vector mesons with open charm and quarkonia. Meson masses are plotted both for $c=0$ (solid lines), $c \neq 0$ (dashed lines) cases without involving the factor $F(T) = (1-T^2/T_0^2)$.