How do chiral condensates affect color superconducting quark matter under charge neutrality constraints?

Abstract

We investigate the effects of the dynamical formation of the chiral condensates on color superconducting phases under the electric and color neutrality constraints at vanishing temperature. We shall show that the phase appearing next to the color-flavor-locked (CFL) phase down in density depends on the strength of the diquark coupling. In particular, the gapless CFL (gCFL) phase is realized only in a weak coupling regime. We give a qualitative argument on why the gCFL phase in the weak coupling region is replaced by some other phases in the strong coupling, once the competition between dynamical chiral symmetry breaking and the Cooper pair formation is taken into account. 25.75.Nq On the basis of the asymptotic-free nature of QCD and the attraction between quarks due to gluon exchanges, we now believe that the ground state of the quark matter composed of u, d and s quarks at extremely high densities is a special type of color superconducting phases [1,2]; that is the color-flavor locked (CFL) phase where all the quarks equally participate in pairing [3,4].In reality, nature may not, however, allow such an extremely high-density matter to exist, even in the core of neutron stars and in possible quark stars. In such systems at relatively low density corresponding to the quark chemical potential of, say, 500 MeV, the following two ingredients become important for the fate of the CFL phase and determining the pattern of color superconductivities [5,6,7]: Firstly, one can not neglect the effect of the strange quark mass M s which ranges from around 100 MeV to 500 MeV depending on the quark density. Secondly, the constraints of the color and electric neutrality must be satisfied as well as β-equilibrium under the weak interaction. The former causes Fermi-momentum mismatch [8,9,10], and the latter pulls up or down the Fermi momentum of each species of quarks [6,7]; as the density goes lower, the symmetric CFL pairing would cease to be the ground state at some critical density, and some phases other than the CFL phase would appear.One of the recent findings of such novel pairing patterns is the gapless CFL (gCFL) phase [11,12], which is a non-BCS state having some quarks with gapless dispersions despite the same symmetry breaking pattern as the CFL phase. Historically, a possible realization of the stable gapless state was first discussed for the two-flavor color superconducting phase [13]: It was shown that the local charge neutrality gives a so strong constraint that such an exotic state, called the g2SC phase, exists stably; this is in contrast with the case of the electronic superconductivity in metals [14], where the possible gapless state is unstable against the spatial separation into the Pauli-paramagnetic and superconducting phases because of the absence of a long-range force mediated by gauge fields. The gCFL phase is the three flavor analogue of the g2SC phase. Successive detailed studies have revealed a rich phase structure of superconducting quark matter at zero and nonzero temperatures [15,16]. It shoul...

Extensive study of phase diagram for charge-neutral homogeneous quark matter affected by dynamical chiral condensation: unified picture for thermal unpairing transitions from weak to strong coupling

“…Accordingly, the number of gapped quasi-quark modes decrease as 9 (CFL) → 7 (gCFL) → 0 (UQM) at T = 0 as shown in the previous work [24]. Next, we will discuss how the situation is changed in the T = 0 case.…”

“…The value of G s is chosen so that the dynamical quark mass at µ = 0 is 400 MeV for the cutoff Λ = 800 MeV just for comparison with our previous work [24]. Note, however, that this coupling is a little larger than the value extracted in the NJL model analysis of the meson spectroscopy with instanton induced six-quark coupling [38], i.e., G S Λ 2 = 1.835 which is adopted in [29].…”

“…The formulation made above is a straightforward extension of our previous work [24] to the (T = 0) case [29,30].…”

“…We start with the following Lagrangian as in [24] L =q(i/ ∂ − m 0 + µγ 0 )q + G d (qP t ηq )( t qP η q)…”

“…As a measure of coupling constant G d , we shall mainly use the gap energy (∆ 0 ) in the pure CFL phase at µ = 500 MeV and T = 0 in the chiral SU(3) limit, as in [11,23,24].…”