We study the hadron-quark mixed phase within a two-phase model for symmetric and asymmetric matter. For the quark sector we employ the (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>2</mn><mo>+</mo><mn>1</mn></mrow></math>) Polyakov-extended Nambu–Jona-Lasinio model (PNJL) with vector interactions. We investigate how the hadronic equation of state affects the phase diagram and the thermodynamic properties inside the mixed phase. The behavior of isentropic trajectories in the mixed phase depends on the fixed entropy per baryon (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>s</mi><mo>/</mo><msub><mi>ρ</mi><mi>B</mi></msub></math>), with trajectories near the critical end point (CEP) exhibiting a pronounced cooling pattern, while isentropic trajectories with low entropy per baryon undergo pronounced heating as the baryonic density increases. The adiabatic squared speed of sound displays characteristic peak and dip structures that depend on <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>s</mi><mo>/</mo><msub><mi>ρ</mi><mi>B</mi></msub></math>. The polytropic index along isentropic and isothermal trajectories, including in the vicinity of the CEP are also investigated. The effects of vector interactions and isospin asymmetry on thermodynamic observables likewise depend on the chosen <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>s</mi><mo>/</mo><msub><mi>ρ</mi><mi>B</mi></msub></math> value. Finally, we discuss the population of hyperons along isentropic trajectories and their influence on the phase diagram. The main effect of hyperons is to shift the onset of deconfinement to larger densities and decrease the density extension of the mixed phase.

Portugal

Eduardo L.G. Salgado

Pedro Costa

Constança Providência

Isentropic thermodynamics across the hadron-quark mixed phase in a two-phase model with a PNJL quark description

We employ the renormalization group optimized perturbation theory (RGOPT) resummation method to evaluate the equation of state (EoS) for strange (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>f</mi></msub><mo>=</mo><mn>2</mn><mo>+</mo><mn>1</mn></math>) and nonstrange (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>f</mi></msub><mo>=</mo><mn>2</mn></math>) cold quark matter at next-to-leading order. 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 next-to-next-to-leading order. Choosing the renormalization scale to generate maximum star masses of order <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>M</mi><mo>=</mo><mn>2</mn><mo>−</mo><mn>2.6</mn><msub><mi>M</mi><mo stretchy="false">⊙</mo></msub></math>, 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.

United States

Brazil

Tulio E. Restrepo

France

Jean-Loïc Kneur

Marcus Benghi Pinto

Comparing strange and nonstrange quark stars within resummed QCD at NLO

We have conducted an extensive study using a diverse set of equations of state (EoSs) to uncover strong relationships between neutron star (NS) observables and the underlying EoS parameters using symbolic regression method. These EoS models, derived from a mix of agnostic and physics-based approaches, considered neutron stars composed of nucleons, hyperons, and other exotic degrees of freedom in beta equilibrium. The maximum mass of a NS is found to be strongly correlated with the pressure and baryon density at an energy density of approximately 800 MeV.fm &#8722;3. We have also demonstrated that the EoS can be expressed as a function of radius and tidal deformability within the NS mass range 1-2 <math altimg='si1.svg'><msub><mrow><mi>M</mi></mrow><mrow><mo>&#8857;</mo></mrow></msub></math>. These insights offer a promising and efficient framework to decode the dense matter EoS directly from the accurate knowledge of NS observables.

Hong Kong

India

N.K. Patra

Tuhin Malik

Helena Pais

Germany

Kai Zhou

B.K. Agrawal

Inferring the equation of state from neutron star observables via machine learning

We propose the 3-momentum sphere intersection regularization applied to the one- and two-fermion line integrals at finite temperature and chemical potential. The quark-antiquark polarization function in this new regularization approach is equivalent to the usual 3-momentum regularization, when the absolute value of the external 3-momentum of the polarization is zero. Additionally, it respects the particle-antiparticle symmetry of meson states in the Nambu–Jona-Lasinio (NJL) model for all values of temperature and chemical potential. Without this symmetry, in-medium cross sections calculated in the 3-momentum regularized NJL model are not consistent. To demonstrate the difference between the usual 3-momentum regularization with the one proposed in this work, we study the quark-quark and quark-antiquark cross sections in both regularization schemes. To this end we use the standard <math><mrow><mtext>SU</mtext><mo>(</mo><mn>3</mn><mo>)</mo></mrow></math> NJL model, with four- and six-quark interactions. We observe major quantitative and qualitative differences when comparing quark-quark cross sections in both schemes. The quark-antiquark cross sections, on the other hand, are very similar in both regularizations, owning to the equivalence between the regularizations when the absolute value of the external 3-momentum is zero.

