Low energy properties of color-flavor locked superconductors

Abstract

We discuss some low energy properties of color-flavor locked (CFL) superconductors. First, we study how an external magnetic field affects their Goldstone physics in the chiral limit, stressing that there is a long-range component of the field that penetrates the superconductor. We note that the most remarkable effect of the applied field is giving a mass to the charged pions and kaons. By estimating this effect, we see that for values $e B \sim 2 f_\pi \Delta$, where $\Delta$ is the quark gap, and $f_\pi$ the pion decay constant, the charged Goldstone bosons become so heavy, that they turn out to be unstable. The symmetry breaking pattern is then changed, agreeing with that of the magnetic color-flavor locked (MCFL) phase, recently proposed in hep-ph/0503162. Finally, we discuss the physics of the superfluid phonon of the CFL phase, compare it with that of the phonon of a Bose-Einstein condensate, and discuss transport phenomena at low temperature. Astrophysical implications of all the above low energy properties are also commented.