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Marcus B. Pinto

Publications and source records attributed to Marcus B. Pinto.

At least 19 recordsLinked to original sources
arXiv2021

Nambu--Jona-Lasinio $SU(3)$ model constrained by lattice QCD: thermomagnetic effects in the magnetization

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 UA(1) symmetry. We incorporate thermomagnetic effects in the four-quark coupling. The model predicts magnetic catalysis at low temperatures and inverse magnetic catalysis at temperatures close to the pseudocritical temperature of the QCD transition, in agreement with lattice QCD results. 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.

hep-ph↗
arXiv2021

Regularizing thermo and magnetic contributions within nonrenormalizable theories

The importance of implementing a proper regularization procedure in order to treat thermo and magnetic contributions within nonrenormalizable theories is investigated. Our study suggests that potential divergences should be isolated into the vacuum and purely magnetic contributions and then regularized while the convergent thermomagnetic contributions should be integrated over the full momentum range. This prescription is illustrated by applying the proper time formalism to the two flavor Polyakov--Nambu--Jona-Lasinio model, whose magnetic field dependent coupling has been recently determined. Observables such as the pressure, magnetization, speed of sound squared, and specific heat evaluated within our scheme are compared with results furnished by other three possible prescriptions. We show that these quantities display a thermomagnetic behavior which is physically more consistent when our scheme is adopted. In particular, we demonstrate that naively regulating the (entangled) vacuum, magnetic and thermomagnetic contributions leads to physically inconsistent results especially at the high temperature domain.

hep-ph↗
arXiv2017

The role of strangeness and isospin in low density expansions of hadronic matter

We compare relativistic mean field models with their low density expansion counterparts used to mimic non-relativistic models by consistently expanding the baryonic scalar density in powers of the baryonic number density up to ${\cal O}(13/3)$, which goes two orders beyond the order considered in previous works. We show that, due to the non-trivial density dependence of the Dirac mass, the convergence of the expansion is very slow, and the validity of the non-relativistic approximation {\bf is} questionable even at subsaturation densities. In order to analyze the roles played by strangeness and isospin we consider $n-Λ$ and $n-p$ matter separately. Our results indicate that these degrees of freedom play quite different roles in the expansion mechanism and $n-Λ$ matter can be better described by low density expansions than $n-p$ matter in general.

nucl-th↗
arXiv2017

Asymptotically Free Theory with Scale Invariant Thermodynamics

A recently developed variational resummation technique, incorporating renormalization group properties consistently, has been shown to solve the scale dependence problem that plagues the evaluation of thermodynamical quantities, e.g., within the framework of approximations such as in the hard-thermal-loop resummed perturbation theory. This method is used in the present work to evaluate thermodynamical quantities within the two-dimensional nonlinear sigma model, which, apart from providing a technically simpler testing ground, shares some common features with Yang-Mills theories, like asymptotic freedom, trace anomaly and the nonperturbative generation of a mass gap. The present application confirms that nonperturbative results can be readily generated solely by considering the lowest-order (quasi-particle) contribution to the thermodynamic effective potential, when this quantity is required to be renormalization group invariant. We also show that when the next-to-leading correction from the method is accounted for, the results indicate convergence, apart from optimally preserving, within the approximations here considered, the sought-after scale invariance.

hep-ph↗
arXiv2016

Properties of magnetized neutral mesons within a full RPA evaluation

We consider the two flavor Nambu--Jona-Lasinio model within the RPA framework to evaluate the masses of the $σ$ and $π^0$ mesons and the $π^0$ decay constant in the presence of a magnetic field at vanishing temperatures and baryonic densities. The present work extends other RPA applications by fully considering the external momenta, which enter the integrals representing the magnetized polarization tensor, so that more accurate results can be obtained in the evaluation of physical quantities containing pionic contributions. As we show, this technical improvement generates results which agree well with those produced by lattice simulations and chiral perturbation theory. Our method may also prove to be useful in future evaluations of quantities such as the shear viscosity and the equation of state of magnetized quark matter with mesonic contributions.

hep-ph↗
arXiv2014

Quark matter subject to strong magnetic fields: phase diagram and applications

In the present work we are interested in understanding various properties of quark matter subject to strong magnetic fields described by the Nambu-Jona-Lasinio model with Polyakov loop. We start by analysing the differences arising from two different vector interactions in the Lagrangian densities, at zero temperature, and apply the results to stellar matter. We then investigate the position of the critical end point for different chemical potential and density scenarios.

