arXiv subjects

A. G. Grunfeld

Publications and source records attributed to A. G. Grunfeld.

At least 19 recordsLinked to original sources

arXiv2026

Finite-Size Effects on the Critical End Point of Magnetized Quark Matter in the Nonlocal PNJL Model

We investigate finite-size effects in the $T$-$μ$ phase diagram of magnetized quark matter within the framework of a nonlocal extension of the Polyakov--Nambu--Jona-Lasinio (PNJL) model. Finite-size corrections are incorporated through the multiple reflection expansion (MRE) formalism, which describes a spherical quark droplet of radius $R$ and modifies the density of states by including surface and curvature contributions. We consider two-flavor quark matter at finite temperature and chemical potential in the presence of a uniform magnetic field with strengths ranging from $eB=0$ to $1$ GeV$^{2}$, and droplet radii from $R=3$ fm to the bulk limit. The nonlocal PNJL (nlPNJL) model naturally reproduces both magnetic catalysis at low temperatures and inverse magnetic catalysis near the chiral transition, in agreement with lattice QCD results. We analyze the chiral condensate, the traced Polyakov loop, the normalized quark condensate, and the corresponding susceptibilities. We find that finite-size effects do not modify the overall structure of the phase diagram, and that the coincidence of the chiral restoration and deconfinement transitions persists for all magnetic field strengths and system sizes explored, within the present implementation in which finite-size corrections are restricted to the fermionic sector. However, the critical end point (CEP) is notably shifted as a function of both the magnetic field strength and the system size: it moves toward higher chemical potentials and lower temperatures as the system size decreases, an effect that is significantly amplified by strong magnetic fields. Our results have potential implications for the physics of phase conversion in compact stars and for the interpretation of relativistic heavy-ion collision experiments.

hep-ph↗

arXiv2026

Self-bound quark stars with a first-order two-to-three flavor phase transition

We investigate self-bound quark stars in a flavor-dependent quark-mass density-dependent model with an excluded-volume correction. We chart the parameter space at zero pressure to identify self-bound regimes, including parametrizations in which self-bound two-flavor matter undergoes a genuine first-order $ud \to uds$ transition at finite pressure. We construct cold, $β$-equilibrated stellar sequences and compute the corresponding global properties (mass-radius relation, tidal deformability, and moment of inertia). For a wide region of the model parameter space, we find that the onset of a $uds$ core occurs before the maximum-mass configuration is reached, yielding self-bound hybrid stars that follow the typical strange-quark-star sequence morphology but develop a characteristic kink at $p_c=p_{\rm tr}$ along the stellar curves. The excluded-volume parameter $κ$ controls the stiffness of the equation of state and thus masses, radii, tidal deformabilities, and moments of inertia; intermediate repulsion typically reconciles $M_{\max}\!\gtrsim\!2\,M_\odot$ with current astrophysical constraints. We further identify two equation-of-state-insensitive trends: dimensionless moment of inertia versus compactness and gravitational versus baryonic compactness. These results provide model-guided priors and tools for discriminating between hadronic and self-bound equations of state with multimessenger data.

astro-ph.HE↗

arXiv2025

Exploring Anisotropic Effects in Magnetized Quark Matter

We investigate the thermodynamic properties of cold magnetized quark matter within a nonlocal Nambu Jona Lasinio (nlNJL) model. Our study addresses the equation of state, anisotropic pressures, quark density, speed of sound, and magnetic susceptibility, with direct comparison to the chiral limit. Strong magnetic fields are found to generate marked anisotropy: the longitudinal pressure and speed of sound are enhanced, approaching the causal bound in the lowest Landau-level (LLL) regime, while the transverse components are systematically reduced. The quark density exhibits magnetic catalysis, increasing with both the chemical potential and the magnetic field strength. At moderate to high fields, the critical chemical potential decreases with increasing $eB$, signaling the occurrence of inverse magnetic catalysis at finite chemical potential ($μ$IMC). Magnetic susceptibility displays oscillations around zero in low fields, driven by de Haas van Alphen like effects, and settles at positive values for strong fields, consistent with an overall growth of magnetization. Compared with the chiral limit, the inclusion of finite current quark masses does not modify the overall oscillatory behavior, but changes the nature of the Landau level transitions, which become weakly first order instead of second order.

