Parametrization of a nonlocal, chiral quark model in the instantaneous three-flavor case. Basic formulas and tables

In these notes we describe the basic formulation of the parametrization scheme for the instantaneous nonlocal chiral quark model in the three flavor case. We choose to discuss the Gaussian, Lorentzian-type, Woods-Saxon and sharp cutoff (NJL) functional forms of the momentum dependence for the formfactor of the separable interaction. The four parameters: light and strange quark mass, coupling strength (G_S) and range of the interaction (Lambda) have been fixed by the same phenomenological inputs: pion and kaon mass, pion decay constant and light quark mass in vacuum. The Wood-Saxon and Lorentzian-type formfactor is suitable for an interpolation between sharp cutoff and soft momentum dependence. Results are tabulated for applications in models of hadron structure and quark matter at finite temperatures and chemical potentials where separable models have proven successful.Comment: 11 pages, 3 figures, 11 table

Cooling Evolution of Hybrid Stars

The cooling of compact isolated objects for different values of the gravitational mass has been simulated for two alternative assumptions. One is that the interior of the star is purely hadronic and second that the star can have a rather large quark core. It has been shown that within a nonlocal chiral quark model the critical density for a phase transition to color superconducting quark matter under neutron star conditions can be low enough for these phases to occur in compact star configurations with masses below 1.3 M_sun. For a realistic choice of parameters the equation of state (EoS) allows for 2SC quark matter with a large quark gap ~ 100 MeV for u and d quarks of two colors that coexists with normal quark matter within a mixed phase in the hybrid star interior. We argue that, if in the hadronic phase the neutron pairing gap in 3P_2 channel is larger than few keV and the phases with unpaired quarks are allowed, the corresponding hybrid stars would cool too fast. Even in the case of the essentially suppressed 3P_2 neutron gap if free quarks occur for M < 1.3 M_sun, as it follows from our EoS, one could not appropriately describe the neutron star cooling data existing by today. It is suggested to discuss a "2SC+X" phase, as a possibility to have all quarks paired in two-flavor quark matter under neutron star constraints, where the X-gap is of the order of 10 keV - 1 MeV. Density independent gaps do not allow to fit the cooling data. Only the presence of an X-gap that decreases with increase of the density could allow to appropriately fit the data in a similar compact star mass interval to that following from a purely hadronic model.Comment: 10 pages, 5 figures, Talk given at Joint Meeting Heidelberg-Liege-Paris-Rostock (HLPR 2004), Spa, Belgium, 16-18 Dec 200

Model of the Phase Transition Mimicking the Pasta Phase in Cold and Dense Quark-Hadron Matter

A simple mixed phase model mimicking so-called "pasta" phases in the quark-hadron phase transition is developed and applied to static neutron stars for the case of DD2 type hadonic and NJL type quark matter models. The influence of the mixed phase on the mass-radius relation of the compact stars is investigated. Model parameters are chosen such that the results are in agreement with the observational constraints for masses and radii of pulsars.Comment: 6 pages, 4 figure