Thermal Pions at Finite Isospin Chemical Potential

Abstract

The density corrections, in terms of the isospin chemical potential ${\mu }_I$, to the mass of the pions are studied in the framework of the SU(2) low energy effective chiral lagrangian. The pion decay constant $f_{\pi }(T,{\mu }_I)$ is also analized. As a function of temperature for ${\mu }_I=0$, 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 ${\pi }^{\pm }$ should condensate when ${\mu }_I=\mp m_{\pi }$. This is not longer valid anymore at finite $T$. The mass of the ${\pi }_0$ acquires also a non trivial dependence on ${\mu }_I$ due to the finite temperature.

Comments: 13 pages, 5 figures