Recent observations of massive pulsars having masses of the order of two solar mass pose a new challenge for compact objects such as hybrid stars and neutron stars. Extensions of the bag model and the Nambu-Jona-Lasino model have been used to model these stars to get higher mass stars. Quark matter has been predicted in the cores of these massive stars. In this work we show that an extension of the bag model, with a chemical potential dependent bag parameter can lead to an isentropic phase transition in the core of the neutron star. Our model shows that an EoS having all three quarks $u$, $d$ and $s$ would lead to massive stars with stable quark matter. We find that the mass of the stars not only depends on the bag constant but also on the mass of the strange quark. The mass - radius ratio which determines the redshift values on the surface, indicates that it is possible to obtain stable self bound strange quark matter stars with reasonable values of the bag pressure which correspond to the recent observations of large mass stars.
The electric and magnetic bag radiuses of the proton can be determined by MIT bag model based on electric and magnetic form factors of the proton. Also we determined electric and magnetic root mean squared radiuses of the proton, using of bag radius and compared with other results suggests a suitable compatibility.
We study the effects of the ground state entropy of colored quarks upon the bag pressure at low temperatures. The vacuum expectation values of the quark and gluon fields are used to express the interactions in QCD ground state in the limit of low temperatures and chemical potentials. Apparently, the inclusion of this entropy in the equation of state provides the hadron constituents with an additional heat which causes a decrease in the effective latent heat inside the hadronic bag and consequently decreases the non-perturbative bag pressure. We have considered two types of baryonic bags, $Δ$ a…
The modified quark-meson coupling model, which features a density dependent bag constant and bag radius in nuclear matter, is checked against the EMC effect within the framework of dynamical rescaling. Our emphasis is on the change in the average bag radius in nuclei, as evaluated in a local density approximation, and its implication for the rescaling parameter. We find that when the bag constant in nuclear matter is significantly reduced from its free-space value, the resulting rescaling parameter is in good agreement with that required to explain the observed depletion of the structure funct…
The quark-meson coupling model for nuclear matter, which describes nuclear matter as non-overlapping MIT bags bound by the self-consistent exchange of scalar and vector mesons, is modified by introducing medium modification of the bag constant. We model the density dependence of the bag constant in two different ways: one invokes a direct coupling of the bag constant to the scalar meson field, and the other relates the bag constant to the in-medium nucleon mass. Both models feature a decreasing bag constant with increasing density. We find that when the bag constant is significantly reduced in…
In this article we have calculated the structure properties of a strange quark star in static model in the presence of a strong magnetic field using MIT bag model with a density dependent bag constant. To parameterize the density dependence of bag constant, we have used our results for the lowest order constrained variational calculation of the asymmetric nuclear matter. By calculating the equation of state of strange quark matter, we have shown that the pressure of this system increases by increasing both density and magnetic field. Finally, we have investigated the effect of density dependen…
The effect of magnetic field on the structure properties of hot spin polarized strange quark stars has been investigated. For this purpose, we use the MIT bag model with a density dependent bag constant to calculate the thermodynamic properties of spin polarized strange quark matter such as energy and equation of state. We see that the energy and equation of state of strange quark matter changes significantly in a strong magnetic field. Finally, using our equation of state, we compute the structure of spin polarized strange quark star at different temperatures and magnetic fields.
In this work we study different variations of the MIT bag model. We start with the so called non-ideal bag model and discuss it in detail. Then we implement a vector interaction in the MIT bag model that simulates a meson exchange interaction and fix the quark-meson coupling constants via symmetry group theory. At the end we propose an original model, inspired by the Boguta-Bodmer models, which allows us to control the repulsion interaction at high densities. For each version of the model we obtain a stability window as predicted by the Bodmer-Witten conjecture and discuss its thermodynamic co…
The stability of magnetized strange quark matter (MSQM) is studied in the MIT bag model with the density dependent bag pressure. In the consistent thermodynamic description of MSQM, the quark chemical potentials, the total thermodynamic potential and the anisotropic pressure acquire the corresponding additional term proportional to the density derivative of the bag pressure. The model parameter space is determined, for which MSQM is absolutely stable, i.e., its energy per baryon is less than that of the most stable $^{56}$Fe nucleus under the zero external pressure and vanishing temperature. I…
Recent developments in the density dependence of the MIT bag radius and parameters in nuclear matter are discussed. Starting from the MIT bag lagrangian density, the calculations are specialized for symmetric homogeneous isotropic nuclear matter. A simultaneous description of the density dependence of MIT bag model is derived from the Quantum Hadrodynamics and an extended Quark Meson Coupling model. Results are in agreement with those derived from Scaling Model.
