Condensate In Nuclear Matter Research Articles

Charmonium mass in nuclear matter

The mass shift of charmonium states in nuclear matter is studied in the perturbative QCD approach. The leading-order effect due to the change of gluon condensate in nuclear matter is evaluated using the leading-order QCD formula, while the higher-twist effect due to the partial restoration of chiral symmetry is estimated using a hadronic model. We find that while the mass of $J/\ensuremath{\psi}$ in nuclear matter decreases only slightly, those of $\ensuremath{\psi}(3686)$ and $\ensuremath{\psi}(3770)$ states are reduced appreciably. Experimental study of the mass shift of charmonium states in nuclear matter can thus provide valuable information on the changes of the QCD vacuum in nuclear medium.

Superfluid states with moving condensate in nuclear matter

Superfluid states of symmetric nuclear matter with finite total momentum of Cooper pairs (nuclear LOFF phase) are studied with the use of Fermi-liquid theory in the model with Skyrme effective forces. It is considered the case of four-fold splitting of the excitation spectrum due to finite superfluid momentum and coupling of T=0 and T=1 pairing channels. It has been shown that at zero temperature the energy gap in triplet-singlet (TS) pairing channel (in spin and isospin spaces) for the SkM$^*$ force demonstrates double-valued behavior as a function of superfluid momentum. As a consequence, the phase transition at the critical superfluid momentum from the LOFF phase to the normal state will be of a first order. Behavior of the energy gap as a function of density for TS pairing channel under increase of superfluid momentum changes from one-valued to universal two-valued. It is shown that two-gap solutions, describing superposition of states with singlet-triplet (ST) and TS pairing of nucleons appear as a result of branching from one-gap ST solution. Comparison of the free energies shows that the state with TS pairing of nucleons is thermodynamically most preferable.

Density dependence of nucleon bag constant, radius and mass in an effective field theory model of QCD

With the global color symmetry model (GCM) being extended to finite chemical potential, the density dependence of the bag constant, the total energy and the radius of a nucleon, as well as the quark condensate in nuclear matter are investigated. A maximal nuclear matter density for the existence of the bag with three quarks confined within is obtained. The calculated results indicate that, before the maximal density is reached, the bag constant, the total energy of a nucleon and the quark condensate decrease gradually, and the radius of a nucleon increases, with the increasing of the nuclear matter density. Nevertheless no sudden change emerges. As the maximal nuclear matter density is reached, a phase transition from nucleons to quarks takes place and the chiral symmetry is restored.

Calculation of Quark Condensate in Nuclear Matter with the Chiral Symmetry Spontaneous Breaking Lagrangian**The project supported in part by National Natural Science Foundation of China

Using the chiral symmetry spontaneous breaking Lagrangian with mean-field approximation, we investigate the in-medium quark condensate . It is found that the condensate decreases as the nuclear matter density increases. Meanwhile, the desent deviates from the linear decrease and becomes remarkably slow as the density of the nuclear matter further increases. It shows that the chiral symmetry spontaneous breaking is only partially restored in densed nuclear matter.

Quark and gluon condensates in nuclear matter with Brown-Rho scaling

Quark and gluon condensates in nuclear matter are investigated in a density-dependent relativistic mean-field theory. The in-medium quark condensate decreases rapidly as the density of nuclear matter increases, if the Brown-Rho scaling is included. The decrease in the in-medium quark condensate with the nuclear matter density is consistent with the result predicted by the partial chiral symmetry restoration. The gluon condensate and the influence of the strange quark contents on the gluon condensate in nuclear matter are discussed.

Saturation from nuclear pion dynamics

We construct an equation-of-state for nuclear matter based on the chiral Lagrangian. The relevant scales are discussed and an effective chiral power expansion scheme, which is constructed to work around the nuclear saturation density, is presented. A realistic equation-of-state is obtained by adjusting one free parameter, when the leading and subleading terms in the expansion are included. The saturation mechanism is due to correlations induced by the one-pion-exchange interaction. Furthermore, we find a substantial deviation from the Fermi-gas estimate of the quark condensate in nuclear matter already at the saturation density.

In-medium QMC model parameters and quark condensate in nuclear matter

A new method is proposed to determine the in-medium QMC model parameters self-consistently. Our results show that the bag constant and the nucleon radius are greatly influenced by nuclear matter. However, the parameter of the zero-point motion keeps its value in vacuum. Then the effects of the in-medium QMC model parameters on the equation of state and the quark condensate in nuclear matter can be calculated systematically.

Chiral symmetry breaking in dense matter

The quark condensate in nuclear matter is studied. We relate it to the nuclear sigma commutator, and then treat it as sigma commutator for quasi- particles in a self-consistent way. We find that the deviation from the linear expression is large at high density.

Chiral dynamics of the nuclear equation of state

We present a new chiral power expansion scheme for the nuclear equation of state. The scheme is effective in the sense that it is constructed to work around nuclear saturation density. The leading and subleading terms are evaluated and are shown to provide an excellent equation of state. As a further application we considered the chiral quark condensate in nuclear matter. Already at nuclear saturation density we predict a substantially smaller reduction of the condensate as compared to conventional approaches.

Is the mean-field approximation reliable for charged boson condensation?

The necessary condition is found that the coherent state assumed in the mean-field approximation is reliable for describing the charged boson condensation. The relevance to the kaon condensation in nuclear matter is also discussed.

