arXiv subjects

Marcus Benghi Pinto

Publications and source records attributed to Marcus Benghi Pinto.

At least 19 recordsLinked to original sources

arXiv2026

Quark and hybrid stars with renormalization group improvement of NNLO perturbative QCD

Recently, the NNLO perturbative QCD pressure of cold and dense symmetric matter, with arbitrary quark masses, has been resummed within the renormalization-group-optimized perturbation theory (RGOPT) framework. By being imbued with renormalization group properties, the resulting pressure is less sensitive to renormalization scale ($Λ\equiv X μ_B/3$) variations than the NNLO perturbative QCD pressure. Here, we extend this by considering $β$-equilibrium and charge neutrality to evaluate the corresponding equation of state (EoS). We provide a compact ``pocket" fitting formula for the EoS for $N_f=2+1$ massive quarks at different renormalization scale parameter ($X$) values. We describe pure quark stars as well as hybrid stars with quark-cores. Pure quark stars compatible with astrophysical observations were obtained with $X=3.08-3.58$, whereas a larger value (4.10) is needed if the low mass object of the observation GW190814 represents a neutron star. Hybrid stars were built considering three representative hadron models based on a relativistic mean-field description, and chosen to produce soft and stiff EoSs. Stable hybrid stars with masses compatible with the massive pulsar PSR J0740+6620 were obtained considering $X$ of the order of 2 to 2.60-2.98, the largest scale giving rise to hybrid stars with a large quark core with a radius of 5 to 8 km, and the smallest to a small quark core at the center of the star.

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arXiv2026

Scale dependence improvement of the quartic scalar field thermal effective potential in the optimized perturbation theory

Perturbation theory, as well as most thermal field resummation methods widely used to study finite-temperature quantum field theories, presents a non-negligible renormalization scale dependence. To address this limitation, we propose an alternative method that combines the renormalization group improvement prescription for the thermal effective potential with the optimized perturbation theory variational resummation technique. Here, we apply this new framework, termed variational renormalization group, to evaluate the effective potential of the scalar $λϕ^4$ theory at finite temperatures, which represents a benchmark model for phase transition studies. We show that the proposed approach significantly improves scale stability, compared to the use of optimized perturbation theory alone, across key thermodynamic quantities, including the effective potential, critical temperature, and pressure. These results establish the variational renormalization group as a robust alternative tool for precision studies of thermal phase transitions, with direct implications for cosmological applications (e.g., early-Universe thermodynamics) and condensed matter systems.

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arXiv2025

Two-flavor chirally imbalanced quark matter beyond large $N_c$

We investigate a chirally imbalanced medium in the context of the two-flavor Nambu--Jona-Lasinio model using both the large-$N_c$ (LN) and beyond large-$N_c$ (BLN) approximations. To incorporate BLN effects, we consider the optimized perturbation theory (OPT) to the first nontrivial order, which includes two-loop (exchange) contributions. This procedure allows us to explicitly explore how finite $N_c$ corrections affect the thermodynamics as well as the phase diagram of chirally imbalanced quark matter. We then compare the results obtained with a sharp three-dimensional cutoff -- generically referred to as the traditional regularization scheme -- and with an alternative procedure called the medium separation scheme (MSS). In the first case, we observe that the pseudocritical temperature decreases as the chiral chemical potential increases, an effect dubbed inverse chiral catalysis. On the other hand, when considering the MSS regularization, which properly isolates the medium contributions from the vacuum, we find the opposite result. We show that the results obtained with MSS are consistent with well-established LQCD data in both the LN and BLN approximations. Finally, we suggest that to cope with the high-density limit, the standard OPT interpolation prescription must be modified with the inclusion of an extra variational parameter.

hep-ph↗

arXiv2025

Comparing strange and non-strange quark stars within resummed QCD at NLO

We employ the renormalization group optimized perturbation theory (RGOPT) resummation method to evaluate the equation of state (EoS) for strange ($N_f=2+1$) and non-strange ($N_f=2$) cold quark matter at NLO. This allows us to obtain the mass-radius relation for pure quark stars and compare the results with the predictions from perturbative QCD (pQCD) at NNLO. Choosing the renormalization scale to generate maximum star masses of order $M=2 - 2.6 M_\odot$, we show that the RGOPT can produce mass-radius curves compatible with the masses and radii of some recently observed pulsars, regardless of their strangeness content. The scale values required to produce the desired maximum masses are higher in the strange scenario since the EoS is softer in this case. The possible reasons for such behavior are discussed. Our results also show that, as expected, the RGOPT predictions for the relevant observables are less sensitive to scale variations than those furnished by pQCD.