As we go from center toward the surface of a neutron star, the state of baryonic matter changes from the de-confined quark-gluon to a mixed phase of quark and hadronic matter, and a thin crust of hadronic matter. For the quark matter, within MIT bag model, the total energy density of the system is the kinetic energy for non-interacting quarks plus a bag constant. In this article first we have considered a density dependent bag constant obtained using the recent experimental results of CERN SPS on the formation of a quark-gluon plasma. For calculations of the hadron phase, we use the lowest ord…
We study the effect of a very strong homogeneous magnetic field B on the thermal deconfinement transition within the simplest phenomenological approach: the MIT bag pressure for the quark- gluon plasma and a gas of pions for the hadronic sector. Even though the model is known to be crude in numerical precision and misses the correct nature of the (crossover) transition, it provides a simple setup for the discussion of some subtleties of vacuum and thermal contributions in each phase, and should provide a reasonable qualitative description of the critical temperature in the presence of B. We fi…
Using the volume coupling version of the cloudy bag model, the quark-meson coupling model is extended to study the role of pion field and the properties of nuclear matter. The extended model includes the effect of gluon exchange as well as the pion-cloud effect, and provides a good description of the nuclear matter properties. The relationship between the extended model and the EFT approach to nuclear matter is also discussed.
If instantons are introduced into the MIT bag model in such a way that bag radii are allowed to vary, the MIT bag interior can accommodate instanton density which is by an order of magnitude larger than in the case when the radii are fixed (although it is still significantly smaller than in the nonperturbative QCD vacuum). The instanton contribution to baryon mass shifts is also correspondingly larger. The instanton-induced part of the scalar strangeness of the nucleon MIT bag is an order of magnitude larger than found previously, within the linearized approximation. The decrease of the model …
The improved quark mass density-dependent model (IQMDD) based on soliton bag model is studied at finite temperature. Appling the finite temperature field theory, the effective potential of the IQMDD model and the bag constant $B(T)$ have been calculated at different temperatures. It is shown that there is a critical temperature $T_{C}\simeq 110 \mathrm{MeV}$. We also calculate the soliton solutions of the IQMDD model at finite tmperature. It turns out that when $T<T_{C}$, there is a bag constant $B(T)$ and the soliton solutions are stable. However, when $T>T_{C}$ the bag constant $B(T)=0$ and …
The quark-meson coupling (QMC) model for nuclear matter, which describes nuclear matter as non-overlapping MIT bags bound by the self-consistent exchange of scalar and vector mesons is modified by the introduction of a density dependent bag constant. The density dependence of the bag constant is related to that of the in-medium effective nucleon mass through a scaling ansatz suggested by partial chiral symmetry restoration in nuclear matter. This modification overcomes drawbacks of the QMC model and leads to the recovery of the essential features of relativistic nuclear phenomenology. This sug…
In the present work we use the modified versions of the MIT bag model, on which both a vector field and a self-interacting term are introduced, to obtain hot quark matter and to investigate the QCD phase diagram. We first analyze two-flavored quark matter constrained to both the freeze-out and the liquid-gas phase transition at the hadronic phase. Later, three-flavored quark matter subject to $β$ equilibrium and charge neutrality is used to compute quark star macroscopic properties, which are confronted with recent observational massive and canonical star radius results. Finally, a comparison …
A method for obtaining the low chemical potential dependence of the dressed quark propagator from an effective quark-quark interaction model is developed. From this the chemical potential dependence of the chiral quark condensate and bag constant are evaluated. It is found that the chiral order parameter decreases with the increasing chemical potential $μ$, which is qualitatively different from the results given by some authors in the literature. The reason for this discrepancy is discussed.
