Single-flavour and two-flavour pairing in three-flavour quark matter

Abstract

We study single-flavour quark pairing ("self-pairing") in colour-superconducting phases of quark matter, paying particular attention to the difference between scenarios where all three flavours undergo single-flavour pairing, and scenarios where two flavours pair with each other ("2SC" pairing) and the remaining flavour self-pairs. We perform our calculations in the mean field approximation using a pointlike four-fermion interaction based on single gluon exchange. We confirm the result from previous weakly-coupled-QCD calculations, that when all three flavours self-pair the favored channel for each is colour-spin-locked (CSL) pseudoisotropic pairing. However, we find that when the up and down quarks undergo 2SC pairing, they induce a colour chemical potential that disfavors the CSL phase. The strange quarks then self-pair in a "polar" channel that breaks rotational invariance, although the CSL phase may survive in a narrow range of densities.

What do exotic equations of state have to offer?

“…However, those approaches were based on perturbative schemes, and therefore obtained (quite consistently) gaps of the order of 1 MeV or so, much smaller than the natural scales of the problem (say, the quark chemical potential). The recent works (Alford and Cowan 2006;Gómez Dumm et al 2006 and references therein) have tried to calculate the phase diagram more directly, without resorting to perturbative schemes. As a result, several pairing possibilities (u and d quarks only, 2SC phase; all u, d and s quarks at a common Fermi momentum-not energy!-, the CFL state) were found with gaps as large as 100 MeV.…”

“…This property is related to the linearity of the EOS, and holds approximately if the latter is not strict. When pairing energy is present, the free energy of the paired mixture Ω CFL is smaller than the unpaired version by a term quadratic both in the gap Δ and the chemical potential μ (Alford and Reddy 2003)…”

Spin-one color superconductivity in compact stars?—an analysis within NJL-type models

“…They have been introduced first in Schafer (2000) and Alford et al (2000) and their properties have been investigated later more in detail, see Schmitt (2004) and more recently Alford & Cowan (2006). Among many possible pairing patterns (polar, planar, A, CSL), the transverse Color-Spin-Locking phase (CSL) has been demonstrated to be the ground state of a spin-1 color superconductor at T = 0 having the largest pressure (Schmitt (2004)).…”

“…First, NJL model calculations show that when a moderate coupling constant for the usual 2SC phase is considered, two flavor normal quark matter dominates the intermediate region of the phase diagram (Ruster et al (2005); Blaschke et al (2005)). Then, recently in Alford & Cowan (2006) model calculations performed with massless u − d quarks and the mass of the s quark taken through an effective chemical potential, show that for large strange quark mass, CSL dominates the phase diagram at low temperature and a second order phase transition to unpaired quark matter occurs as the temperature increases. So, we expect that when the densities in the interior of a compact star are high enough to allow for two-flavor quark matter but not so high to have the strange quark deconfined, and the temperature has fallen below T c , a CSL quark core might develop.…”

Single-Flavor Color Superconductivity in a Magnetic Field

“…To avoid the technical complexity of the onegluon exchange, we shall work with a NJL-like effective action which picks up only the dominant pairing channel of the former, the transverse pairing, in the ultrarelativistic limit. The Hamiltonian of the effective action reads [6] TABLE I. This table shows possible phases under a magnetic field for both two-flavor and three-flavor cases with each flavor forming spin-one CSC or remaining normal state.…”