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Description
The fundamental theory of strong interactions, known as Quantum ChromoDynamics (QCD), exhibits rich symmetry properties that underlie the behavior of hadronic matter. In the limit of $N_f$ light quark masses, QCD possesses an approximate chiral symmetry $U(1)_V\otimes U(1)_A\otimes SU(N_f)_V\otimes SU(N_f)_A$. The special unitary part of this symmetry group is spontaneously broken to its vectorial subgroup $SU(N_f)_V$ at low temperatures, leading to the emergence of pseudo-Goldstone bosons. At temperatures above a critical value $T_c^{(N_f)}$, however, lattice simulations show that the chiral condensate $\langle\overline{\psi}\psi\rangle$, which is the order parameter of the breaking process, vanishes and the chiral symmetry $SU(N_f)_V\otimes SU(N_f)_A$ is approximately restored. Conversely, $U(1)_A$ symmetry remains broken at every temperature because of a quantum anomaly. Whether the $U(1)_A$ symmetry is effectively restored at temperatures higher than $T_c^{(N_f)}$, as the magnitude of the anomalous term decreases, remains a subject of active research.
In this work, expanding on previous analyses [1,2], we employ the extended linear sigma ($EL_{\sigma}$) model to investigate the mass spectrum of scalar and pseudoscalar mesons in a realistic $N_f=2+1$ flavor scenario (with degenerate up and down quarks and a heavier strange quark: $0