We study the hadron-quark phase transition in the interior of neutron stars (NS). For the hadronic sector, we use a microscopic equation of state (EOS) involving nucleons and hyperons derived within the Brueckner-Bethe-Goldstone many-body theory, with realistic two-body and three-body forces. For the description of quark matter, we employ both the MIT bag model with a density dependent bag constant, and the color dielectric model. We calculate the structure of NS interiors with the EOS comprising both phases, and we find that the NS maximum masses are never larger than 1.7 solar masses, no mat…
In this paper, incorporating the property of the vacuum negative pressure, namely, the bag constant, we presented a new model of the equation of state (EOS) of quark matter at finite chemical potential and zero temperature. By comparing our EOS with Fraga {\it et~al.}'s EOS and SQM1 model, one find that our EOS is softer than Fraga {\it et~al.}'s EOS and SQM1 model. The reason for this difference is analyzed. With these results we investigate the structure of quark star. A comparison between our model of quark star and other models is made. The obtained mass of quark star is $ 1.3 \sim 1.66 M_…
A self-consistent description of the MIT bag parameters as functions of the nuclear matter density is presented. The subnuclear degrees of freedom are treated in the Quark-Meson Coupling Model, considering the equilibrium conditions for the bag in the nuclear medium. The hadronic interaction is described in the framework of the quantum field theory of hadrons through several models. We have obtained the behavior of the bag radius and the bag parameters $B$ and $z_0$, taking their derivatives with respect to the mean field value of the scalar meson as free parameters. A discussion on the variat…
In this work we revisit the MIT bag model to describe quark matter within both the usual Fermi-Dirac and the Tsallis statistics. We verify the effects of the non-additivity of the latter by analysing two different pictures: the first order phase transition of the QCD phase diagram and stellar matter properties. While, the QCD phase diagram is visually affected by the Tsallis statistics, the resulting effects on quark star macroscopic properties are barely noticed.
We study the gluon polarization contribution at the quark model renormalization scale to the proton spin, $Γ$, in the chiral bag model. It is evaluated by taking the expectation value of the forward matrix element of a local gluon operator in the axial gauge $A^+=0$. It is shown that the confining boundary condition for the color electric field plays an important role. When a solution satisfying the boundary condition for the color electric field, which is not the conventionally used but which we favor, is used, the $Γ$ has a positive value for {\it all} bag radii and its magnitude is comparab…
Short-range quark-quark correlations in hot nuclear matter are examined within the modified quark-meson coupling model (MQMC) by adding repulsive scalar and vector quark-quark interactions. Without these correlations, the bag radius increases with the baryon density. However when the correlations are introduced the bag size shrinks as the bags overlap. Also as the strength of the scalar quark-quark correlation is increased, the decrease of the effective nucleon mass $M^{*}_N$ with the baryonic density is slowed down and tends to saturate at high densities. Within this model we study the phase …
We prove that when the bag surface is allowed to move radially, the equations of motion derived from the MIT bag Lagrangian with massless quarks and a spherical boundary admit only one solution, which corresponds to a bag expanding at the speed of light. This result implies that some new physics ingredients, such as coupling to meson fields, are needed to make the dynamical bag a consistent model of hadrons.
At $ T = 0 $ the surface tension $ σ^{1/3} $ in the MIT bag model for a single hadron is known to be negligible as compared to the bag pressure $ B^{1/4}$. We show that at finite temperature it has a substantial value of 50 - 70 MeV which also differ from hadron to hadron. We also find that the dynamics of the Quark-Gluon Plasma is such that the creation of hybrids $(s\bar{s}g)$ with massive quarks will predominate over the creation of $ (s\bar{s}) $ mesons.
