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Phase Structure and Instability Problem in Color Superconductivity
| Content Provider | Semantic Scholar |
|---|---|
| Author | Fukushima, Kenji |
| Copyright Year | 2005 |
| Abstract | We address the phase structure of color superconducting quark matter at high quark density. Under the electric and color neutrality conditions there appear various phases as a result of the Fermi surface mismatch among different quark flavors induced by finite strange quark mass; the color-flavor locked (CFL) phase where quarks are all energy gapped, the u-quark superconducting (uSC) phase where u-quarks are paired with either dor s-quarks, the d-quark superconducting (dSC) phase that is the dquark analogue of the uSC phase, the two-flavor superconducting (2SC) phase where uand d-quarks are paired, and the unpaired quark matter (UQM) that is normal quark matter without pairing. Besides these possibilities, when the Fermi surface mismatch is large enough to surpass the gap energy, the gapless superconducting phases are expected. We focus our discussion on the chromomagnetic instability problem related to the gapless CFL (gCFL) onset and explore the instability regions on the phase diagram as a function of the temperature and the quark chemical potential. We sketch how to reach stable physical states inside the instability regions. PACS. 12.38.-t Quantum chromodynamics – 12.38.Aw General properties of QCD 1 Family of color superconducting phases The phase structure of matter composed of quarks and gluons described by Quantum Chromodynamics (QCD) has been investigated for many years, and in the high temperature and low baryon (or quark if deconfined) density region which is accessible in heavy-ion collisions interesting discoveries have been reported both in theories and in experiments. In the high density and low temperature region, on the other hand, our knowledge is still poor as compared with the rich physics expected in this region. Heavy-ion collisions are not suitable for the purpose to probe dense and cold quark matter, and such a system could be realized, if any, only in the cores of compact stellar objects. The experimental data from the universe is, however, quite limited and there is no smoking-gun for color superconductivity so far. Nevertheless, the theoretical challenge to explore the QCD phase structure is of great interest on its own. Also it would be potentially important in studying the structure and evolution of neutron stars. In order to look into a dense quark system, some of concepts known in condensed matter physics have been imported into QCD in hope of analogous phenomena taking place. In this sense the physics of dense quark matter is, so to speak, “condensed matter physics of QCD” as articulated clearly in the review [1]. Superconductivity is definitely one of them. In general the Cooper instability inevitably occurs wherever there are a sharp Fermi surface below which particles are degenerated and an attractive interaction between particles on the Fermi surface. Even QCD matter is not an exception and the condensation of quark Cooper pairs leads to color superconductivity. A major difference between ordinary electric superconductivity in metals and color superconductivity in quark matter arises from the fact that quarks have three colors and three flavors in addition to spin, so that quark matter allows for many pairing patterns. The color and flavor degrees of freedom make the dense QCD phase structure so complicated that subtleties still remain veiled. In this article we shall argue what has been clarified by now and what should be solved in the future mainly following the discussions in my recent papers [2,3]. 1.1 Pairing patterns Many theoretical works have revealed that the predominant pairing pattern is anti-symmetric in spin (spin zero), anti-symmetric in color (color triplet), and anti-symmetric in flavor (flavor triplet). Moreover, the color-flavor locking is known to be favored in energy, so that the color and flavor indices are locked together. Then there are three independent diquark condensates or gap parameters [4]; 〈ψ i Cγ5ψ b j〉 ∼ ∆1ǫ ǫij1 +∆2ǫ ǫij2 +∆3ǫ ǫij3, (1) where (i, j) and (a, b) represent the flavor indices (u, d, s) and the color triplet indices (red,green,blue) respectively. 2 Kenji Fukushima: Phase Structure and Instability Problem in Color Superconductivity Gap Parameters Phase ∆1 6= 0, ∆2 6= 0, ∆3 6= 0 CFL ∆1 = 0, ∆2 6= 0, ∆3 6= 0 uSC ∆1 6= 0, ∆2 = 0, ∆3 6= 0 dSC ∆1 = ∆2 = 0, ∆3 6= 0 2SC ∆1 = ∆2 = ∆3 = 0 UQM Table 1. A family of color superconducting phases; the colorflavor locked (CFL) phase, the u-quark superconducting (uSC) phase, the d-quark superconducting (dSC) phase, and the twoflavor superconducting (2SC) phase. UQM is unpaired quark matter. The sSC, 2SCsu, and 2SCds phases would not appear in the QCD phase diagram. The charge conjugation C and the Dirac matrix γ5 are required to make (1) a Lorenz scalar. Of course you can consider other kind of pairing between quarks which are totally anti-symmetric under exchange, and even different types of condensates may coexist. Actually diquark condensates such as spin-zero pairing in the color symmetric (color sextet) channel and spin-one pairing between quarks of the same flavor have been analyzed quantitatively [5,6,7,8] and known to be much smaller than the predominant condensate. In this article we shall simply neglect them. Under the pairing ansatz (1), ∆1 is a gap parameter for the Cooper pairing between d and s flavors and green and blue colors. That is, ∆1 is for bd-gs and gd-bs quarks and ∆2 and ∆3 are to be understood likewise; ∆1 bd-gs gd-bs ∆2 rs-bu bs-ru ∆3 gu-rd ru-gd Each gap parameter is either zero or finite and there are 2 = 8 combinations accordingly. Only five of eight phase possibilities as listed in Table 1 are of our interest relevant to the QCD phase diagram. When three gap parameters are all nonzero, this state is called the colorflavor locked (CFL) phase. When only ∆1 is zero, this is the u-quark superconducting (uSC) phase named after the fact that remaining ∆2 and ∆3 are gap parameters for pairing involving u-quarks. The d-quark superconducting (dSC) phase is understood in the same way. The two-flavor superconducting (2SC) phase has only ∆3 which is nonvanishing. The question is; where and how they show up on the phase diagram. The next section is devoted to this issue. It is worth mentioning that these phases can be characterized by global symmetry breaking patterns. In particular the second-order phase transitions between the CFL phase and the uSC or dSC phase belong to the universality class same as an O(2) vector model [9]. In QCD, neither the sSC (s-quark superconducting), 2SCsu (2SC of sand u-quarks), nor 2SCds (2SC of dand s-quarks) phase is realized actually because any pairing containing massive s-quarks is disfavored by the Fermi surface mismatch energy. (The solution branch of the gap equations belonging δμ μ+δμ/2 μ−δμ/2 ∆ < δμ/2 ∆ > δμ/2 hole-1 particle-1 hole-2 |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://cds.cern.ch/record/899334/files/0510299.pdf |
| Alternate Webpage(s) | http://arxiv.org/pdf/hep-ph/0510299v1.pdf |
| Language | English |
| Access Restriction | Open |
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| Content Type | Text |
| Resource Type | Article |