nucl-th↗
arXiv2014

Repulsive Vector Interaction in Three Flavor Magnetized Quark and Stellar Matter

The effect of the vector interaction on three flavor magnetized matter is studied within the SU(3) Nambu--Jona-Lasiono quark model. We have considered cold matter under a static external magnetic field within two different models for the vector interaction in order to investigate how the form of the vector interaction and the intensity of the magnetic field affect the equation of state as well as the strangeness content. It was shown that the flavor independent vector interaction predicts a smaller strangeness content and, therefore, harder equations of state. On the other hand, the flavor dependent vector interaction favors larger strangeness content the larger the vector coupling. We have confirmed that at low densities the magnetic field and the vector interaction have opposite competing effects: the first one softens the equation of state while the second hardens it. Quark stars and hybrid stars subject to an external magnetic field were also studied. Larger star masses are obtained for the flavor independent vector interaction. Hybrid stars may bare a core containing deconfined quarks if neither the vector interaction nor the magnetic field are too strong. Also, the presence of strong magnetic fields seems to disfavor the existence of a quark core in hybrid stars.

nucl-th↗
arXiv2012

Chiral Transition Within Effective Quark Models Under Magnetic Fields

We consider the simplest versions of the Nambu--Jona-Lasinio (NJL) model and the Linear Sigma Model (LSM), in the Mean Field Approximation (MFA), in order to analyze hot and dense two flavor quark matter subject to strong magnetic fields. We pay especial attention to the case of a finite chemical potential, which has not yet been fully explored. Our results, for the NJL model, are in qualitative agreement with other recent applications showing that, for stronger fields, the first order segment of the transition line increases with the magnetic strength while the coexistence chemical potential value, at low temperatures, decreases. In the present work, one of the most important results is related to the analysis of how these features affect the phase coexistence region in the $T-ρ_B$ plane. We find that the coexistence boundary oscillates around the B=0 value for magnetic fields of the order $eB \lesssim 9.5\, m_π^2$ which can be understood by investigating the filling of Landau levels at vanishing temperature. So far, most investigations have been concerned with the effects of the magnetic field over the $T-μ$ plane only while other thermodynamical quantities such as the adiabats, the quark number susceptibility, the interaction measure and the latent heat have been neglected. Here, we take a step towards filling this gap by investigating the influence of a magnetic field over these quantities. Finally, we argue that a naive application of the MFA does not seem to be appropriate to treat the LSM in the presence of magnetic fields.

hep-ph↗
arXiv2012

The Surface Tension of Quark Matter in a Geometrical Approach

The surface tension of quark matter plays a crucial role for the possibility of quark matter nucleation during the formation of compact stellar objects, because it determines the nucleation rate and the associated critical size. However, this quantity is not well known and the theoretical estimates fall within a wide range, $γ_0 \approx 5-300 MeV/fm^2$. We show here that once the equation of state is available one may use a geometrical approach to obtain a numerical value for the surface tension that is consistent with the model approximations adopted. We illustrate this method within the two-flavor linear σmodel and the Nambu--Jona-Lasinio model with two and three flavors. Treating these models in the mean-field approximation, we find $γ_0 \approx 7-30 MeV/fm^2$. Such a relatively small surface tension would favor the formation of quark stars and may thus have significant astrophysical implications. We also investigate how the surface tension decreases towards zero as the temperature is raised from zero to its critical value.

hep-ph↗
arXiv2012

The QCD Critical End Point Under Strong Magnetic Fields

We use the three-flavor Nambu--Jona-Lasinio model, which includes strangeness and quark physical masses in the mean field approximation, to investigate the influence of strong magnetic fields on the QCD phase diagram covering the whole $T-μ$ plane. It is found that the size of the first order transition line increases as the field strength increases so that a larger coexistence region for hadronic and quark matter should be expected for strong magnetic fields. The location of the critical end point is also affected by the presence of magnetic fields which invariably increase the temperature value at which the first order line terminates. On the other hand, the critical end point chemical potential value displays a subtle oscillation around the B=0 value for magnetic fields within the $10^{17}-10^{20} \, {\rm G}$ range. These findings may have non trivial consequences for the physics of magnetars and heavy ion collisions.

hep-ph↗
arXiv2010

Multiple Critical Points in Effective Quark Models

We consider the two flavor version of the Linear Sigma Model as well as of the Nambu Jona-Lasinio model, at finite temperature and quark chemical potential, beyond the Mean Field Approximation. Using parameter values for the pion and quark current masses which weakly break chiral symmetry we show that both models can present more than one critical end point. In particular, we explicitly show that the appearance of a new critical point associated with a first order line at high temperature and low densities could help to conciliate some lattice results with model predictions. Using different techniques, we perform an extensive thermodynamical analysis to understand the physical nature of the different critical points. For both models, our results suggest that the new first order line which starts at vanishing chemical potential has a more chiral character than the usual line which displays a character more reminiscent of a liquid-gas phase transition.

nucl-th↗
arXiv2008

Critical Dopant Concentration in Polyacetylene and Phase Diagram from a Continuous Four-Fermi Model

The Optimized Perturbation Theory (OPT) method, at finite temperature and finite chemical potential, is applied to the field theory model for polyacetylene. The critical dopant concentration in trans-polyacetylene is evaluated and compared with the available experimental data and with previous calculations. The results obtained within the OPT go beyond the standard mean field (or large-N) approximation (MFA) by explicitly including finite N effects. A critical analysis of the possible theoretical prescriptions to implement and interpret these corrections to the mean field results, given the available data, is given. For typical temperatures probed in the laboratory, our results show that the critical dopant concentration is only weakly affected by thermal effects.

