New phases in color-flavor-locked quark matter

Abstract

We consider O(αs) corrections to the squared masses of the pseudo-Goldstone excitations about the ground state of dense quark matter. We show that these contributions tend to destabilize the vacuum, leading to a surprisingly complex phase structure for quark matter as a function of quark mass, even for small αs. In particular we find two new phases of CFL quark matter possibly relevant for the real world, for whichθQCD = π/2. 03.75.Fi,26.60.+c, The dependence of the QCD vacuum on the masses of the light quarks is most efficiently analyzed by means of a chiral Lagrangian, which allows one to systematically compute corrections to the chirally symmetric vacuum in a power expansion in the quark masses. The utility of the chiral Lagrangian approach is that it properly accounts for the lightest QCD excitations, the pseudo Goldstone bosons (PGBs), whose masses vanish in the chiral limit and which therefore have the most important role in determining the vacuum structure for small quark mass. In addition to allowing one to compute perturbative corrections to the vacuum structure, the chiral Lagrangian also allows one to investigate phase transitions at critical values of the quark masses. An example of such a phase transition was first discovered by Dashen In hadronic matter at nonzero baryon density, more complicated phase transitions have been investigated using chiral Lagrangians, including both pion [2] and kaon condensation [3,4]. More recently, chiral Lagrangians have been used to analyze the vacuum structure of dense quark matter near the chiral limit. It has been convincingly argued that for degenerate quarks such a system should be color superconducting [5], and that for three massless flavors the color-flavor-locked (CFL) ground state is preferred [6,7,8]. Chiral perturbation theory can be used to describe the ground state and excitations of CFL matter away from the chiral limit [9,10,11]. It is already known that the phase structure is much more complicated than in the vacuum case. In particular, an analysis to leading order in both quark masses * abk4@phys.washington.edu † dbkaplan@phys.washington.edu ‡ thomas schaefer@ncsu.edu and the QCD coupling constant α s reveals a phase transition to a kaon condensed phase along a line in the m s -m plane [12,13,14], where m s is the strange quark mass, and for simplicity we are considering the isospin limit, m u = m d = m. In this Letter we show that the leading order calculation does not capture the full complexity of the quark matter ground state, and that there exist new phases revealed at sub-leading order in α s at small quark mass in the m s -m plane which could be relevant for the real world.The reason that O(α s ) effects are important is that the leading order result exhibits an accidental degeneracy which is only lifted at next-to-leading order. Once O(α s ) effects are included the meson masses receive negative corrections to their squared masses which can be larger than the leading order contributions, even for small α s . In particular, a meson of mass M...

The phase diagram of dense QCD

“…In particular, the electron contribution to the thermodynamic potential in the CFL phase favours the K 0 condensation (the CFL-K 0 phase) [200,201,202,203]. The phase structure with the CFL-K 0 state and its variants have been also investigated in the NJL-type model [204,205].…”

Color-flavor locked phase of high density QCD at nonzero strange quark mass

“…Also we will neglect meson mass terms generated by quark masses. Quark mass terms connect particles and antiparticles and the resulting meson mass terms are generally suppressed by powers of ∆/µ ∝ Exp(−const/g s ) and/or α s [13,14,20].…”

Two Lectures on Color Superconductivity*

“…In this case, the CFL phase is expected to undergo a phase transition to a phase with a meson (e.g., kaon or/and eta) condensate [57,58,59]. In the low-energy action of the corresponding phase, additional Nambu-Goldstone bosons with very unusual properties can appear [60].…”