A commonly applied quark matter model in astrophysics is the thermodynamic bag model (tdBAG). The original MIT bag model approximates the effect of quark confinement, but does not explicitly account for the breaking of chiral symmetry, an important property of Quantum Chromodynamics (QCD). It further ignores vector repulsion. The vector-interaction-enhanced bag model (vBag) improves the tdBAG approach by accounting for both dynamical chiral symmetry breaking and repulsive vector interactions. The latter is of particular importance to studies of dense matter in beta-equilibriumto explain the tw…
We considered the quark-meson coupling model for a nucleon. The model describes a nucleon as an MIT bag, in which quarks are coupled to the scalar and the vector mesons. A set of coupled equations for the quark and the meson fields are obtained and are solved in a self-consistent manner. We show that the mass of a dressed MIT bag interacting with $σ$- and $ω$-meson fields differs considerably from the mass of the free MIT bag. The effects of the density-dependent bag constant are investigated. The results of our calculations imply that the self-energy of the bag in the quark-meson coupling mod…
The radiative capture process $n p \to d γ$ is considered within the framework of a recently developed six-quark dressed-bag model for the nucleon-nucleon interaction. The calculations presented here include both the nucleon current and the meson-exchange current contributions. The latter uses short-range hadronic form factors for the pion exchange currents consistent with the soft cut-off parameter $Λ_{πNN}$ from the $NN$-potential. Contributions of the pion exchange current and $Δ$-isobar current to the total cross section still cannot explain the discrepancy between the theoretical and expe…
Possible variations of the quark-meson coupling (QMC) model are examined in which the bag constant decreases in the nuclear medium. The reduction is supposed to depend on either the mean scalar field or the effective mass of the nucleon. It is shown that the electric and magnetic radii of the bound nucleon are almost linearly correlated with the bag constant. Using the fact that the size of the bound nucleon inside a nucleus is strongly constrained by $y$-scaling data in quasielastic, electron-nucleus scattering, we set a limit for the reduction allowed in the bag constant for these two models…
We propose the new quark mean-field bag (QMFB) model by incorporating the bag confinement mechanism in the original quark mean-field model. Nuclear matter and neutron star properties are studied with the QMFB model. For the study of the bag effect, we newly fit 12 parameter sets by reproducing the empirical saturation properties of nuclear matter. Quark confinement is found to be mainly demonstrated by the bag after it is included in the model, instead of the confining potential. For nuclear matter, the bag decreases the binding energy and increases the symmetry energy. For neutron star, the b…
Using the quark-meson coupling model with the cloudy bag, we construct the equation of state for neutron stars with hyperons in SU(3) flavor symmetry. The hyperfine interaction due to the gluon exchange and the pion-cloud effect inside a baryon is taken into account in vacuum and nuclear matter. We investigate how the quark degrees of freedom and the exchanges of gluon and pion between two quarks affect the properties of nuclear and neutron-star matter. It is found that the variation of baryon substructure in matter plays an important role in supporting massive neutron stars.
The effects of quantum entropy on the bag constant are studied at low temperatures and small chemical potentials. The inclusion of the quantum entropy of the quarks in the equation of state provides the hadronic bag with an additional heat which causes a decrease in the effective latent heat inside the bag. We have considered two types of baryonic bags, $Δ$ and $Ω^-$. In both cases we have found that the bag constant without the quantum entropy almost does not change with the temperature and the quark chemical potential. The contribution from the quantum entropy to the equation of state clearl…
The quark-meson coupling model for a nucleon is considered. The model describes a nucleon as an MIT bag, in which quarks are coupled to scalar and vector mesons. A set of coupled equations for the quark and the meson fields are obtained and are solved in a self-consistent way. It is shown that the mass of a nucleon as a dressed MIT bag interacting with sigma- and omega-meson fields significantly differs from the mass of a free MIT bag. A few sets of model parameters are obtained so that the mass of a dressed MIT bag becomes the nucleon mass. The results of our calculations imply that the self-…
In 1991, we proposed a model in which nucleus is treated as a spherical symmetric MIT bag and nucleon satisfies the MIT bag model boundary condition. The model was employed to calculate nuclear magnetic moments. The results are in good agreement with experiment data. Now, we found this model is still interesting and illuminating.
The rate of quark-gluon plasma droplet nucleation in superheated hadronic matter is calculated within the MIT bag model. The requirements of color singletness and (to less extent) fixed momentum suppress the nucleation rate by many orders of magnitude, making thermal nucleation of quark-gluon plasma droplets unlikely in ultrarelativistic heavy-ion collisions if the transition is first order and reasonably described by the bag model.
