Thermal pions at a finite isospin chemical potential

The density corrections, in terms of the isospin chemical potential μI, 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,μI) is also analyzed. As a function of temperature for μI=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 μI=∓m_π. This is no longer valid at finite T. The mass of π₀ acquires also a nontrivial dependence on μI due to the finite temperature.