On the ground state of gapless two flavor color superconductors

This paper is devoted to the study of some aspects of the instability of two flavor color-superconductive quark matter. We find that, beside color condensates, the Goldstone boson related to the breaking of U(1)(A) suffers from a velocity instability. We relate this wrong sign problem, which implies the existence of a Goldstone current in the ground state or of gluonic condensation, to the negative squared Meissner mass of the 8th gluon in the gapless two flavor color superconductor (g2SC) phase. Moreover we investigate the Meissner masses of the gluons and the squared velocity of the Goldstone in the multiple-plane-wave Larkin-Ovchinnikov-Fulde-Ferrel (LOFF) states, arguing that in such phases both the chromomagnetic instability and the velocity instability are most probably removed. We also do not expect Higgs instability in such multiple-plane-wave LOFF, at least when one considers fluctuations with small momenta. The true vacuum of gapless two flavor superconductors is thus expected to be a multiple-plane-wave LOFF state.