In this paper, we investigate the newborn strange quark stars with constant entropy. We also use the MIT bag model to calculate the thermodynamic properties in two cases; the density-dependent bag constant and the fixed bag constant (B = 90 MeV). We show that the equation of state becomes stiffer by using the density dependent bag constant and by increasing the entropy. Furthermore, we show that the adiabatic index of the system reaches to 4/3 at high densities. Later, we calculate the structure of a strange quark star using the equation of state and the general relativistic equations of hydro…
An ansatz for the curvature contribution to the density of states for massive quarks in a bag is given and shown to reproduce exact mode-filling calculations. A mass-formula for spherical lumps of 3-flavor quark matter is derived self-consistently from an asymptotic expansion within the MIT bag model, taking into account bulk, surface, and curvature contributions. Shell model calculations are performed for a variety of strange quark masses and bag constants, and the results shown to match nicely with the asymptotic expansion.
We reevaluate a quark model prediction using the new QCD evolution function calculated to the 3 loop order and conclude that this model compares favorably with the new experimental results.
We evaluate the nucleon sigma term and in-medium quark condensate in the modified quark-meson coupling model which features a density-dependent bag constant. We obtain a nucleon sigma term consistent with its empirical value, which requires a significant reduction of the bag constant in the nuclear medium similar to those found in the previous works. The resulting in-medium quark condensate at low densities agrees well with the model independent linear order result. At higher densities, the magnitude of the in-medium quark condensate tends to increase, indicating no tendency toward chiral symm…
Density-dependent relations among saturation properties of symmetric nuclear matter and hyperonic matter, properties of hadron-(strange) quark hybrid stars are discussed by applying the conserving nonlinear $σ$-$ω$-$ρ$ hadronic mean-field theory. Nonlinear interactions that will be renormalized as effective coupling constants, effective masses and sources of equations of motion are constructed self-consistently by maintaining thermodynamic consistency to the mean-field approximation. The coupling constants expected from the hadronic mean-field model and SU(6) quark model for the vector couplin…
We investigate the properties of an antikaon in medium, regarding itas a MIT bag. We first construct the MIT bag model for a kaon with$σ^*$ and $ϕ$ in order to describe the interaction of$s$-quarks in hyperonic matter in the framework of the modifiedquark-meson coupling model. The coupling constant $g'^{B_K}_σ$in the density-dependent bag constant $B(σ)$ is treated as afree parameter to reproduce the optical potential of a kaon in asymmetric matter and all other couplings are determined by usingSU(6) symmetry and the quark counting rule. With various values ofthe kaon potential, we calculate t…
The effect of model parameters in the equation of state for quark matter on the magnitude of the maximum mass of hybrid stars is examined. Quark matter is described in terms of the extended MIT bag model including corrections for one-gluon exchange. For nucleon matter in the range of densities corresponding to the phase transition, a relativistic equation of state is used that is calculated with two particle correlations taken into account based on using the Bonn meson-exchange potential. The Maxwell construction is used to calculate the characteristics of the first order phase transition and …
The QCD equation of state at finite temperature and densities of conserved charges is considered in the framework of a Hagedorn bag-like model, incorporating both the finite sizes of hadrons as well as their exponential mass spectrum. Augmented with non-zero masses of quarks and gluons in the bag spectrum, the model yields a fair quantitative description of lattice data on thermodynamic functions, the conserved charges susceptibilities, and Fourier coefficients of net-baryon density. Both at zero and finite baryon densities a broad crossover transition between hadronic and quark-gluon matter i…
We study the hadron-quark phase transition in the interior of protoneutron stars. For the hadronic sector, we use a microscopic equation of state involving nucleons and hyperons derived within the finite-temperature Brueckner-Bethe-Goldstone many-body theory, with realistic two-body and three-body forces. For the description of quark matter, we employ the MIT bag model both with a constant and a density-dependent bag parameter. We calculate the structure of protostars with the equation of state comprising both phases and find maximum masses below 1.6 solar masses. Metastable heavy hybrid proto…
The typical transverse momentum of a quark in the proton is a basic property of any QCD based model of nucleon structure. However, calculations in phenomenological models typically give rather small values of transverse momenta, which are difficult to reconcile with the larger values observed in high energy experiments such as Drell-Yan reactions and Semi-inclusive deep inelastic scattering. In this letter we calculate the leading twist transverse momentum dependent distribution functions (TMDs) using a generalization of the Adelaide group's relativistic formalism that has previously given goo…
We analyze the effect of color superconductivity in the transition from hot hadron matter to quark matter in the presence of a gas of trapped electron neutrinos. We adopt a two-phase picture in which the hadronic phase is described trough a nonlinear Walecka model and just deconfined matter through the MIT bag model including color superconductivity. We compare the present results with those obtained within the NJL model.