Renan Câmara Pereira

João Moreira

New approach to the 3-momentum regularization of the in-medium one- and two-fermion line integrals with applications to cross sections in the Nambu–Jona-Lasinio model

We investigate the probable existence of dark matter in the interior of neutron stars. Despite the current state of knowledge, the observational properties of neutron stars have not definitively ruled out the possibility of dark matter. Our research endeavors to shed light on this intriguing mystery by examining how certain neutron star properties, including mass, radius, and tidal deformability, might serve as constraints for the dark matter model. In our investigation, we adopt a two-fluid approach to calculate the properties of neutron stars. For the nuclear matter equation-of-state (EOS), we employ several realistic EOS derived from the relativistic mean field model (RMF), each exhibiting varying stiffness and composition. In parallel, we look into the dark matter EOS, considering fermionic matter with repulsive interaction described by a relativistic mean field Lagrangian. A reasonable range of parameters is sampled meticulously. Our study primarily focuses on exploring correlations between the dark matter model parameters and different neutron star properties using a rich set of EOSs. Interestingly, our results reveal a promising correlation between the dark matter model parameters and stellar properties, particularly when we ignore the uncertainties in the nuclear matter EOS. However, when introducing uncertainties in the nuclear sector, the correlation weakens, suggesting that the task of conclusively constraining any particular dark matter model might be challenging using global properties alone, such as mass, radius, and tidal deformability. Notably, we find that dark-matter admixed stars tend to have higher central baryonic density, potentially allowing for non-nucleonic degrees of freedom or direct Urca processes in stars with lower masses. There is also a tantalizing hint regarding the detection of stars with the same mass but different surface temperatures, which may indicate the presence of dark matter. With our robust and extensive dataset, we delve deeper and demonstrate that even in the presence of dark matter, the semiuniversal C-Love relation remains intact. This captivating finding adds another layer of complexity to the interplay between dark matter and neutron star properties.

Prashant Thakur

Poland

Arpan Das

T. K. Jha

Exploring robust correlations between fermionic dark matter model parameters and neutron star properties: A two-fluid perspective

The recently developed resummation technique known as renormalization group optimized perturbation theory (RGOPT) is employed in the evaluation of the equation of state (EOS) describing nonstrange cold quark matter at next-to leading order. 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 next-to-next-to leading order. 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 <math><mrow><mi>M</mi><mo>=</mo><mn>2</mn><mo>−</mo><mn>2.3</mn><msub><mrow><mi>M</mi></mrow><mrow><mo>⊙</mo></mrow></msub></mrow></math>, one obtains a mass-radius curve compatible with the masses and radii of the pulsars PSR <math><mrow><mi>J</mi><mn>0740</mn><mo>+</mo><mn>6620</mn></mrow></math>, PSR <math><mrow><mi>J</mi><mn>0030</mn><mo>+</mo><mn>0451</mn></mrow></math>, 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.

Nonstrange quark stars within resummed QCD

The effect of conserved baryon, isospin, and strangeness charges on the behavior of phase transitions in dense matter is studied. Baryonic matter is described within the three-flavor Polyakov–Nambu–Jona-Lasinio model and several charge fractions <math><msub><mi>Y</mi><mi>Q</mi></msub></math> are considered. The role of the vector interaction, which can be important to describe dense systems, is discussed. Special attention is given to the case with charge fraction <math><msub><mi>Y</mi><mi>Q</mi></msub><mo>=</mo><mn>0.4</mn></math>, due to its importance in heavy-ion collisions and core-collapse supernova matter. It is shown that the possible formation of chiral-symmetric quark matter in the laboratory will be favored in asymmetric matter. Besides, the inclusion of the vector interaction reinforces the formation of quark matter at lower densities.