cond-mat.soft↗
arXiv2004

Exact 1/N and Optimized Perturbative Evaluation of mu_c for Homogeneous Interacting Bose Gases

In the framework of the O(N) three-dimensional effective scalar field model for homogeneous dilute weakly interacting Bose gases we use the 1/N expansion to evaluate, within the large N limit, the parameter r_c which is directly related to the critical chemical potential mu_c. This quantity enters the order-a^2 n^{2/3} coefficient contributing to the critical temperature shift Delta T_c where a represents the s-wave scattering length and n represents the density. Compared to the recent precise numerical lattice simulation results, our calculation suggests that the large N approximation performs rather well even for the physical case N=2. We then calculate the same quantity but using different forms of the optimized perturbative (variational) method, showing that these produce excellent results both for the finite N and large-N cases.

cond-mat.other↗
arXiv2003

Asymptotically Improved Convergence of Optimized Perturbation Theory in the Bose-Einstein Condensation Problem

We investigate the convergence properties of optimized perturbation theory, or linear $δ$ expansion (LDE), within the context of finite temperature phase transitions. Our results prove the reliability of these methods, recently employed in the determination of the critical temperature T_c for a system of weakly interacting homogeneous dilute Bose gas. We carry out the explicit LDE optimized calculations and also the infrared analysis of the relevant quantities involved in the determination of $T_c$ in the large-N limit, when the relevant effective static action describing the system is extended to O(N) symmetry. Then, using an efficient resummation method, we show how the LDE can exactly reproduce the known large-N result for $T_c$ already at the first non-trivial order. Next, we consider the finite N=2 case where, using similar resummation techniques, we improve the analytical results for the nonperturbative terms involved in the expression for the critical temperature allowing comparison with recent Monte Carlo estimates of them. To illustrate the method we have considered a simple geometric series showing how the procedure as a whole works consistently in a general case.

cond-mat.soft↗
arXiv2002

Convergent resummed linear delta expansion in the critical O(N) (ϕ_i^2)^2_{3d} model

The nonperturbative linear delta expansion (LDE) method is applied to the critical O(N) phi^4 three-dimensional field theory which has been widely used to study the critical temperature of condensation of dilute weakly interacting homogeneous Bose gases. We study the higher order convergence of the LDE as it is usually applied to this problem. We show how to improve both, the large-N and finite N=2, LDE results with an efficient resummation technique which accelerates convergence. In the large N limit, it reproduces the known exact result within numerical integration accuracy. In the finite N=2 case, our improved results support the recent numerical Monte Carlo estimates for the critical transition temperature of Bose-Einstein condensation.

cond-mat.soft↗
arXiv2002

Unusual Transition Patterns in Bose-Einstein Condensation

We analyze the possible transition patterns exhibited by an effective non-relativistic field model describing interacting binary homogeneous dilute Bose gases whose overall potential is repulsive. We evaluate the temperature dependence of all couplings and show that at intermediate temperatures the crossed interaction, which is allowed to be attractive, dominates, leading to smooth re-entrant phases. At higher temperatures this interaction suffers a sudden sign inversion leading to an abrupt discontinuous transition back to the normal gas phase. This situation may suggest an alternative way to observe collapsing and exploding condensates. Our results also suggest that such binary systems may offer the possibility of observing Bose-Einstein condensation at higher critical temperatures.

cond-mat.soft↗
arXiv2002

Higher Order Evaluation of the Critical Temperature for Interacting Homogeneous Dilute Bose Gases

We use the nonperturbative linear δexpansion method to evaluate analytically the coefficients c_1 and c_2^{\prime \prime} which appear in the expansion for the transition temperature for a dilute, homogeneous, three dimensional Bose gas given by T_c= T_0 \{1 + c_1 a n^{1/3} + [ c_2^{\prime} \ln(a n^{1/3}) +c_2^{\prime \prime} ] a^2 n^{2/3} + {\cal O} (a^3 n)\}, where T_0 is the result for an ideal gas, a is the s-wave scattering length and n is the number density. In a previous work the same method has been used to evaluate c_1 to order-δ^2 with the result c_1= 3.06. Here, we push the calculation to the next two orders obtaining c_1=2.45 at order-δ^3 and c_1=1.48 at order-δ^4. Analysing the topology of the graphs involved we discuss how our results relate to other nonperturbative analytical methods such as the self-consistent resummation and the 1/N approximations. At the same orders we obtain c_2^{\prime\prime}=101.4, c_2^{\prime \prime}=98.2 and c_2^{\prime \prime}=82.9. Our analytical results seem to support the recent Monte Carlo estimates c_1=1.32 \pm 0.02 and c_2^{\prime \prime}= 75.7 \pm 0.4.

cond-mat.soft↗