The density corrections, in terms of the isospin chemical potential µ I , to the mass of the pions are studied in the framework of the SU (2) low energy effective chiral lagrangian. The pion decay constant f π (T, µ I ) is also analized. As a function of temperature for µ I = 0, the mass remains quite stable, starting to grow for very high values of T , confirming previous results. However, there are interesting corrections to the mass when both effects (temperature and chemical potential) are simultaneously present. At zero temperature the π ± should condensate when µ I = ∓m π . This is not longer valid anymore at finite T . The mass of the π 0 acquires also a non trivial dependence on µ I due to the finite temperature.

We apply a recently constructed model of analytic QCD in the Operator Product Expansion (OPE) analysis of the τ lepton decay data in the V +A channel. The model has the running coupling A1(Q 2 ) with no unphysical singularities, i.e., it is analytic. It differs from the corresponding perturbative QCD coupling a(Q 2 ) at high squared momenta |Q 2 | by terms ∝ (1/Q 2 ) 5 , hence it does not contradict the ITEP OPE philosophy and can be consistently applied with OPE up to terms of dimension D = 8. In evaluations for the Adler function we use a Padé-related renormalizationscale-independent resummation, applicable in any analytic QCD model. Applying the Borel sum rules in the Q 2 plane along rays of the complex Borel scale and comparing with ALEPH data of 1998, we obtain the gluon condensate value (αs/π)G 2 = 0.0055 ± 0.0047 GeV

We study the thermo-magnetic properties of the strong coupling constant G and quark mass M entering the Nambu-Jona-Lasinio model. For this purpose, we compute the quark condensate and compare it to lattice QCD (LQCD) results to extract the behavior of G and M as functions of the magnetic field strength and temperature. We find that at zero temperature, where the LQCD condensate is found to monotonically increase with the field strength, M also increases whereas G remains approximately constant. However, for temperatures above the chiral/deconfinement phase transitions, where the LQCD condensate is found to monotonically decrease with increasing field, M and G also decrease monotonically. For finite temperatures, below the transition temperature, we find that both G and M initially grow and then decrease with increasing field strength. To study possible consequences of the extracted temperature and magnetic field dependence of G and M , we compute the pressure and compare to LQCD results, finding an excellent qualitative agreement. In particular, we show that the transverse pressure, as a function of the field strength, is always negative for temperatures below the transition temperature whereas it starts off being positive and then becomes negative for temperatures above the transition temperature, also in agreement with LQCD results. We also show that for the longitudinal pressure to agree with LQCD calculations, the system should be described as a diamagnet. We argue that the turnover of M and G as functions of temperature and field strength is a key element that drives the behavior of the quark condensate going across the transition temperature and provides clues for a better understanding of the inverse magnetic catalysis phenomenon.

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We describe the deconfining critical temperature dependence on the pion mass and on the isospin chemical potential in remarkably good agreement with lattice data. Our framework incorporates explicit dependence on quark masses, isospin and baryonic chemical potentials for the case of two flavors through ingredients from well-known high-and low-energy theories. In the low-energy sector, the system is described by a minimal chiral perturbation theory effective action, corresponding to a hot gas of pion quasiparticles and heavy nucleons. For the high-temperature sector we adopt a simple extension of the fuzzy bag model. We also briefly discuss the effects of mass asymmetry and baryon chemical potential.Introduction. The phase diagram of quark matter has been the object of intense investigation during the last years, and yet several open questions within the thermodynamics of strong interactions still remain unsolved [1,2]. In this quest, Lattice QCD represents the main non-perturbative approach within the full theory [3], always complemented by effective models [4].In this article we investigate the effects of finite quark masses and isospin number on the equation of state of hot and dense strongly interacting matter and on the deconfining phase transition within a framework inspired by chiral perturbation theory (χPT) and lattice results for the pressure and the trace anomaly. The setting we propose is simple and completely fixed by vacuum QCD properties (measured or simulated on the lattice) and lattice simulations of finite temperature QCD. More explicitly, there is no fitting of mass or isospin chemical potential dependence at all. Nevertheless, our findings for the behavior of the critical temperature as a function of both the pion mass and the isospin chemical potential are in remarkably good agreement with lattice data. It is crucial to note that several detailed studies of chiral models failed to describe T c (m π ) [5,6,7], while Polyakov-loop models, whose predictions can be fitted to the lattice points for T c (m π ) [5], cannot at the present form address isospin effects. In this approach, we can also investigate in a straightforward manner the effects of quark-mass asymmetry and nonzero baryon chemical potential, physical cases in which the Sign Problem develops, constraining systematic lattice studies. The predictions within our framework for these regimes which are not yet fully probed by lattice QCD are left for a longer publication (for preliminary results, see [8]). Throughout the present paper, the baryon chemical potential is fixed to zero. It is not our aim in this short paper to provide a complete description of the full richness of the QCD phase diagram. Still, we present a description of the dependence of the critical deconfining temperature on the quark-average mass and on the isospin chemical potential simultaneously.Small quark masses and a nonzero baryon chemical po-

We study the nature of the chiral transition for an effective theory with spontaneous breaking of symmetry, where charged bosons and fermions are subject to the effects of a constant external magnetic field. The problem is studied in terms of the relative intensity of the magnetic field with respect to the mass and the temperature. When the former is the smallest of the scales, we present a suitable method to obtain magnetic and thermal corrections up to ring order at high temperature. By these means, we solve the problem of the instability in the boson sector for these theories, where the squared masses, taken as functions of the order parameter, can vanish and even become negative. The solution is found by considering the screening properties of the plasma, encoded in the resummation of the ring diagrams at high temperature. We also study the case where the magnetic field is the intermediate of the three scales and explore the nature of the chiral transition as we vary the field strength, the coupling constants and the number of fermions. We show that the critical temperature for the restoration of chiral symmetry monotonically increases from small to intermediate values of the magnetic fields and that this temperature is always above the critical temperature for the case when the magnetic field is absent.Comment: 13 pages, 6 figures, added comments. Version to appear in Phys. Rev

We discuss the charged pion condensation phenomenon in the linear sigma model, in the presence of an external uniform magnetic field. The critical temperature is obtained as a function of the external magnetic field, assuming the transition is of second order, by considering a dilute gas at low temperature. As a result we found magnetic catalysis for high values of the external magnetic field. This behavior confirms previous results with a single charged scalar field.

We study the deconfinement transition of hadronic matter into quark matter under neutron star conditions assuming color and flavor conservation during the transition. We use a two-phase description. For the hadronic phase we use different parameterizations of a non-linear Walecka model which includes the whole baryon octet. For the quark matter phase we use an SU (3) f Nambu-Jona-Lasinio effective model including color superconductivity. Deconfinement is considered to be a first order phase transition that conserves color and flavor. It gives a short-lived transitory colorlessquark-phase that is not in β-equilibrium, and decays to a stable configuration in τ ∼ τ weak ∼ 10 −8 s. However, in spite of being very short lived, the transition to this intermediate phase determines the onset of the transition inside neutron stars. We find the transition free-energy density for temperatures typical of neutron star interiors. We also find the critical mass above which compact stars should contain a quark core and below which they are safe with respect to a sudden transition to quark matter. Rather independently on the stiffness of the hadronic equation of state (EOS) we find that the critical mass of hadronic stars (without trapped neutrinos) is in the range of ∼ 1.5 -1.8 solar masses. This is in coincidence with previous results obtained within the MIT Bag model.