Chromomagnetic Instability and Gluonic Phase *

It has been suggested that quark matter might exist inside central regions of compact stars. At sufficiently high baryon density, cold quark matter is expected to be in a color superconducting (CSC) state. This is one of the reasons why the color superconductivity has been intensively studied. Bulk matter in the compact stars must be in β-equilibrium and be electrically and color neutral. The electric and color neutrality conditions play a crucial role in the dynamics of quark pairing. In addition, the strange quark mass cannot be neglected in moderately dense quark matter. Then a mismatch δμ between the Fermi surfaces of the pairing quarks is induced. As the mismatch δμ grows, the CSC state tends to be destroyed. However, the dynamics is not yet solved completely. It is one of the central issues in this field to reveal the phase structure. The problem is that the (gapped/gapless) two-flavor color superconducting phase (2SC/g2SC) suffers from the chromomagnetic instability connected with tachyonic Meissner screening masses of gluons. While the Meissner mass for the 8th gluon is imaginary in the g2SC phase δμ > ∆, where ∆ is a diquark gap, the chromomagnetic instability for the 4-7th gluons appears in δμ > ∆/ √ 2. Such a chromomagnetic instability has been found also in the gapless color-flavor locked (gCFL) phase. Since the Meissner masses are defined at zero momentum and thus not