QUARK AND GLUON CONDENSATES IN THE QUARK–MESON COUPLING MODEL

Using the quark–meson coupling (QMC) model, we study the density dependence of the quark and gluon condensates in nuclear matter. We show that the change of the quark condensate is mainly driven by the scalar field in the medium and that the reduction of the quark condensate is suppressed at high density, even in the mean-field approximation. The gluon condensate decreases by 4–6% at nuclear saturation density. We also give a simple relationship between the change of the quark condensate and that of a hadron mass in the medium.

Quark condensates in nuclear matter with vacuum effects

On the basis of a bosonized Nambu- Jona-Lasinio (NJL) model with derivative expansions, quark condensates in nuclear matter are studied at one-quark loop level and the dependence of meson masses and couplings on the constituent quark mass is investigated. The condensate ratio obtained here ρB / vac is roughly 0.66 with constituent quark mass of 313 MeV, which yields a corresponding σ N value to be roughly 42.2 MeV at the mean field level and σ N =31.4 MeV with the vacuum dependence, where the model parameters describing a Lorentz scalar and a vector field are self-determined.

Quark condensate in nuclear matter based on nuclear Schwinger-Dyson formalism

The effects of higher order corrections of ring diagrams for the quark condensate are studied by using the bare vertex nuclear Schwinger-Dyson formalism based on {sigma}-{omega} model. The correction of the ring diagrams affects the quark condensate when the {sigma} meson {open_quotes}{sigma} term{close_quotes} is large. {copyright} {ital 1997} {ital The American Physical Society}

Chiral symmetry and QCD sum rules for the nucleon mass in matter

The quark condensate in nuclear matter contains a term of order ϱm π , arising from the contribution of low-momentum virtual pions to the πN sigma commutator. Standard treatments of QCD sum rules for a nucleon in matter generate a similar term in the nucleon effective mass, although this is inconsistent with chiral perturbation theory. We show how an improved treatment of pionic contributions on the phenomenological side of the sum rules can cancel out this unwanted piece. Our results also show that factorisation ansatz for the four-quark condensate cannot be valid in matter.

What does a change in the quark condensate say about restoration of chiral symmetry in matter?

The contribution of nucleons to the quark condensate in nuclear matter includes a piece of first order in ${m}_{\ensuremath{\pi}}$, arising from the contribution of low-momentum virtual pions to the $\ensuremath{\pi}N$ $\ensuremath{\sigma}$ commutator. Chiral symmetry requires that no term of this order appears in the $\mathrm{NN}$ interaction. The mass of a nucleon in matter thus cannot depend in any simple way on the quark condensate alone. More generally, pieces of the quark condensate that arise from low-momentum pions should not be associated with partial restoration of chiral symmetry.

The chiral condensate in nuclear matter

We investigate the density dependence of the chiral order parameter or quark condensate 〈 qq〉 in nuclear matter using relativistic Brueckner-Hartree-Fock theory. While the leading behavior linear in the density is known to be determined model independently by the pion-nucleon sigma term, we demonstrate that higher order corrections are extremely sensitive to the interpretation of the scalar “σ”-meson and its substructure.

Vanishing condensates and anomalously light Goldstone modes in medium

We show that in a uniform medium, the vanishing of a particular condensate along with spontaneously broken symmetry imply the existence of an anomalously light pseudo-Goldstone mode. The consequences for a vanishing chiral condensate in nuclear matter are discussed.

Quark condensate in nuclear matter

Higher-order contributions to the quark condensate in nuclear matter due to nucleon-nucleon interactions are evaluated in the Dirac-Brueckner approach with the Bonn one-boson-exchange potential. We find that at normal nuclear matter density the quark condensate with higher-order contributions is about 5% larger than the model-independent leading-order result obtained from the pion-nucleon sigma term and usually used in theoretical discussions. At higher densities, the higher-order contributions become increasingly important, leading to a hindrance of chiral restoration. Possible reasons for this behaviour are discussed.

Hole-hole contact interaction in the t-J model.

Using an analytical variational approach we calculate the hole-hole contact interaction on the N\'{e}el background. Solution of the Bethe-Salpeter equation with this interaction gives bound states in $d$- and p-waves with binding energies close to those obtained by numerical methods. At $t/J \ge 2-3$ the bound state disappears. In conclusion we discuss the relation between short range and long range interactions and analogy with the problem of pion condensation in nuclear matter.

Quark condensate at finite baryon density.

We discuss a recently derived, model-independent relation that expresses the value of a medium-modified quark condensate in terms of the vacuum value of the condensate and the value of the nucleon sigma term, [sigma][sub [ital N]]. Our goal is to calculate the value of the quark condensate in nuclear matter, [l angle]NM[vert bar][ital [bar q]](0)[ital q](0)[vert bar]NM[r angle], using some standard many-body techniques. Here, we comment on the mean-field calculations of Cohen, Furnstahl, and Griegel and others. We then calculate the value of the nuclear matter quark condensate using linear response theory. In a sigma-dominance model, the linear response calculation relates the modification of the vacuum condensate to the matrix element of the operator [ital [bar q]q] taken between a state of the sigma meson and the vacuum. (That matrix element may be used to define a sigma decay constant, [ital f][sub [sigma]].) We also provide some additional insight into the relation between the dynamics of the quark condensate and the scalar fields of relativistic nuclear physics.