We apply a non-perturbative analytical method, known as the Optimized Perturbation Theory (OPT), ... more We apply a non-perturbative analytical method, known as the Optimized Perturbation Theory (OPT), to the Polyakov Nambu Jona-Lasinio (PNJL) model in order to investigate physical quantities associated with the QCD phase transitions. We consider the Taylor expansion of the pressure in powers of μ/T obtaining the second cumulant (c2) which is associated to the quark number susceptibility. We discuss how the OPT nite Nc radiative (quantum) corrections induce a contribution to the pressure which behaves as a vector repulsion even when such a channel is absent in the original classical potential. Our results are then compared with the ones furnished by lattice QCD simulations and by the large-Nc approximation showing that, physically, the OPT results resemble those furnished by the latter approximation when a repulsive vector channel is explicitly included in the classical potential. In this case, both approximations fail to correctly describe the Stefan-Boltzmann limit at high temperatur...
We use a three-flavor Nambu-Jona-Lasinio model to study the thermodynamics of strange quark matte... more We use a three-flavor Nambu-Jona-Lasinio model to study the thermodynamics of strange quark matter under a strong magnetic field. The model Lagrangian features flavor SU(3) four-quark interactions and six-quark interactions that break the U A (1) symmetry. We incorporate thermomagnetic effects in the four-quark coupling by fitting lattice results for the average of u and d quark condensates close to the pseudocritical temperature. We compute the pressure at the mean field level and obtain the magnetization of quark matter. We adopt the recently proposed vacuum magnetic regularization (VMR) scheme, in that divergent quark mass independent contributions are not subtracted, thereby avoiding unphysical results for the magnetization. We devote special attention to the renormalized magnetization, a projected quantity that allows for direct comparisons with lattice QCD simulations. Our results are in very good agreement with lattice data indicating a paramagnetic behavior for quark matter.
Vacuum corrections in nuclear matter are evaluated on basis of the modified relativistic Hartree ... more Vacuum corrections in nuclear matter are evaluated on basis of the modified relativistic Hartree approximation, applied to the Walecka sigma-omega model, and the relativistic Hartree approximation, employed on the non-linear model. Comparing the two approaches, we have determined the physical constraint between the compression modulus of nuclear matter and the nucleon effective mass. Moreover, the results in our work suggest we can find, for same pairs of these quantities, additional physical roots for the quartic order scalar meson self-coupling parameter of the non-linear treatment.
In order to analyze optimization issues related to the non-perturbative optimized perturbation th... more In order to analyze optimization issues related to the non-perturbative optimized perturbation theory method we consider the effective potential as well as the fermionic mass for the 2d Gross–Neveu model. A direct comparison within the large-N approximation shows that the results obtained from the effective potential optimization are more efficient unless one uses the renormalization group to improve the mass.
The influence of nonlinear cubic and quartic self-couplings of the scalar meson field in nuclear ... more The influence of nonlinear cubic and quartic self-couplings of the scalar meson field in nuclear matter is investigated. In summing the leading tadpole corrections for the Dirac-vacuum, we compare two approaches, the modified relativistic Hartree approximation, applied to the Walecka model, and the relativistic Hartree approximation, employed to the nonlinear model, respectively. These two approaches render similar expressions for the equation of state of nuclear matter up to the fifth order in the scalar meson field. We find that, by exploring the parameter dependence of the two models, they yield similar results for the bulk static properties of nuclear matter. However, increasing the baryon density the two models start to deviate significantly, such as in the predictions for the maximal mass of a neutron star or in the role of hyperon degrees of freedom in dense matter. The results indicate that with increasing density, scalar meson self-couplings beyond the fourth order seem to ...
Journal of Physics A: Mathematical and General, 2006
We review how the phenomena of inverse symmetry breaking (and symmetry nonrestoration) may arise ... more We review how the phenomena of inverse symmetry breaking (and symmetry nonrestoration) may arise in the context of relativistic as well as nonrelativistic multi-scalar field theories. We discuss how the consideration of thermal effects on the couplings produce different transition patterns for both theories. For the relativistic case, these effects allow the appearance of inverse symmetry breaking (and symmetry nonrestoration) at arbitrarily large temperatures. On the other hand, the same phenomena are suppressed in the nonrelativistic case, which is relevant for condensed matter physics. In this case, symmetry nonrestoration does not happen while inverse symmetry is allowed only to be followed by symmetry restoration characterizing a reentrant phase. The aim of this paper is to give more insight concerning the, qualitatively correct, results obtained by using one loop perturbation theory in the evaluation of thermal masses and couplings.