The $p{}^4He$ elastic scattering at the energy range from 0.695 to 393 GeV is analyzed in the framework of the Glauber theory. The Glauber amplitudes were evaluated using isospin-averaged nucleon-nucleon amplitudes and the ${}^4He$ wave function as a superposition of the Gaussian functions. The values of the calculated differential cross sections usually exceed the experimental ones. In order to overcome the discrepancy, it is assumed following to the paper by L.G. Dakno and N.N. Nikolaev (Nucl. Phys. {\bf A436} (1985) 653) that the ground state wave function of ${}^4He$ has an admixture of a …
Hadronic matter undergoes a deconfinement transition to quark matter at high temperature and/or high density. It would be realized in collapsing cores of massive stars. In the framework of MIT bag model, the ambiguities of the interaction are encapsulated in the bag constant. Some progenitor stars that invoke the core collapses explode as supernovae, and other ones become black holes. The fates of core collapses are investigated for various cases. Equations of state including the hadron-quark phase transition are constructed for the cases of the bag constant B=90, 150 and 250 MeV fm^{-3}. To d…
We consider the transition from quark to hadronic matter which may result during the cooling/expansion of the quark-gluon plasma formed in energetic collisions of weakly isospin-asymmetric ions. This transition involves the energy density of u and d quark matter and the one of nearly isospin-symmetric nuclear matter. Within bag models, the former entails knowledge of the bag pressure, a poorly constrained quantity. The bag pressure at high density can be fixed imposing equality of quark and nucleonic energy densities at the (assumed known) transition point. We find this value to be very model …
The He-4 d elastic scattering at the momentum of 19.8 GeV/c is analyzed in the framework of the Glauber theory. The scattering amplitude was evaluated using different sets of values of the nucleon-nucleon amplitude parameters and the He-4 density function as a superposition of the Gaussian functions. It is shown that it is impossible to describe simultaneously the pHe-4 and dHe-4 elastic scattering cross sections using the same set of the NN-amplitude parameters. Inclusion of the twelve quark bag admixture to the ground state of the He-4 nucleus in the calculations allows one to reproduce the …
Leading and subleading twist transverse momentum dependent parton distribution functions (TMDs) are studied in a quark model framework provided by the bag model. A complete set of relations among different TMDs is derived, and the question is discussed how model-(in)dependent such relations are. A connection of the pretzelosity distribution and quark orbital angular momentum is derived.
We have studied strange quark stars in the framework of the MIT bag model, allowing the bag parameter B to depend on the density of the medium. We have also studied the effect of Cooper pairing among quarks, on the stellar structure. Comparison of these two effects shows that the former is generally more significant. We studied the resulting equation of state of the quark matter, stellar mass-radius relation, mass-central-density relation, radius-central-density relation, and the variation of the density as a function of the distance from the centre of the star. We found that the density-depen…
The Quark Meson Coupling Model which describes nuclear matter as a collection of non-overlapping MIT bags interacting by the self-consistent exchange of scalar and vector mesons is used to study nuclear matter at finite temperature. In its modified version, the density dependence of the bag constant is introduced by a direct coupling between the bag constant and the scalar mean field. In the present work, the coupling of the scalar mean field with the constituent quarks is considered exactly through the solution of the Dirac equation. Our results show that a phase transition takes place at a c…
The quark-meson coupling (QMC) model for nuclear matter, which describes nuclear matter as non-overlapping MIT bags bound by the self-consistent exchange of scalar and vector mesons is modified by the introduction of a density dependent bag constant. It is found that when the bag constant is significantly reduced in nuclear medium with respect to its free space value, large canceling isoscalar Lorentz scalar and vector potentials for the nucleon in nuclear matter emerge naturally. Such potentials are comparable to those suggested by relativistic nuclear phenomenology. This suggests that the mo…