hep-ph↗

arXiv2024

Testing the equivalence between the planar Gross-Neveu and Thirring models at $N=1$

It is known that the Fierz identities predict that the Gross-Neveu and Thirring models should be equivalent when describing systems composed of a single fermionic flavor, $N=1$. Here, we consider the planar version of both models within the framework of the optimized perturbation theory at the two-loop level, in order to verify if the predicted equivalence emerges explicitly when different temperature and density regimes are considered. At vanishing densities, our results indicate that both models indeed describe exactly the same thermodynamics, provided that $N=1$. However, at finite chemical potentials we find that the $N=1$ Fierz equivalence no longer holds. After examining the relevant free energies, we have identified the contributions which lead to this puzzling discrepancy. Finally, we discuss different frameworks in which this (so far open) problem could be further understood and eventually circumvented.

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arXiv2023

First order phase transitions within Weyl type of materials at low temperatures

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.

cond-mat.str-el↗

arXiv2023

Non-strange quark stars within resummed QCD

The recently developed resummation technique known as {\it renormalization group optimized perturbation theory} (RGOPT) is employed in the evaluation of the EoS describing non-strange cold quark matter at NLO. Inspired by recent investigations, which suggest that stable quark matter can be made only of up and down quarks, the mass-radius relation for two flavor pure quark stars is evaluated and compared with the predictions from perturbative QCD (pQCD) at NNLO. This comparison explicitly shows that by being imbued with renormalization group properties, and a variational optimization procedure, the method allows for an efficient resummation of the perturbative series. Remarkably, when the renormalization scale is chosen so as to reproduce maximum mass stars with M=$2-2.3M_\odot$, one obtains a mass-radius curve compatible with the masses and radii of the pulsars PSR J0740+6620, PSR J0030+0451, and the compact object HESS J1731-347. Moreover, the scale dependence of the EoS (and mass-radius relation) obtained with the RGOPT is greatly improved when compared to that of pQCD. This seminal application to the description of quark stars shows that the RGOPT represents a robust alternative to pQCD when describing compressed quark matter.

hep-ph↗

arXiv2023

Equation of state for strange quark matter: Linking the Nambu--Jona-Lasinio model to perturbative QCD

Neutron star constraints and {\it ab initio} pQCD evaluations require the EoS representing cold quark matter to be stiff at intermediate baryonic densities and soft at high-$n_B$. Here, I suggest that the three flavor NJL model with a density dependent repulsive coupling, $G_V(μ)$, can generate an EoS which interpolates between these two regimes. Such an interpolation requires repulsion to start decreasing with the chemical potential just after chiral transition takes place. The conjecture behind this mechanism is that repulsion should be necessary only as long as the quark condensates, which dress the effective masses, have non-vanishing values. This assumption guarantees that an initially hard EoS suffers a conspicuous change of slope at ${\cal E} \simeq 0.7 \,{\rm GeV fm^{-3}}$ converging to the pQCD results at higher energy densities. Then, the speed of sound naturally reaches a non-conformal maximum at $n_B = 3.23 \, n_0 = 0.52 \, {\rm fm}^{-3}$ while the trace anomaly remains positive for all densities, in agreement with recent investigations. These non-trivial results {\it cannot} be simultaneously obtained when $G_V$ vanishes or has a fixed value. Therefore, the simple model proposed here is able to link the (non-perturbative) region of intermediate densities to the region where pQCD becomes reliable.

hep-ph↗

arXiv2022

Repulsive vector interaction as a trigger for the non-conformal peak in $V_s^2$

Considering the NJL model with a repulsive vector channel, parametrized by $G_V$, I show that one may generate a non-monotonic behavior for the speed of sound which peaks at $V_s^2 > 1/3$. This can be achieved by assuming $G_V$ 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 $V_s^2$ 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.

hep-ph↗

arXiv2022

Quantum phase transitions in a bidimensional $O(N) \times {\mathbb{Z}_2}$ scalar field model