hep-ph↗

arXiv2025

Scaling and universality in strange quark stars

We derive scaling laws that connect certain macroscopic observables of strange quark stars with key microscopic properties of self-bound quark matter, such as the energy per baryon at zero pressure and the strength of repulsive interactions. We also identify universal relations linking global properties of strange quark stars - specifically, their moment of inertia, tidal deformability, and both gravitational and baryonic compactness. Remarkably, these relations hold for two substantially different microscopic models - the quark-mass density-dependent model with excluded-volume corrections and the vector MIT bag model - underscoring their robust, model-independent nature. We demonstrate that the universal relations for strange quark stars differ significantly from those previously established for neutron stars composed of hadronic matter, thus enabling discrimination between the two types of objects without requiring detailed knowledge of their equations of state. Moreover, observational constraints on the maximum mass of compact stars could place bounds on both the depth of quark-matter self-binding and the strength of quark repulsive interactions.

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arXiv2025

Anisotropy in Magnetized Quark Matter in the Chiral Limit

We investigate the behavior of cold quark matter under strong magnetic fields in the frame of a nonlocal NJL model in the chiral limit. Our analysis focuses on deconfinement, chiral symmetry restoration, and the anisotropy in pressure induced by the external magnetic field. For $eB\lesssim 0.07~ \text{GeV}^2$, the critical chemical potential remains largely insensitive to the magnetic field, whereas at higher field strengths, transitions to chirally restored phases occur at progressively lower chemical potentials. The parallel and perpendicular pressures, respect to the magnetic field, exhibit distinct behaviors, reflecting the anisotropic nature of the system. Oscillations in the quark number density, driven by the de Haas van Alphen effect, reflect the quantized behavior of quarks in a magnetic field. Similarly, the magnetization displays oscillatory behavior, driven by the sequential filling of Landau levels. At lower external magnetic field strengths, contributions from orbital angular momentum and the population of higher Landau levels further modulate these oscillations. These results provide deeper insights into the thermodynamic and magnetic properties of quark matter under strong magnetic fields, with implications for astrophysical studies.

hep-ph↗

arXiv2024

Surface and curvature tensions of cold dense quark matter: a term-by-term analysis within the Nambu-Jona-Lasinio model

In this paper, we conduct a thorough investigation of the surface and curvature tensions, $σ$ and $γ$, of three-flavor cold quark matter using the Nambu-Jona-Lasinio (NJL) model with vector interactions. Our approach ensures both local and global electric charge neutrality, as well as chemical equilibrium under weak interactions. By employing the multiple reflection expansion formalism to account for finite size effects, we explore the impact of specific input parameters, particularly the vector coupling constant ratio $η_V$, the radius $R$ of quark matter droplets, as well as charge-per-baryon ratio $ξ$ of the finite size configurations. We focus on the role of the contributions of each term of the NJL Lagrangian to the surface and curvature tensions in the mean field approximation. We find that the total surface tension exhibits two different density regimes: it remains roughly constant at around $100 \, \mathrm{MeV \, fm^{-2}}$ up to approximately $2-4$ times the nuclear saturation density, and beyond this point, it becomes a steeply increasing function of $n_B$. The total surface and curvature tensions are relatively insensitive to variations in $R$ but are affected by changes in $ξ$ and $η_V$. We observe that the largest contribution to $σ$ and $γ$ comes from the regularized divergent term, making these quantities significantly higher than those obtained within the MIT bag model.

