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Register a new userMass formulas and thermodynamic treatment in the mass-density-dependent model of strange quark matter
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The previous treatments for strange quark matter in the quark mass-density-dependent model have unreasonable vacuum limits. We provide a method to obtain the quark mass parametrizations and give a self-consistent thermodynamic treatment which includes the MIT bag model as an extreme. In this treatment, strange quark matter in bulk still has the possibility of absolute stability. However, the lower density behavior of the sound velocity is opposite to previous findings.
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The ambiguities and inconsistencies in previous thermodynamic treatments for the quark mass density-dependent model are addressed. A new treatment is suggested to obtain the self-consistent results. A new independent variable of effective mass is introduced to make the traditional thermodynamic calculation with partial derivative still practicable. The contribution from physical vacuum has been discussed. We find that the properties of strange quark matter given by quark mass density-dependent model are nearly the same as those obtained by MIT bag model after considering the contribution of the physical vacuum.
The previous thermodynamic treatment for models with density and/or temperature dependent quark masses is shown to be inconsistent with the requirement of fundamental thermodynamics. We therefore study a fully self-consistent one according to the fundamental differential equation of thermodynamics. After obtaining a new quark mass scaling with the inclusion of both confinement and leading-order perturbative interactions, we investigate properties of strange quark matter in the fully consistent thermodynamic treatment. It is found that the equation of state become stiffer, and accordingly, the maximum mass of strange stars is as large as about 2 times the solar mass, if strange quark matter is absolutely or metastable.
We study the interface effects in strangelets adopting mean-field approximation (MFA). Based on an equivparticle model, the linear confinement and leading-order perturbative interactions are included with density-dependent quark masses. By increasing the confinement strength, the surface tension and curvature term of strange quark matter (SQM) become larger, while the perturbative interaction does the opposite. For those parameters constrained according to the 2$M_odot$ strange star, the surface tension is $sim$2.4 MeV/fm${}^2$, while unstable SQM indicates a slightly larger surface tension. The obtained results are then compared with those predicted by the multiple reflection expansion (MRE) method. In contrast to the bag model case, it is found that MRE method overestimates the surface tension and underestimates the curvature term. To reproduce our results, the density of states in the MRE approach should be modified by proper damping factors.
The improved quark mass density- dependent model, which has been successfully used to describe the properties of both finite nuclei and bulk nuclear matter, is extended to include the strange quark. The parameters of the model are determined by the saturation properties of bulk matter. Then the given parameter set is employed to investigate both the properties of strange hadronic matter and those of $Lambda$ hypernuclei. Bulk strange hadronic matter consisting of nucleons, $Lambda$- hyperons and $Xi$- hyperons is studied under mean-field approximation. Among others, density dependence of the effective baryon mass, saturation properties and stability of the physical system are discussed. For single-$Lambda$ hypernuclei, single particle energies of $Lambda$ hyperon is evaluated. In particular, it is found that the present model produces a small spin-orbit interaction, which is in agreement with the experimental observations. The above results show that the present model can consistently describe the properties of strange hadronic matter, as well as those of single $Lambda$ hypernuclei within an uniform parameterization.
Correlations between the strange quark mass, strange quark condensate $langle bar s srangle$, and the kaon partially conserved axial current (PCAC) relation are developed. The key dimensionless and renormalization-group invariant quantities in these correlations are the ratio of the strange to non-strange quark mass $r_m=m_s/m_q$, the condensate ratio $r_c=langle bar s srangle/langle bar q qrangle$, and the kaon PCAC deviation parameter $r_p=-m_slangle bar s s+bar q qrangle/2f_K^2m_K^2$. The correlations define a self-consistent trajectory in the ${r_m,r_c,r_p}$ parameter space constraining strange quark parameters that can be used to assess the compatibility of different predictions of these parameters. Combining the constraint with Particle Data Group (PDG) values of $r_m$ results in ${r_c,r_p}$ constraint trajectories that are used to asses the self-consistency of various theoretical determinations of ${r_c,r_p}$. The most precise determinations of $r_c$ and $r_p$ are shown to be mutually consistent with the constraint trajectories and provide improved bounds on $r_p$. In general, the constraint trajectories combined with $r_c$ determinations tend to provide more accurate bounds on $r_p$ than direct determinations. The ${r_c,r_p}$ correlations provide a natural identification of a self-consistent set of strange quark mass and strange quark condensate parameters.
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