Thermal pions and isospin chemical potential effects

The thermal and density corrections, in terms of the isospin chemical potential p,, to the mass of the pions are studied in the framework of the SU(2) low energy effective chiral lagrangian at finite temperature in the so called second phase, when ‖μI‖ > m, being m the tree-level pion mass. As a function of temperature for μ1 = 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 condense when μ1 = ±mπ. At finite T, the condensed pion acquires a thermal mass in such a way that a mixture, like in a superfluid, of a condensed and normal phase appears.