We analyze the possible quantum phase transition patterns occurring within the $O(N) \times {\mathbb{Z}_2}$ scalar multi-field model at vanishing temperatures in $(1+1)$-dimensions. The physical masses associated with the two coupled scalar sectors are evaluated using the loop approximation up to second order. We observe that in the strong coupling regime, the breaking $O(N) \times {\mathbb{Z}_2} \to O(N)$, which is allowed by the Mermin-Wagner-Hohenberg-Coleman theorem, can take place through a second-order phase transition. In order to satisfy this no-go theorem, the $O(N)$ sector must have a finite mass gap for all coupling values, such that conformality is never attained, in opposition to what happens in the simpler ${\mathbb{Z}_2}$ version. Our evaluations also show that the sign of the interaction between the two different fields alters the transition pattern in a significant way. These results may be relevant to describe the quantum phase transitions taking place in cold linear systems with competing order parameters. At the same time the super-renormalizable model proposed here can turn out to be useful as a prototype to test resummation techniques as well as non-perturbative methods.

hep-th↗

arXiv2021

Renormalization group improved pressure for hot and dense quark matter

We apply the renormalization group optimized perturbation theory (RGOPT) to evaluate the quark contribution to the QCD pressure at finite temperatures and baryonic densities, at next-to-leading order (NLO). Our results are compared to NLO and state-of-the-art higher orders of standard perturbative QCD (pQCD) and hard thermal loop perturbation theory (HTLpt). The RGOPT resummation provides a nonperturbative approximation, exhibiting a drastically better remnant renormalization scale dependence than pQCD, thanks to built-in renormalization group invariance consistency. At NLO, upon simply adding to the RGOPT-resummed quark contributions the purely perturbative NLO glue contribution, our results show a remarkable agreement with ab initio lattice simulation data for temperatures $0.25 \lesssim T \lesssim 1 \, {\rm GeV}$, with a remnant scale dependence drastically reduced as compared to HTLpt.

hep-ph↗

arXiv2021

QCD pressure: renormalization group optimized perturbation theory confronts lattice

The quark contribution to the QCD pressure, $P_q$, is evaluated up to next-to-leading order (NLO) within the renormalization group optimized perturbation theory (RGOPT) resummation approach. To evaluate the complete QCD pressure we simply add the perturbative NLO contribution from massless gluons to the resummed $P_q$. Despite of this unsophisticated approximation our results for $P = P_q +P_g$ at the central scale $M\sim 2πT$ show a remarkable agreement with ab initio lattice predictions for $0.25 \lesssim T \lesssim 1 \, {\rm GeV}$. We also show that by being imbued with RG properties, the RGOPT produces a drastic reduction of the embarrassing remnant scale dependence that plagues both standard thermal perturbative QCD and hard thermal loop perturbation theory (HTLpt) applications.

hep-ph↗

arXiv2021

Critical behavior of the 2d scalar theory: resumming the ${\rm N}^8{\rm LO}$ perturbative mass gap

We apply the optimized perturbation theory (OPT) to resum the perturbative series describing the mass gap of the bidimensional $ϕ^4$ theory in the $\mathbb{Z}_2$ symmetric phase. Already at NLO (one loop) the method is capable of generating a quite reasonable non-perturbative result for the critical coupling. At order-$g^7$ we obtain $g_c = 2.779(25)$ which compares very well with the state of the art ${\rm N}^8{\rm LO}$ result, $g_c = 2.807(34)$. As a novelty we investigate the supercritical region showing that it contains some useful complimentary information that can be used in extrapolations to arbitrarily high orders.

