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Register a new userScalar susceptibility and chiral symmetry restoration in nuclei
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We study the nuclear modification of the scalar QCD susceptibility, calculated as the derivative of the quark condensate with respect to the quark mass. We show that it has two origins. One is the low lying nuclear excitations. At normal nuclear density this part is constrained by the nuclear incompressibility. The other part arises from the individual nucleon response and it is dominated by the pion cloud contribution. Numerically the first contribution dominates. The resulting increase in magnitude of the scalar susceptibility at normal density is such that it becomes close to the pseudoscalar susceptibility, while it is quite different in the vacuum. We interpret it as a consequence of chiral symmetry restoration in nuclei.
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Recent topics on mesons in nuclei are discussed by especially emphasizing the role of the partial restoration of chiral symmetry in the nuclear medium. The spontaneously broken chiral symmetry in vacuum is considered to be incompletely restored in finite nuclear density systems with moderate reduction of the magnitude of the quark condensate. On the partial restoration of chiral symmetry, the wave function renormalization is important to be taken into account for the Nambu-Goldstone bosons. We also discuss the possible change of the meson properties in the nuclear medium and meson-nucleus systems for the $bar K$, $eta$, $K^{+}$ and $eta^{prime}$ mesons.
The partial restoration of chiral symmetry in nuclear medium is investigated in a model independent way by exploiting operator relations in QCD. An exact sum rule is derived for the quark condensate valid for all density. This sum rule is simplified at low density to a new relation with the in-medium quark condensate <bar{q}q>*, in-medium pion decay constant F_{pi}^t and in-medium pion wave-function renormalization Z_{pi}*. Calculating Z_{pi}*at low density from the iso-scalar pion-nucleon scattering data and relating F_{pi}^t to the isovector pion-nucleus scattering length b_1^*, it is concluded that the enhanced repulsion of the s-wave isovector pion-nucleus interaction observed in the deeply bound pionic atoms directly implies the reduction of the in-medium quark condensate. The knowledge of the in-medium pion mass m_{pi}* is not necessary to reach this conclusion.
Based on an equivparticle model, we investigate the in-medium quark condensate in neutron stars. Carrying out a Taylor expansion of the nuclear binding energy to the order of $rho^3$, we obtain a series of EOSs for neutron star matter, which are confronted with the latest nuclear and astrophysical constraints. The in-medium quark condensate is then extracted from the constrained properties of neutron star matter, which decreases non-linearly with density. However, the chiral symmetry is only partially restored with non-vanishing quark condensates, which may vanish at a density that is out of reach for neutron stars.
The results of an extensive campaign of measurements of the pi -> pi pi process in the nucleon and nuclei at intermediate energies are presented. The measurements were motivated by the study of strong pi pi correlations in nuclei. The analysis relies on the composite ratio C_{pi pi}^A, which accounts for the clear effect of the nuclear medium on the (pi pi) system. The comparison of the C_{pi pi}^A distributions for the (pi pi)_{I=J=0} and (pi pi)_{I=0,J=2} systems to the model predictions indicates that the C_{pi pi}^A behavior in proximity of the 2m_pi threshold is explainable through the partial restoration of chiral symmetry in nuclei.
We study the phase structure of dense hadronic matter including $Delta(1232)$ as well as N(939) based on the parity partner structure, where the baryons have their chiral partners with a certain amount of chiral invariant masses. We show that, in symmetric matter, $Delta$ enters into matter in the density region of about one to four times of normal nuclear matter density, $rho_B sim 1 - 4rho_0$. The onset density of $Delta$ matter depends on the chiral invariant mass of $Delta$, $m_{Delta0}$: The lager $m_{Delta0}$, the bigger the onset density. The $Delta$ matter of $rho_B sim 1 - 4rho_0$ is unstable due to the existence of $Delta$, and the stable $Delta$-nucleon matter is realized at about $rho_B sim 4rho_0$, i.e., the phase transition from nuclear matter to $Delta$-nucleon matter is of first order for small $m_{Delta0}$, and it is of second order for large $m_{Delta0}$. We find that, associated with the phase transition, the chiral condensate changes very rapidly, i.e., the chiral symmetry restoration is accelerated by Delta matter. As a result of the accelerations, there appear $N^*$(1535) and $Delta$(1700), which are the chiral partners to N(939) and ${Delta}$(1232), in high density matter, signaling the partial chiral symmetry restoration. Furthermore, we find that complete chiral symmetry restoration itself is delayed by $Delta$ matter. We also calculate the effective masses, pressure and symmetry energy to study how the transition to $Delta$ matter affects such physical quantities. We observe that the physical quantities change drastically at the transition density.
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