Thermal Pions at 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 $π^{\pm}$ should condensate when $μ_{I} = \mp m_π$. 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.