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arXiv2024

Strange quark stars: the role of excluded volume effects

We study cold strange quark stars employing an enhanced version of the quark-mass density-dependent model which incorporates excluded volume effects to address non-perturbative QCD repulsive interactions. We provide a comparative analysis of our mass formula parametrization with previous models from the literature. We identify the regions within the parameter space where three-flavor quark matter is more stable than the most tightly bound atomic nucleus (stability window). Specifically, we show that excluded volume effects do not change the Gibbs free energy per baryon at zero pressure, rendering the stability window unaffected. The curves of pressure versus energy density exhibit various shapes -- convex upward, concave downward, or nearly linear -- depending on the mass parametrization. This behavior results in different patterns of increase, decrease, or constancy in the speed of sound as a function of baryon number density. We analyze the mass-radius relationship of strange quark stars, revealing a significant increase in maximum gravitational mass and a shift in the curves towards larger radii as the excluded volume effect intensifies. Excluded volume effects render our models compatible with all modern astrophysical constraints, including the properties of the recently observed low-mass compact object HESSJ1731.

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arXiv2024

Thermal twin stars within a hybrid equation of state based on a nonlocal chiral quark model compatible with modern astrophysical observations

We investigate the extension to finite temperatures and neutrino chemical potentials of a recently developed nonlocal chiral quark model approach to the equation of state of neutron star matter. We consider two light quark flavors and current-current interactions in the scalar-pseudoscalar, vector, and diquark pairing channels, where the nonlocality of the currents is taken into account by a Gaussian form factor that depends on the spatial components of the 4-momentum. Within this framework, we analyze order parameters, critical temperatures, phase diagrams, equations of state, and mass-radius relations for different temperatures and neutrino chemical potentials. For parameters of the model that are constrained by recent multi-messenger observations of neutron stars, we find that the mass-radius diagram for isothermal hybrid star sequences exhibits the thermal twin phenomenon for temperatures above 30 MeV.

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arXiv2023

Excluded volume effects in the quark-mass density-dependent model: implications for the equation of state and compact star structure

We present a significant extension of the quark mass density-dependent model (QMDDM), initially revised in our prior study (Lugones and Grunfeld, Phys. Rev. D 107, 043025 (2023)), where thermodynamic inconsistencies were addressed. Our current work enriches the QMDDM by incorporating excluded volume effects, as a step towards a more realistic representation of the quark matter equation of state (EOS) at zero temperature. We introduce the concept of ``available volume'' in the Helmholtz free energy formulation, accounting for the space excluded by each quasiparticle due to its finite size or repulsive interactions. We present a methodology to modify the EOS for point-like particles, allowing for a simple and direct incorporation of excluded volume effects. This is first addressed in a simple one-flavor model and then extended to a more realistic three-flavor system, incorporating both mass and volume dependencies on the baryon number density. We examine various ansatzes for the excluded volume, ultimately adopting one that aligns with the asymptotic freedom behavior of Quantum Chromodynamics (QCD). The EOS for electrically neutral systems in chemical equilibrium is computed, focusing on self-bound and hybrid matter scenarios. We show that the incorporation of excluded volume effects renders the EOS stiffer and that excluded volume effects are essential to align the mass-radius relation of self-bound and hybrid stars with modern astrophysical constraints.

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arXiv2023

$T {-} μ$ quark matter phase transitions and critical end point in nonlocal PNJL models

We study the $T {-} μ$ phase diagram of quark matter under the influence of a strong uniform magnetic field in the framework of a nonlocal extension of the Polyakov Nambu Jona Lasinio model (PNJL). The existence of a critical end point (CEP) is found for the whole considered range of the magnetic field (up to 1 $GeV^{2}$). We analyze the location of this CEP as a function of the external field and discuss the presence of inverse magnetic catalysis for nonzero chemical potentials. Our results show that the temperature of the CEP decreases with the magnetic field, in contrast to the behavior observed in local NJL/PNJL models.

hep-ph↗

arXiv2023

Cold dense quark matter with phenomenological medium effects: a self-consistent formulation of the quark-mass density-dependent model