hep-th↗

arXiv2020

Three dimensional Yukawa models and CFTs at strong and weak couplings

The massless three dimensional Gross-Neveu-Yukawa (GNY) and Nambu--Jona-Lasinio--Yukawa (NJLY) models at finite temperatures are analyzed within the mean field framework considering all coupling values. When the number of Dirac fermions is taken to be $N_f=1/4$ (GNY) and $N_f=1/2$ (NJLY) these models relate to the supersymmetric Wess-Zumino (WZ) theory with cubic superpotential and one superfield. In this case the results show that the strong-weak entropy density ratio decreases from the Stefan-Boltzmann value, in the weak limit, to $s/s_{free}=31/35$ at strong couplings. This value agrees with the one recently obtained by applying the large-$N$ approximation to the supersymmetric $O(N)$ WZ model with quartic superpotential and $N$ superfields. When $N_f=0$ one obtains $s/s_{free}=4/5$ recovering, as expected, the ratio predicted in the context of the $O(N)$ scalar model. However, contrary to the $O(N)$ WZ model the simple Yukawa models analyzed here do not behave as CFTs for all couplings since the conformal measure exactly vanishes only at the extreme weak and strong limits although the speed of sound indicates that the deviation, at intermediate couplings, appears to be rather small. By comparing the thermal masses behavior in each case one can trace this difference as being a consequence that in the GNY/NJLY case the fermionic mass vanishes for all couplings while within the $O(N)$ WZ it only vanishes at the weak and strong limits. On the other hand, the Yukawa bosonic dimensionless masses display a more universal behavior decreasing from $2 \ln [(1+\sqrt{5})/2]$, at infinite coupling, to zero (at vanishing coupling).

hep-th↗

arXiv2019

Renormalization group improved pressure for cold and dense QCD

We apply the renormalization group optimized perturbation theory (RGOPT)to evaluate the QCD (matter) pressure at the two-loop level considering three flavors of massless quarks in a dense and cold medium. Already at leading order ($α_s^0$), which builds on the simple one loop (RG resummed) term, our technique provides a non-trivial non-perturbative approximation which is completely renormalization group invariant. At the next-to-leading order the comparison between the RGOPT and the pQCD predictions shows that the former method provides results which are in better agreement with the state-of-the-art $higher \, order$ perturbative results, which include a contribution of order $α_s^3 \ln^2 α_s$. At the same time one also observes that the RGOPT predictions are less sensitive to variations of the arbitrary $\bar{\rm MS}$ renormalization scale than those obtained with pQCD. These results indicate that the RGOPT provides an efficient resummation scheme which may be considered as an alternative to lattice simulations at high baryonic densities.

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arXiv2018

Evaluation of particle--anti-particle scaled correlation within effective models

Correlations and fluctuations of physical quantities are known to play an important role in phase transitions and critical phenomena. In recent years some experimental attempts were made in the scope of the Beam Energy Scan program to locate a possible critical point in the QCD phase diagram. In this work we use the Nambu--Jona-Lasinio model to investigate the off-diagonal quark susceptibility, which is related to the quark--anti-quark scaled correlation at the mean field level. We show that this correlation has a significant peak near the critical point and, therefore, may be a useful quantity to measure in experiment. We further study the effects of a repulsive vector coupling, which reduces the strength of the scaled correlation near the critical point.

nucl-th↗

arXiv2018

Optimized Perturbation Theory Applied to a Model with Flavour Symmetry $SU_f(3)$

The \textit{optimized perturbation theory} (OPT) is implemented in the $SU_f(3)$ flavor symmetric Nambu--Jona-Lasinio (NJL) model to generate non-pertubative corrections to the quark pressure beyond the large-$N$ approximation. The correctness of this implementation is verified by the recovery of the already known non-perturbative results in the Hartree-Fock approximation, and by having the large-$N$ approximation as a limiting case. This formalism is then used to revisit a discussion on the discordance between the lattice data and the two flavor model prediction of the dynamical vector repulsive interactions, beyond the pseudocritical temperature. It is shown that these contradictory predictions can be corrected by considering a three quark flavor system.

nucl-th↗

arXiv2017

$π_0$ pole mass calculation in a strong magnetic field and lattice constraints

The $π_0$ neutral meson pole mass is calculated in a strongly magnetized medium using the SU(2) Nambu-Jona-Lasinio model within the random phase approximation (RPA) at zero temperature and zero baryonic density. We employ a magnetic field dependent coupling, $G(eB)$, fitted to reproduce lattice QCD results for the quark condensates. Divergent quantities are handled with a magnetic field independent regularization scheme in order to avoid unphysical oscillations. A comparison between the running and the fixed couplings reveals that the former produces results much closer to the predictions from recent lattice calculations. In particular, we find that the $π_0$ meson mass systematically decreases when the magnetic field increases while the scalar mass remains almost constant. We also investigate how the magnetic background influences other mesonic properties such as $f_{π_0}$ and $g_{π_0 q q}$.

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