Derivation of Meson Masses in SU(3) and SU(4) Extended Linear-Sigma Model at Finite Temperature

TL;DR

This paper derives analytical expressions for meson masses in SU(3) and SU(4) extended linear-sigma models at finite temperature, exploring relationships between meson states across flavor configurations and their temperature dependence.

Contribution

It provides the first analytical derivation of meson masses for both noncharmed and charmed states in SU(3) and SU(4) models at finite temperature, enabling detailed comparisons.

Findings

Derived expressions for 17 noncharmed mesons.

Derived expressions for 29 charmed mesons.

Facilitated analytical comparison of meson states across SU(3) and SU(4).

Abstract

The present study focuses on the mesonic potential contributions to the Lagrangian of the extended linear-sigma model (eLSM) for scalar and pseudoscalar meson fields across various quark flavors. The present study focuses on the low-energy phenomenology associated with quantum chromodynamics (QCD), where mesons and their interactions serve as the pertinent degrees of freedom, rather than the fundamental constituents of quarks and gluons. Given that SU(4) configurations are completely based on SU(3) configurations, the possible relationships between meson states in SU(3) and those in SU(4) are explored at finite temperature. Meson states, which are defined by distinct chiral properties, are grouped according to their orbital angular momentum $J$, parity $P$, and charge conjugation $C$. Consequently, this organization yields scalar mesons with quantum numbers $J^{PC}=0^{++}$, pseudoscalar mesons with $J^{PC}=0^{-+}$, vector mesons with $J^{PC}=1^{--}$, and axialvector mesons with $J^{PC}=1^{++}$. We accomplished the derivation of analytical expressions for a total of seventeen noncharmed meson states and twenty-nine charmed meson states so that an analytical comparison of the noncharmed and charmed meson states at different temperatures becomes feasible and the contributions SU(3) and SU(4) configurations can be estimated, analytically.