We revisit the quark-mass density-dependent model -- a phenomenological equation of state for deconfined quark matter in the high-density low-temperature regime -- and show that thermodynamic inconsistencies that have plagued the model for decades, can be solved if the model is formulated in the canonical ensemble instead of the grand canonical one. Within the new formulation, the minimum of the energy per baryon occurs at zero pressure, and the Euler's relation is verified. Adopting a typical mass-formula, we first analyze in detail a simple model with one particle species. We show that a ``bag'' term that produces quark confinement naturally appears in the pressure (and not in the energy density) due to density dependence of the quark masses. Additionally, the chemical potential gains a new term as in other models with quark repulsive interactions. Then, we extend the formalism to the astrophysically realistic case of charge-neutral three-flavor quark matter in equilibrium under weak interactions, focusing on two different mass formulae: a flavor dependent and a flavor blind one. For these two models, we derive the equation of state and analyze its behavior for several parameter choices. We systematically analyze the parameter space and identify the regions corresponding to self-bound 2-flavor and 3-flavor quark matter, hybrid matter and causal behavior.

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arXiv2022

Quark matter phase diagram under the influence of strong magnetic fields with a nonlocal chiral model

We study the phase diagram in the $T-μ$ plane for quark matter under the influence of a strong uniform magnetic field $\vec{B}$, in the framework of a non-local extension of the two-flavor Polyakov Nambu-Jona-Lasinio model. We analyze the deconfinement and chiral symmetry restoration transitions in the mean field approximation. For the considered parameterization, it is found that there is always a critical end point (CEP) in the $T-μ$ plane that separates a first-order transition line from a smooth crossover. The location of the CEP is studied as a function of the magnetic field.

hep-ph↗

arXiv2022

Quark-nuclear hybrid equation of state for neutron stars under modern observational constraints

We study a family of equations of state for hybrid neutron star matter. The hybrid EOS are obtained by a Maxwell construction of the first-order phase transition between a hadronic phase described by the relativistic density-functional EOS of the "DD2" class with excluded volume effects and a deconfined quark matter phase modeled by an instantaneous nonlocal version of the Nambu-Jona-Lasinio model in SU(2)$_f$ with vector interactions and color superconductivity. The form factor in the nonlocal quark matter model is fitted to lattice QCD results in the Coulomb gauge. Owing to strong coupling in the vector meson and diquark channels, a coexistence phase of color superconductivity and chiral symmetry breaking occurs. Our results show an approximately constant behavior for the squared speed of sound with values of 0.4 - 0.6 in the density region relevant for neutron star interiors. To simultaneously fulfill the constraints from the Neutron Star Interior Composition Explorer radius measurement for PSR J0740+6620 and tidal deformability from GW170817 it is necessary to consider a $μ$-dependent bag pressure that mimics confinement.

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arXiv2021

Vector interactions inhibit quark-hadron mixed phases in neutron stars

We investigate the surface tension $σ$ and the curvature energy $γ$ of quark matter drops in the MIT bag model with vector interactions. Finite size corrections to the density of states are implemented by using the multiple reflection expansion (MRE) formalism. We find that $σ$ and $γ$ are strongly enhanced by new terms arising from vector interactions. With respect to the noninteracting case they are increased by a large factor, which can be as high as $\sim 10$ when the vector coupling constant $g$ varies within the range used in the literature. This behavior may have major consequences for the hadron-quark mixed phase speculated to exist at neutron star (NS) interiors, which may be totally suppressed or have its extension substantially reduced.

