Flavors, quarks

To get the ground state of the system, we need to know the thermodynamical potential. For simplicity, we use Nambu-Jona-Lasinio (NIL) model [14] to describe 2-flavor quark matter,... 

We have discussed the homogeneous 2-flavor quark matter when charge neutrality conditions are satisfied locally, and found that the local charge neutrality conditions impose very strong constraints on determining the ground state of the system. 

The pressure of the main three phases of two-flavor quark matter as a function of the baryon and electrical chemical potentials is shown in Figure 7 at r/ = 0.75. In this figure, we also show the pressure of the neutral normal quark and gapless 2SC phases (two dark solid lines). The surface of the g2SC phase extends only over a finite range of the values of //,. It merges with the pressure surfaces of the normal quark phase (on the left) and with the ordinary 2SC phase (on the right). 

As a first step in this direction we will discuss here the two flavor color superconducting (2SC) quark matter phase which occurs at lower baryon densities than the color-flavor-locking (CFL) one, see [18, 32], Studies of three-flavor quark models have revealed a very rich phase structure (see [32] and references therein). However, for applications to compact stars the omission of the strange quark flavor within the class of nonlocal chiral quark models considered here may be justified by the fact that central chemical potentials in stable star configurations do barely reach the threshold value at which the mass gap for strange quarks breaks down and they appear in the system [20], Therefore we will not discuss here first applications to calculate compact star configurations with color superconducting quark matter phases that have employed non-dynamical quark models... 

In Ref. [24] it has been investigated whether with the above three- flavor quark matter EoS of the NCQM strange quark matter can appear in the interior of compact stars. The constraints of fl equilibrium and charge neutrality have been applied (see below) in order to constrain the partial densities of electrons and up-, down-, strange quarks, see Fig. 3. It can be seen that strange... 

Figure 3. Composition of three-flavor quark matter in fi equilibrium with electrons.

Figure 16. Schematic protoquark star evolution corresponding to Fig. 15 plotted in the phase diagram for 2-flavor quark matter...

From this expression we can obtain the value of Tc corresponding to a given value of L. For L 1 fm, which is a value of the order of confining lengths for hadrons, we obtain Tc 0.438 /m 1 87.6 MeV. This gives us a crude estimate of the Casimir contribution of a single quark flavor for the deconfining transition for hadrons. 

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. 

Figure 3 compares P(s) of full QCD with Nf = 3 flavors and quark mass ma = 0.05 to the RMT result. In the confinement as well as in the deconfinement phase we observe agreement with RMT up to very high [3 (not shown). The observation that P(s) is not influenced by the presence of dynamical quarks is expected from the results of Ref. (Fox and Kahn, 1964), which apply to the case of massless quarks. Our... 

Abstract. Low-momentum quark determinant and effective action in the presence of current quark mass and external flavor fields is derived. The results of the calculations of various correlators are briefly presented. We conclude that, this approach is a reliable tool for the hadron physics, especially including strange quarks. 

We see that B is the extension of Lee-Bardeen s matrix B, taking into account the presence of the external fields V and with an account of the quark current mass m without making expansion over current mass m and also extended to a few flavors case. 

In Eq. (37) soft external and a fields, carrying momentum q p l. were assumed. Then, they are present inside of the form-factor F in above mentioned form. If v, a external fields are flavor matrices then form-factor F also becomes matrix Nf x Nf. So, we get the partition function Z[m,V], where W are multi-quark interaction terms in the presence of current quark mass m and external fields V. 

Figure 3. The quasiparticle fit (solid line) of the lattice data [9] (open symbols) for the pressure in QCD with Nj = 2 light flavors. The full symbols, representing data with large quark masses, agree with the results for the pure SU(3) plasma (hatched band) for details see [10].

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]... 

For Nf = 3 light flavors at very high chemical potential dynamical computations suggest that the preferred phase is a superconductive one and the following ansatz for a quark-quark type of condensate is energetically favored ... 

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. 

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,... 

Here To = y 11/ is proportional to the unit matrix in flavor space. The quark field ip now contains a third component in flavor space, the strange quark, and consequently the mass matrix rh, see Eq. (4), is equally enlarged by the current strange quark mass, ms, which can in general be different from up and down quark masses. This interaction consists of a U(3)l x U(3)ft-syrnmetric 4-point interaction and a 7 Hooft-type 6-point interaction which breaks the UA (1) symmetry. 

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