Scaled Hadron Masses Research Articles

RMF models with $\sigma$-scaled hadron masses and couplings for the description of heavy-ion collisions below 2 A GeV

Within the relativistic mean-field framework with hadron masses and coupling constants dependent on the mean scalar field we study properties of nuclear matter at finite temperatures, baryon densities and isospin asymmetries relevant for heavy-ion collisions at laboratory energies below 2$A$ GeV. Previously constructed (KVORcut-based and MKVOR-based) models for the description of the cold hadron matter, which differ mainly by the density dependence of the nucleon effective mass and symmetry energy, are extended for finite temperatures. The baryon equation of state, which includes nucleons and $\Delta$ resonances is supplemented by the contribution of the pion gas described either by the vacuum dispersion relation or with taking into account the $s$-wave pion-baryon interaction. Distribution of the charge between components is found. Thermodynamical characteristics on $T-n$ plane are considered. The energy-density and entropy-density isotherms are constructed and a dynamical trajectory of the hadron system formed in heavy-ion collisions is described. The effects of taking into account the $\Delta$ isobars and the $s$-wave pion-nucleon interaction on pion differential cross sections, pion to proton and $\pi^-/\pi^+$ ratios are studied. The liquid-gas first-order phase transition is studied within the same models in isospin-symmetric and asymmetric systems. We demonstrate that our models yield thermodynamic characteristics of the phase transition compatible with available experimental results. In addition, we discuss the scaled variance of baryon and electric charge in the phase transition region. Effect of the non-zero surface tension on spatial redistribution of the electric charge is considered for a possible application to heavy-ion collisions at low energies.

Hyperons, Δ resonances and condensate of charged ρ mesons within relativistic mean-field models with scaled hadron masses and couplings

We study equation of state of cold and dense baryon matter within the relativistic mean-field framework with hadron masses and coupling constants dependent on the mean scalar field. Previously constructed models with included hyperons and Δ isobars are extended taking into account possibility of the condensation of charged ρ mesons. We demonstrate that the results obtained in the models with the charged ρ-meson condensation taken into account exhibit a strong model dependence. In some of our (so-called KVORcut-based) models the charged ρ condensation does not significantly affect the value of the neutron star maximum mass. In other (so called MKVOR-based) models the neutron star maximum mass decreases substantially. All thus constructed models pass the observational constraint on the minimal value of the maximum neutron star mass.

The effect of inclusion of Δ resonances in relativistic mean-field model with scaled hadron masses and coupling constants

Knowledge of the equation of state of the baryon matter plays a decisive role in the description of neutron stars. With an increase of the baryon density the filling of Fermi seas of hyperons and Δ isobars becomes possible. Their inclusion into standard relativistic mean-field models results in a strong softening of the equation of state and a lowering of the maximum neutron star mass below the measured values. We extend a relativistic mean-field model with scaled hadron masses and coupling constants developed in our previous works and take into account now not only hyperons but also the Δ isobars. We analyze available empirical information to put constraints on coupling constants of Δs to mesonic mean fields. We show that the resulting equation of state satisfies majority of presently known experimental constraints.

Relativistic mean-field models with scaled hadron masses and couplings: Hyperons and maximum neutron star mass

An equation of state of cold nuclear matter with an arbitrary isotopic composition is studied within a relativistic mean-field approach with hadron masses and coupling constants depending self-consistently on the scalar mean-field. All hadron masses decrease universally with the scalar field growth, whereas meson–nucleon coupling constants can vary differently. More specifically we focus on two modifications of the KVOR model studied previously. One extension of the model (KVORcut) demonstrates that the equation of state stiffens if the increase of the scalar-field magnitude with the density is bounded from above at some value for baryon densities above the saturation nuclear density. This can be realized if the nucleon vector–meson coupling constant changes rapidly as a function of the scalar field slightly above the desired value. The other version of the model (MKVOR) utilizes a smaller value of the nucleon effective mass at the nuclear saturation density and a saturation of the scalar field in the isospin asymmetric matter induced by a strong variation of the nucleon isovector–meson coupling constant as function of the scalar field. A possibility of hyperonization of the matter in neutron star interiors is incorporated. Our equations of state fulfill majority of known empirical constraints including the pressure-density constraint from heavy-ion collisions, direct Urca constraint, gravitational-baryon mass constraint for the pulsar J0737-3039B, and the constraint on the maximum mass of the neutron stars.