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arXiv2021

Bayesian analysis of multimessenger M-R data with interpolated hybrid EoS

We introduce a family of equations of state (EoS) for hybrid neutron star (NS) matter that is obtained by a two-zone parabolic interpolation between a soft hadronic EoS at low densities and a set of stiff quark matter EoS at high densities within a finite region of chemical potentials $μ_H < μ< μ_Q$. Fixing the hadronic EoS as the APR one and choosing the color-superconducting, nonlocal NJL model with two free parameters for the quark phase, we perform Bayesian analyses with this two-parameter family of hybrid EoS. Using three different sets of observational constraints that include the mass of PSR J0740+6620, the tidal deformability for GW170817, and the mass-radius relation for PSR J0030+0451 from NICER as obligatory (set 1), while set 2 uses the possible upper limit on the maximum mass from GW170817 as an additional constraint and set 3 instead of the possibility that the lighter object in the asymmetric binary merger GW190814 is a neutron star. We confirm that in any case, the quark matter phase has to be color superconducting with the dimensionless diquark coupling approximately fulfilling the Fierz relation $η_D=0.75$ and the most probable solutions exhibiting a proportionality between $η_D$ and $η_V$, the coupling of the repulsive vector interaction that is required for a sufficiently large maximum mass. We used the Bayesian analysis to investigate with the method of fictitious measurements the consequences of anticipating different radii for the massive $2~M_\odot$ PSR J0740+6220 for the most likely equation of state. With the actual outcome of the NICER radius measurement on PSR J0740+6220 we could conclude that for the most likely hybrid star EoS would not support a maximum mass as large as $2.5~M_\odot$ so that the event GW190814 was a binary black hole merger.

astro-ph.HE↗

arXiv2021

Surface and curvature properties of charged strangelets in compact objects

Droplets of absolutely stable strange quark matter (strangelets) immersed in a lepton background may be the energetically preferred composition of strange star crusts and of the interior of a new class of stars known as strangelet dwarfs. In this work we calculate the surface tension $σ$ and the curvature coefficient $γ$ of charged strangelets as a function of the baryon number density, the temperature, the chemical potential of trapped neutrinos, the strangelet size, the electric potential and the electric charge at their boundary. Strange quark matter in chemical equilibrium and with global electric charge neutrality is described within the MIT bag model. We focus on three different astrophysical scenarios, namely cold strange stars, proto strange stars and post merger strange stars. Finite size effects are implemented within the multiple reflection expansion framework. We find that $σ$ decreases significantly as the strangelet's boundary becomes more positively charged. This occurs because $σ$ is dominated by the contribution of $s$ quarks which are the most massive particles in the system. Negatively charged $s$-quarks are suppressed in strangelets with a large positive electric charge, diminishing their contribution to $σ$ and resulting in smaller values of the total $σ$. We verify that the more extreme astrophysical scenarios, with higher temperatures and higher neutrino chemical potentials, allow higher positive values of the strangelet's electric charge at the boundary and consequently smaller values of $σ$. In contrast, $γ$ is strongly dominated by the density of light ($u$ and $d$) quarks and is quite independent of the charge-per-baryon ratio, the temperature and neutrino trapping. We discuss the relative importance of surface and curvature effects as well as some astrophysical consequences of these results.

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arXiv2021

Cold magnetized quark matter at finite density in a nonlocal chiral quark model

We study the behavior of two-flavor dense quark matter under the influence of an external magnetic field in the framework of a nonlocal chiral quark model with separable interactions. The nonlocality is incorporated in the model by using a Gaussian form factor. It is found that for low and moderate values of magnetic field there is a decrease of the critical chiral restoration chemical potential $μ_c$, i.e. an inverse magnetic catalysis effect is observed. For larger values of $eB$ the behavior of $μ_c$ becomes more or less flat, depending on the parametrization. Within the considered parametrization range we do not find a significant growth of the critical chemical potential for large magnetic fields, as occurs in the case of the local NJL model.

hep-ph↗

arXiv2020

The role of quark matter surface tension in magnetars

In spite of its key role in compact star physics, the surface tension of quark matter is not well comprehended yet. In this work we analyze the behavior of the surface tension of three-flavor quark matter in the outer and inner core of cold deleptonized magnetars, proto magnetars born in core collapse supernovae, and hot magnetars produced in binary neutron stars mergers. We explore the role of temperature, baryon number density, trapped neutrinos, droplet size, and magnetic fields within the multiple reflection expansion formalism. Quark matter is described within the MIT bag model and is assumed to be in chemical equilibrium under weak interactions. We discuss some astrophysical consequences of our results.

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