Role of the conserved charges in the chiral symmetry restoration phase transition

Within the covariant density functional theory of hypernuclear matter we build a series of equations of state for hypernuclear compact stars, by calibrating the coupling constants of the <math><mi>Ξ</mi></math>-hyperon to the experimental binding energy of the single-<math><mi>Ξ</mi></math> hypernuclei <math><mrow><mmultiscripts><mrow><mi>C</mi></mrow><mprescripts></mprescripts><mrow><msup><mrow><mi>Ξ</mi></mrow><mrow><mo>−</mo></mrow></msup></mrow><mrow><mn>15</mn></mrow></mmultiscripts></mrow></math> and <math><mrow><mmultiscripts><mrow><mi>Be</mi></mrow><mprescripts></mprescripts><mrow><msup><mrow><mi>Ξ</mi></mrow><mrow><mo>−</mo></mrow></msup></mrow><mrow><mn>12</mn></mrow></mmultiscripts></mrow></math>. Coupling constants of the <math><mi>Λ</mi></math>-hyperon to nucleons have been calibrated on a vast collection of experimental data on single <math><mi>Λ</mi></math> hypernuclei and we employ those values. Uncertainties on the couplings of the <math><mi>Σ</mi></math>-hyperon to nuclear matter, due to lack of experimental data, are accounted for by allowing for a wide variation of the well depth of <math><mi>Σ</mi></math> at rest in symmetric saturated nuclear matter. To account for uncertainties in the nucleonic sector at densities much larger than <math><msub><mi>n</mi><mn>0</mn></msub></math>, a rich collection of parametrizations is employed, some of them in agreement with existing constraints from nuclear physics and astrophysics. Neutron star properties are investigated with all these calibrated equations of state. The effects of the presence of hyperons on the radius, on the tidal deformability, on the moment of inertia, and on the nucleonic direct Urca process are discussed. The sensitivity of the hyperonic direct Urca processes to uncertainties in the nucleonic and hyperonic sectors is also addressed. It is shown that the relative variations of the radius, tidal deformability and moment of inertia from the values that characterize purely nucleonic stars are linearly correlated with the strangeness fraction. The maximum radius deviation, obtained for most massive neutron stars, is <math><mo>≈</mo><mn>10</mn><mo>%</mo></math>. The reduction of the maximum mass, triggered by nucleation of strangeness, is estimated at <math><mrow><mo>≈</mo><mn>15</mn><mo>%</mo><mi>–</mi><mn>20</mn><mo>%</mo></mrow></math>, out of which 5% comes from insufficient information on the <math><mi>Σ</mi></math>-hyperon interactions. A total of 44 calibrated hyperonic equations of state are published as Supplemental Material.

Morgane Fortin

Romania

Adriana R. Raduta

Sidney Avancini

Relativistic hypernuclear compact stars with calibrated equations of state

In order to obtain the equation of state and construct hybrid stars, we calculate the thermodynamic potential in the two-flavor Nambu–Jona-Lasinio model with tensor-type four-point interaction between quarks. In addition, we impose the <math><mi>β</mi></math> equilibrium and charge neutrality conditions on the system. We show that the tensor condensate appears at large chemical potential, however, it is difficult to hold hybrid stars with two-solar mass by using the equation of state with the tensor interaction. Although we cannot obtain the stars with two-solar mass because of the absence of the repulsive interaction, the estimated magnetic moment density is very large. Therefore, we expect that the tensor interaction describes the magnetic fields of compact stars.

Japan

Hiroaki Matsuoka

Yasuhiko Tsue

João da Providência

Masatoshi Yamamura

Hybrid stars from the NJL model with a tensor interaction

The net-baryon number fluctuations for three-flavor quark matter are computed within the Polyakov extended Nambu–Jona-Lasinio model. Two models with vanishing and nonvanishing vector interactions are considered. While the former predicts a critical endpoint (CEP) in the phase diagram, the latter predicts no CEP. We show that the nonmonotonic behavior of the susceptibilities in the phase diagram is still present even in the absence of a CEP. Therefore, from the nonmonotonic behavior of the susceptibilities solely, one cannot assume the existence of a CEP. We analyze other possible properties that may distinguish the two scenarios, and determine the behavior of the net-baryon number fluctuations and the velocity of sound along several isentropes, with moderate and small values. It is shown that the value of the susceptibilities ratios and the velocity of sound at two or three isentropic lines could possibly allow to distinguish both scenarios, a phase diagram with or without CEP. Smoother behaviors of these quantities may indicate the nonexistence of a CEP. We also discuss the critical behavior of the strange sector.

Márcio Ferreira

Presence of a critical endpoint in the QCD phase diagram from the net-baryon number fluctuations