We analyze the possible dynamical chiral symmetry breaking patterns taking place within Weyl type... more We analyze the possible dynamical chiral symmetry breaking patterns taking place within Weyl type of materials. Here, these systems are modeled by the (2+1)-dimensional Gross-Neveu model with a tilt in the Dirac cone. The optimized perturbation theory (OPT) is employed in order to evaluate the effective potential at finite temperatures and chemical potentials beyond the traditional large-N limit. The nonperturbative finite-N corrections generated by the OPT method and its associated variational procedure show that a first-order phase transition boundary, missed at large N , exists in the regime of low temperatures and large chemical potentials. This result, which represents our main finding, implies that one should hit a region of mixed phases when exploring the low-temperature range. The associated first order transition line, which starts at T = 0, terminates at a tricritical point such that the transitions taking place at high T are of the second kind. In particular, we discuss how the tilt in the Dirac cone affects the position of the tricritical point as well as the values of critical temperature and coexistence chemical potential among other quantities. Some experimental implications and predictions are also briefly discussed.
We explore the phase structure of dense magnetized quark matter when a repulsive vector interacti... more We explore the phase structure of dense magnetized quark matter when a repulsive vector interaction, parametrized by GV , is present. Our results show that for a given magnetic field intensity (B) one may find a value of GV for which quark matter may coexist at three different baryonic density values leading to the appearance of two triple points in the phase diagram which have not been observed before. Another novel result is that at high pressure and low temperature we observe a first order transition which presents a negative slope in the P − T that is reminiscent of the solidliquid transition line observed within the water phase diagram. These unusual patterns occur for GV and B values which lie within the range presently considered in many investigations related to the study of magnetars.
Considering the NJL model with a repulsive vector channel, parametrized by GV , I show that one m... more Considering the NJL model with a repulsive vector channel, parametrized by GV , I show that one may generate a non-monotonic behavior for the speed of sound which peaks at V 2 s > 1/3. This can be achieved by assuming GV to be density dependent so that the resulting EoS is stiff/repulsive at low densities and soft/non-repulsive at high densities. The interpolation between the two regimes happens through a cross-over which takes place after the first order chiral transition sets in. The model explicitly shows that a non-conformal peak in V 2 s is not in tension with the QCD trace anomaly being positive at all densities, supporting recent claims in this direction. A brief discussion on how the running coupling may affect the mass-radius relation is carried out in the context of simple non-strange quark stars.
We apply a non-perturbative analytical method, known as the Optimized Perturbation Theory (OPT), ... more We apply a non-perturbative analytical method, known as the Optimized Perturbation Theory (OPT), to the Polyakov Nambu Jona-Lasinio (PNJL) model in order to investigate physical quantities associated with the QCD phase transitions. We consider the Taylor expansion of the pressure in powers of μ/T obtaining the second cumulant (c2) which is associated to the quark number susceptibility. We discuss how the OPT nite Nc radiative (quantum) corrections induce a contribution to the pressure which behaves as a vector repulsion even when such a channel is absent in the original classical potential. Our results are then compared with the ones furnished by lattice QCD simulations and by the large-Nc approximation showing that, physically, the OPT results resemble those furnished by the latter approximation when a repulsive vector channel is explicitly included in the classical potential. In this case, both approximations fail to correctly describe the Stefan-Boltzmann limit at high temperatur...
We use a three-flavor Nambu-Jona-Lasinio model to study the thermodynamics of strange quark matte... more We use a three-flavor Nambu-Jona-Lasinio model to study the thermodynamics of strange quark matter under a strong magnetic field. The model Lagrangian features flavor SU(3) four-quark interactions and six-quark interactions that break the U A (1) symmetry. We incorporate thermomagnetic effects in the four-quark coupling by fitting lattice results for the average of u and d quark condensates close to the pseudocritical temperature. We compute the pressure at the mean field level and obtain the magnetization of quark matter. We adopt the recently proposed vacuum magnetic regularization (VMR) scheme, in that divergent quark mass independent contributions are not subtracted, thereby avoiding unphysical results for the magnetization. We devote special attention to the renormalized magnetization, a projected quantity that allows for direct comparisons with lattice QCD simulations. Our results are in very good agreement with lattice data indicating a paramagnetic behavior for quark matter.
Vacuum corrections in nuclear matter are evaluated on basis of the modified relativistic Hartree ... more Vacuum corrections in nuclear matter are evaluated on basis of the modified relativistic Hartree approximation, applied to the Walecka sigma-omega model, and the relativistic Hartree approximation, employed on the non-linear model. Comparing the two approaches, we have determined the physical constraint between the compression modulus of nuclear matter and the nucleon effective mass. Moreover, the results in our work suggest we can find, for same pairs of these quantities, additional physical roots for the quartic order scalar meson self-coupling parameter of the non-linear treatment.
