Quark Condensate In Nuclear Matter Research Articles

ϕ meson properties in nuclear matter from QCD sum rules with chirally separated four-quark condensates

The modification of the $\ensuremath{\phi}$ meson spectrum in nuclear matter is studied in an updated QCD sum rule analysis, taking into account recent improvements in properly treating the chiral invariant and breaking components of four-quark condensates. Allowing both mass and decay width to change at finite density, the QCD sum rule analysis determines certain combinations of changes for these parameters that satisfy the sum rules equally well. A comprehensive error analysis, including uncertainties related to the behavior of various condensates at linear order in density, the employed renormalization scale and perturbative corrections of the Wilson coefficients, is used to compute the allowed ranges of these parameter combinations. We find that the $\ensuremath{\phi}$ meson mass shift in nuclear matter is especially sensitive to the strange sigma term ${\ensuremath{\sigma}}_{sN}$, which determines the decrease of the strange quark condensate in nuclear matter. Specifically, we obtain a linear relation between the width ${\mathrm{\ensuremath{\Gamma}}}_{\ensuremath{\phi}}$ and mass shift $\mathrm{\ensuremath{\Delta}}{m}_{\ensuremath{\phi}}$ given as ${\mathrm{\ensuremath{\Gamma}}}_{\ensuremath{\phi}}=a\mathrm{\ensuremath{\Delta}}{m}_{\ensuremath{\phi}}+b{\ensuremath{\sigma}}_{sN}+c$ with $a=({3.947}_{\ensuremath{-}0.130}^{+0.139})$, $b=({0.936}_{\ensuremath{-}0.177}^{+0.180})$ and $c=\ensuremath{-}({7.707}_{\ensuremath{-}5.679}^{+4.791})\text{ }\text{ }\mathrm{MeV}$.

Nucleon sigma term and quark condensate in nuclear matter

We study the bound nucleon sigma term and the quark condensate in nuclear matter. In the quark-meson coupling (QMC) model the nuclear correction to the sigma term is small and negative, i.e., it decelerates the decrease of the quark condensate in nuclear matter. However, the quark condensate in nuclear matter is controlled primarily by the scalar-isoscalar $\sigma$ field. Compared to the leading term, it moderates the decrease more than that of the nuclear sigma term alone at densities around and larger than the normal nuclear matter density.

Quark condensates in nuclear matter in the global color symmetry model of QCD

With the global color symmetry model being extended to finite chemical potential, we study the density dependence of the local and nonlocal scalar quark condensates in nuclear matter. The calculated results indicate that the quark condensates increase smoothly with the increasing of nuclear matter density before the critical value (about 12$\rho_0$) is reached. It also manifests that the chiral symmetry is restored suddenly as the density of nuclear matter reaches its critical value. Meanwhile, the nonlocal quark condensate in nuclear matter changes nonmonotonously against the space-time distance among the quarks.

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.

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.

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.

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.

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.