Strange quark

The formation of quark (strange) stars does not follow unambiguously from the theory, which may be compatible either with the existence or nonexistence of these objects. 

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. 

In detyB we observe the competition between current mass m and overlapping matrix element a p2R 3. With typical instanton sizes p 1/3 fm and inter-instanton distances R 1/to, a is of the order of the strange current quark mass, ms = 150 MeV. So in this case it is very important to take properly into account the current quark mass. 

The saddle-point equation leads to the momentum dependent dynamical quark mass Mf(k) = MfF2(k). Mf here is a function of current mass mf (M.M. Musakhanov, 2002). It was found that that M[m] is a decreasing function and for the strange quark with ms = 0.15 GeV Ms 0.5 Mu>d. This result in a good correspondence with (P. Pobylitsa, 1989), where another method was completely applied - direct sum is of planar diagrams. 

Proposed approach provides reliable tool in hadron physics with the promising perspective of the application to strange quarks. 

Figure 9. Mass-radius relation for pure strange quark matter stars (left) and hybrid stars (right). GO - G4 models of hybrid stars corresponding to different parameters of the model. H pure hadron star, QC star has a quark core, MC star has a mixed core, from Thoma et al. (2003).

Thoma, M.H., Triimper, J., Burwitz, V. (2003). Strange Quark Matter in Neutron Stars - New Results from Chandra and XMM. J.Phys.G30 S471-S478. 

Neutron stars are important laboratories for the physics of high-density matter. Unlike particles in relativistic heavy-ion colliders, the matter in the cores of neutron stars has a thermal energy that is much less than its rest-mass energy. Various researchers have speculated whether neutron star cores contain primarily nucleons, or whether degrees of freedom such as hyperons, quark matter, or strange matter are prevalent (see Lattimer Prakash 2001 for a recent review of high-density equations of state). 

Equations of state involving only nucleonic matter are consistent with all available data. Some hints of evidence for very compact stars have been proposed (Li et al. 1999), which could indicate strange matter, but these are very model-dependent at the present. Even so, exotic states such as quark matter or strange matter are not excluded. 

While the anomaly matching conditions are still in force at nonzero quark chemical potential [32] the persistent mass condition [50] ceases to be valid. Indeed a phase transition, as function of the strange quark mass, between the CEL and the 2SC phases occurs. 

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. 

Let us consider for example the pairing between up and strange quarks in chemical equilibrium. The energy spectrum of up quarks is given as... 

The Fermi sea of up and strange quarks is shown in Fig. 9. Because of the strange quarks mass, they have different Fermi momenta. Note that the Cooperpairing occurs for quarks with same but opposite momenta. Therefore, at least one of the pairing quarks should be excited away from the Fermi surface, costing some energy. Let us suppose that the Cooper-pair gap opens at p p between two Fermi surfaces, psF < p < pf. 

To describe such pairing, we consider small fluctuations of up and strange quarks near p. The energy of such fluctuations of up and down quarks is respectively... 

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 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. 

Qualitatively, the existence of these phases is quite plausible At low values ot jJLq the Fermi momenta of the up and down quarks are relatively similar to each other, whereas the strange quarks are suppressed because of their larger mass. With increasing negative fiQ, however, the up quarks become more and more disfavored and eventually the Fermi momenta are ordered as p f < <... 

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. 

In reality, we are more interested in the intermediate density region, where the color superconducting phase may exist in the interior of neutron stars or may be created in heavy ion collisions. Unfortunately, we have little knowledge about this region we are not sure how the deconfinement and the chiral restoration phase transitions happen, how the QCD coupling constant evolves and how the strange quark behaves in dense matter, etc. Primarily, our current... 

In the framework of the bag model [5], or, in general, under the assumption that the strange quark mass is small [6], one can exclude the 2SC phase in the interior of compact stars when charge neutrality is considered. 

One expects the diquark condensate to dominate the physics at densities beyond the deconfinement/chiral restoration transition and below the critical temperature. Various phases are possible. E.g., the so called 2-color superconductivity (2SC) phase allows for unpaired quarks of one color. There may also exist a color-flavor locked (CFL) phase [7] for not too large value of the strange quark mass ms, for 2A > m2s/fiq, cf. [8], where the color superconductivity... 

Keywords Neutron stars, strange quark core, quark phase transition, new branch of stability,... 

Superdense configurations with a strange quark core. Results and Discussion... 

Figure 3. Mass M versus radius R. On an enlarged scale the new additional local mass maximum is shown for neutron stars with a strange quark core. In the upper left corner of Fig. 3b, the phase transition area is shown for the whole set of EoS.

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