Hyperon puzzle and the RMF model with scaled hadron masses and coupling constants

The equation of state of cold baryonic matter is studied within a relativistic mean-field model with hadron masses and coupling constants depending on a scalar field. We demonstrate that if the effective nucleon mass stops to decrease with a density increase at densities n > n*> n0, where n0 is the nuclear saturation density, the equation of state stiffens for these densities and the limiting neutron star mass increases. The stabilization of the nucleon mass can be realised if in the equation of motion for the scalar mean-field there appear a term sharply varying in a narrow vicinity of the field value corresponding to the density n*. We show several possible realizations of this mechanism getting sufficiently stiff equations of state. The appearance of hyperons in dense neutron star interiors is accounted for. The obtained equations of state remain sufficiently stiff if the reduction of the ϕ meson mass is incorporated. Thereby, the hyperon puzzle can be resolved.

Remarks concerning bulk viscosity of hadron matter in relaxation time ansatz

The bulk viscosity is calculated for hadron matter produced in heavy-ion collisions, being described in the relaxation time approximation withi n the relativistic mean- field-based model with scaled hadron masses and couplings. W e show how different approximations used in the literature affect the result. Nume rical evaluations of the bulk viscosity with three considered models deviate not much from each other confirming earlier results.

Viscosity of hadron matter within relativistic mean-field-based model with scaled hadron masses and couplings

The shear ($\eta$) and bulk ($\zeta$) viscosities are calculated in a quasiparticle relaxation time approximation for a hadron matter described within the relativistic mean-field based model with scaled hadron masses and couplings. Comparison with results of other models is presented. We demonstrate that a small value of the shear viscosity to entropy density ratio required for explaining a large elliptic flow observed at RHIC may be reached in the hadron phase. Large values of the bulk viscosity are noted in case of the baryon enriched matter.

Viscosity coefficients for hadron and quark–gluon phases

The shear ( η) and bulk ( ζ) viscosities are calculated in a quasiparticle relaxation time approximation. The hadron phase is described within the relativistic mean-field-based model with scaled hadron masses and couplings. The quark phase is treated in terms of the heavy quark bag model fitted to the lattice data. A two-phase model allowing for the first-order phase transition from the hadron phase to the strongly coupled quark–gluon plasma is constructed by means of the Gibbs conditions. Temperature and baryon density dependence of the calculated viscosity-to-entropy ratios ( η / s , ζ / s ) are analyzed and compared with those obtained in other models. Special attention is paid to the behavior of viscosity coefficients near the critical temperature, from both hadron and quark–gluon side. Effects of resonance widths on viscosities and viscosity-to-entropy ratios are estimated.

Relativistic mean-field model with scaled hadron masses and couplings

Here we continue to elaborate properties of the relativistic mean-field based model (SHMC) proposed in [A.S. Khvorostukhin, V.D. Toneev, D.N. Voskresensky, Nucl. Phys. A 791 (2007) 180] where hadron masses and coupling constants depend on the σ-meson field. The validity of approximations used in this reference is discussed. We additionally incorporate contribution of meson excitations to the equations of motion. We also estimate the effects of the particle width. It is demonstrated that the inclusion of the baryon–baryon hole and baryon–antibaryon loop terms, if performed perturbatively, destroys the consistency of the model.

Equation of state for hot and dense matter: [formula omitted] model with scaled hadron masses and couplings

The proposed earlier relativistic mean-field model with hadron masses and coupling constants depending on the σ-meson field is generalized to finite temperatures. Within this approach we simulate the in-medium behavior of the hadron masses motivated by the Brown–Rho scaling. The high-lying baryon resonances and boson excitations as well as excitations of the σ, ω and ρ fields interacting via mean fields are incorporated into this scheme. Thermodynamic properties of hot and dense hadronic matter are elaborated with the constructed equation of state. Even at zero baryon density, effective masses of σ – ω – ρ – N excitations abruptly drop down for T ≳ 170 MeV and reach zero at a critical temperature T = T c σ ∼ 210 MeV . Below T c σ (at T ∼ 190 MeV ) the specific heat gets a peak like at crossover. We demonstrate that our EoS can be matched with that computed on the lattice for high temperatures provided the baryon resonance couplings with nucleon are partially suppressed. In this case the quark liquid would masquerade as the hadron one. The model is applied to the description of heavy ion collisions in a broad collision energy range. It might be especially helpful for studying phase diagram in the region near possible phase transitions.