Color, quarks

Color, as used here, has nothing to do with visual color. The manner in which different colored quarks combine in quantum mechanics is suggestive of the way in which visual colors combine. Hadrons are "colorless 7 since they are averages of the three colors. 

It is interesting to note that we have calculated the casimir pressure at finite temperature for parallel plates, a square wave-guide and a cubic box. For a fermion field in a cubic box with an edge of 1.0 fm, which is of the order of the nuclear dimensions, the critical temperature is 100 MeV. Such a result will have implications for confinement of quarks in nucleons. However such an analysis will require a realistic calculation, a spherical geometry, with full account of color and flavor degrees of freedom of quarks and gluons. 

Sedrakian, D. M., Blaschke, D. (2002). Magnetic field of a neutron star with color superconducting quark matter core. Astrofiz., 45 203-212. 

A color superconducting phase is a reasonable candidate for the state of strongly interacting matter for very large quark chemical potential [16-20], Many properties of such a state have been investigated for two and three flavor QCD. In some cases these results rely heavily on perturbation theory, which is applicable for very large chemical potentials. Some initial applications to supemovae explosions and gamma ray bursts can be found in [21] and [22] respectively, see also [27], The interested reader can find a discussion of the effects of color superconductivity on the mass-radius relationship of compact stars in [45]... 

The spectrum in the 2SC state is made of 5 massive Gluons with a mass of the order of the gap, 3 massless Gluons confined (at zero temperature) into light glueballs and gapless up and down quarks in the direction (say) 3 of color. 

While, in the BCS theory, such attractive force for electron Cooper pair is provided by phonons, for dense quark matter, where phonons are absent, the gluon exchange interaction provides the attraction, as one-gluon exchange interaction is attractive in the color anti-triplet channel1 One therefore expects that color anti-triplet Cooper pairs will form and quark matter is color superconducting, which is indeed shown more than 20 years ago [13, 14],... 

There is also an attractive force between quarks and holes in the color octet channel (v- i (—V)ij>j (jJ)) f 0,... 

It is quite likely to find dense quark matter inside compact stars like neutron stars. However, when we study the quark matter in compact stars, we need to take into account not only the charge and color neutrality of compact stars and but also the mass of the strange quark, which is not negligible at the intermediate density. By the neutrality condition and the strange quark mass, the quarks with different quantum numbers in general have different chemical potentials and different Fermi momenta. When the difference in the chemical potential becomes too large the Cooper-pairs breaks or other exotic phases like kaon condensation or crystalline phase is more preferred to the BCS phase. 

S. C. Frautschi, Asymptotic freedom and color superconductivity in dense quark matter, in Proceedings of the Workshop on Hadronic Matter at Extreme Energy Density, N. Cabibbo, Editor, Erice, Italy (1978). 

COLOR SUPERCONDUCTING QUARK MATTER AND THE INTERIOR OF NEUTRON STARS... 

Abstract We investigate the phase structure of color superconducting quark matter at intermediate densities for two- and three flavor systems. We thereby focus our attention on the influence of charge neutrality conditions as well as /3-equilibrium on the different phases. These constraints are relevant in the context of quark matter at the interior of compact stars. We analyze the implications of color superconductivity on compact star configurations using different hadronic and quark equations of state. 

Keywords Quark matter, color superconductivity, neutron stars... 

Most interactions favor a condensation in the scalar color antitriplet channel. There are two different condensation patterns in this channel, depending on whether or not the strange quarks, which are more massive than the light up and down quarks, participate in forming a condensate,... 

Here both, ta and Aa> are the antisymmetric generators of 87/(3), i.e., the antisymmetric Gell-Mann matrices (A, A e 2,5,7 ), acting in flavor and color space, respectively. In the two-flavor color superconducting phase (2SC) where only the light quarks are involved in the condensation, the flavor index in Eq. (1) is restricted to A = 2. In this case it is always possible, without loss of generality, to perform a color rotation such that the 2SC phase is described by s22 / 0 and saa = 0 if (A, A ) (2,2). 

The dispersion law of the four (two flavors, two colors) gapped quarks gets modified by the condensate,... 

Our example deals with quarks of the third color in a phase composed only of up and down quarks. As only quarks of a single color are involved, the pairing must take place in a channel which is symmetric in color. Assuming s-wave condensation in an isospin-singlet channel, a possible candidate is a spin-1 condensate [8], We consider the condensate... 

One of our main interests is to describe quark matter at the interior of a compact star since this is one of the possibilities to find color superconducting matter in nature. It is therefore important to consider electrically and color neutral2 matter in /3-equilibrium. In addition to the quarks we also allow for the presence of leptons, especially electrons muons. As we consider stars older than a few minutes, when neutrinos can freely leave the system, lepton number is not conserved. The conditions for charge neutrality read... 

Here n corresponds to the total quark number density, while ns and ns describe color asymmetries. Note that n/3 also describes the conserved baryon number. The charges are related to four chemical potentials, fi, /13, /tg, and rq, and the chemical potentials of all particles in the system can be expressed through these four chemical potentials. This implies /3-equilibrium,... 

The analysis of Ref. [42] as well as the NJL-type model investigation of Ref. [43] are based on a comparison of homogeneous phases. The neutrality conditions can, however, also be fulfilled giving up the requirement of separately neutral phases and to consider mixed phases in chemical equilibrium which are only neutral in total. This procedure has been pushed forward by Glendenning in the context of the quark-hadron phase transition in neutron stars where a similar problem related to electrical neutrality occurs [44], For the case of electrically and color neutral quark matter the phase boundaries are... 

Table 2. Composition of electrically and color neutral mixed phases, corresponding quark number chemical potentials and average baryon number densities pB = n/3 in unities of nuclear matter saturation density po = 0.17/fm3. The various components are defined in Tab. 1.

Compact stars with a color superconducting quark matter core... 

This section will be devoted to the study of the composition of a compact star including the possibility of a color superconducting quark matter core. Recently this question has been addressed by several authors using a bag-model description of the quark phase [48] or an NJL-type model [49-52], In the following, we will discuss the results of Refs. [49, 52] where -in contrast to Refs. [50, 51]- strange quarks have been taken into account. 

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