In order to analyze optimization issues related to the non-perturbative optimized perturbation th... more In order to analyze optimization issues related to the non-perturbative optimized perturbation theory method we consider the effective potential as well as the fermionic mass for the 2d Gross–Neveu model. A direct comparison within the large-N approximation shows that the results obtained from the effective potential optimization are more efficient unless one uses the renormalization group to improve the mass.
The influence of nonlinear cubic and quartic self-couplings of the scalar meson field in nuclear ... more The influence of nonlinear cubic and quartic self-couplings of the scalar meson field in nuclear matter is investigated. In summing the leading tadpole corrections for the Dirac-vacuum, we compare two approaches, the modified relativistic Hartree approximation, applied to the Walecka model, and the relativistic Hartree approximation, employed to the nonlinear model, respectively. These two approaches render similar expressions for the equation of state of nuclear matter up to the fifth order in the scalar meson field. We find that, by exploring the parameter dependence of the two models, they yield similar results for the bulk static properties of nuclear matter. However, increasing the baryon density the two models start to deviate significantly, such as in the predictions for the maximal mass of a neutron star or in the role of hyperon degrees of freedom in dense matter. The results indicate that with increasing density, scalar meson self-couplings beyond the fourth order seem to ...
Journal of Physics A: Mathematical and General, 2006
We review how the phenomena of inverse symmetry breaking (and symmetry nonrestoration) may arise ... more We review how the phenomena of inverse symmetry breaking (and symmetry nonrestoration) may arise in the context of relativistic as well as nonrelativistic multi-scalar field theories. We discuss how the consideration of thermal effects on the couplings produce different transition patterns for both theories. For the relativistic case, these effects allow the appearance of inverse symmetry breaking (and symmetry nonrestoration) at arbitrarily large temperatures. On the other hand, the same phenomena are suppressed in the nonrelativistic case, which is relevant for condensed matter physics. In this case, symmetry nonrestoration does not happen while inverse symmetry is allowed only to be followed by symmetry restoration characterizing a reentrant phase. The aim of this paper is to give more insight concerning the, qualitatively correct, results obtained by using one loop perturbation theory in the evaluation of thermal masses and couplings.
We analyze the possible dynamical chiral symmetry breaking patterns taking place within Weyl type... more We analyze the possible dynamical chiral symmetry breaking patterns taking place within Weyl type of materials. Here, these systems are modeled by the (2+1)-dimensional Gross-Neveu model with a tilt in the Dirac cone. The optimized perturbation theory (OPT) is employed in order to evaluate the effective potential at finite temperatures and chemical potentials beyond the traditional large-N limit. The nonperturbative finite-N corrections generated by the OPT method and its associated variational procedure show that a first-order phase transition boundary, missed at large N , exists in the regime of low temperatures and large chemical potentials. This result, which represents our main finding, implies that one should hit a region of mixed phases when exploring the low-temperature range. The associated first order transition line, which starts at T = 0, terminates at a tricritical point such that the transitions taking place at high T are of the second kind. In particular, we discuss how the tilt in the Dirac cone affects the position of the tricritical point as well as the values of critical temperature and coexistence chemical potential among other quantities. Some experimental implications and predictions are also briefly discussed.
We explore the phase structure of dense magnetized quark matter when a repulsive vector interacti... more We explore the phase structure of dense magnetized quark matter when a repulsive vector interaction, parametrized by GV , is present. Our results show that for a given magnetic field intensity (B) one may find a value of GV for which quark matter may coexist at three different baryonic density values leading to the appearance of two triple points in the phase diagram which have not been observed before. Another novel result is that at high pressure and low temperature we observe a first order transition which presents a negative slope in the P − T that is reminiscent of the solidliquid transition line observed within the water phase diagram. These unusual patterns occur for GV and B values which lie within the range presently considered in many investigations related to the study of magnetars.
Considering the NJL model with a repulsive vector channel, parametrized by GV , I show that one m... more Considering the NJL model with a repulsive vector channel, parametrized by GV , I show that one may generate a non-monotonic behavior for the speed of sound which peaks at V 2 s > 1/3. This can be achieved by assuming GV to be density dependent so that the resulting EoS is stiff/repulsive at low densities and soft/non-repulsive at high densities. The interpolation between the two regimes happens through a cross-over which takes place after the first order chiral transition sets in. The model explicitly shows that a non-conformal peak in V 2 s is not in tension with the QCD trace anomaly being positive at all densities, supporting recent claims in this direction. A brief discussion on how the running coupling may affect the mass-radius relation is carried out in the context of simple non-strange quark stars.
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Papers by Benghi Pinto