Degeneracy Patterns of Chiral Companions at Finite Temperature

Abstract

Chiral symmetry represents a fundamental concept lying at the core of particle and nuclear physics. Its spontaneous breaking in vacuum can be exploited to distinguish chiral hadronic partners, whose masses differ. In fact, the features of this breaking serve as guiding principles for the construction of effective approaches of QCD at low energies, e.g., the chiral perturbation theory, the linear sigma model, the (Polyakov)–Nambu–Jona-Lasinio model, etc. At high temperatures/densities chiral symmetry can be restored bringing the chiral partners to be nearly degenerated in mass. At vanishing baryochemical potential, such restoration follows a smooth transition, and the chiral companions reach this degeneration above the transition temperature. In this work I review how different realizations of chiral partner degeneracy arise in different effective theories/models of QCD. I distinguish the cases where the chiral states are either fundamental degrees of freedom or (dynamically-generated) composed states. In particular, I discuss the intriguing case in which chiral symmetry restoration involves more than two chiral partners, recently addressed in the literature.

Chiral symmetry restoration with three chiral partners

“…I showed how the lower pole approaches the ground state when f π is 60% of its vacuum value, while the higher pole still remains more massive. This points toward a sequential degeneracy pattern of the chiral symmetry restoration [4]. If such pattern is supported by a more rigorous calculation, its experimental verification could be attempted in heavy-ion collisions at high energies.…”

“…As described in Ref. [4], the additional account for the reduction of the ground states (specially the pion mass) gives an extra decrease of all generated masses of ∆m ∼ −100 MeV. In particular, the lower pole of the D * 0 (2300) gets bound (moving to the first Riemann surface) and becoming very close to the D-meson mass, while the higher-pole mass lies still ∼ 200 MeV above them.…”

“…As a simple calculation to gauge the dependence of f π on the charmed mesons masses, I apply a reduction to this parameter from its vacuum value to the vacuum calculation of the T -matrix equation ( 10) [4]. This isolates the effect of f π , as pure thermal effects played a small role in the meson masses (cf.…”

“…In Ref. [4] I classified different effective field theories (EFTs) of QCD according to the nature of the chiral partners. These could be either fundamental degrees of freedom-represented by quantum fields in the effective action-or generated dynamically via a few-body (e.g.…”

Finite-temperature effects on D-meson properties

“…If the expected decrease of the quark condensate is considered to model the temperature dependence of the pion decay constant ( ) (e.g. via the thermal version of the Gell-Mann-Oakes-Renner relation), then indications of a plausible degeneration of masses can be obtained [9].…”