Thermal pions at a finite isospin chemical potential

Abstract

The density corrections, in terms of the isospin chemical potential µ I , to the mass of the pions are studied in the framework of the SU (2) low energy effective chiral lagrangian. The pion decay constant f π (T, µ I ) is also analized. As a function of temperature for µ I = 0, the mass remains quite stable, starting to grow for very high values of T , confirming previous results. However, there are interesting corrections to the mass when both effects (temperature and chemical potential) are simultaneously present. At zero temperature the π ± should condensate when µ I = ∓m π . This is not longer valid anymore at finite T . The mass of the π 0 acquires also a non trivial dependence on µ I due to the finite temperature.

Nambu–Jona-Lasinio-based study of the QCD critical line

“…Following the analyses previously performed within the chiral Lagrangian approach [13,14], and NJL [17,23] and ladder-QCD [18] studies, we expect a superfluid phase with condensed pions when the isospin chemical potential µ I exceeds a critical value µ C I (µ C I = m π /2 at µ q = T = 0).…”

“…The former has been the subject of several studies within different models, starting from effective Lagrangians [13,14], random matrices [15], NJL [16,17] and ladder-QCD [18] and so apparently a model-independent phenomenon. However, pion (and kaon [19]) condensation would not be accessible from Heavy Ion experiments, but could regard the physics of compact stars.…”

Bose–Einstein condensation and chiral phase transition in linear sigma model

“…For the linear sigma model which has the isospin invariance, one can introduce a chemical potential associated with the isospin charge. For example, in [14], the pion isospin chemical potential is introduced by the third component of the isospin charge and applied to the discussions of the thermal pion mass within the chiral perturbation theory. In our discussion, the isospin chemical potential of pions is introduced to the linear sigma model in the same way.…”

Density Effects on the Pion Dispersion Relation at Finite Temperature

“…The behavior of the pion mass in the presence of an isospin chemical potential has been recently studied in Ref. [7]. But in order to describe a situation in which the number of pions in thermal equilibrium is finite, we need to consider a chemical potential associated with the pion number, instead of its charge.…”