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

The present study focused 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 focused 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) were explored at finite temperature. Meson states, which are defined by distinct chiral properties, were grouped according to their orbital angular momentum J, parity P, and charge conjugation C. Consequently, this organization yielded scalar mesons with quantum numbers JPC=0++, pseudoscalar mesons with JPC=0−+, vector mesons with JPC=1−−, and axial vector mesons with JPC=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 became feasible and the SU(3) and SU(4) configurations could be analytically estimated.