Indications of partial chiral symmetry restoration from pionic atoms

Extensive data on strong interaction effects in pionic atoms are analyzed with a density-dependent isovector scattering amplitude suggested recently by Weise to result from a density dependence of the pion decay constant. Most of the so-called ‘missing s-wave repulsion’ is removed when adopting this approach, thus indicating a partial chiral symmetry restoration in dense matter. The resulting potentials describe quite well also elastic scattering of 20 MeV pions on Ca. Further tests with elastic scattering are desirable.     

Gluon condensates,chiral symmetry breaking and pion wave-function

We consider here chiral symmetry breaking in quantum chromodynamics arising from gluon condensates in vacuum. Through coherent states of gluons simulating a mean field type of approximation, we show that the off-shell gluon condensates of vacuum generate a mass-like contribution for the quarks, giving rise to chiral symmetry breaking. We next note that spontaneous breaking of global chiral symmetry links the four component quark field operator to the pion wave function. This in turn yields many hadronic properties in the light quark sector in agreement with experiments, leading to the conclusion that low energy hadron properties are primarily driven by the vacuum structure of quantum chromodynamics.     

In-medium chiral perturbation theory

We report on how to tackle the problem of establishing a chiral effective field theory in nuclear matter with explicit pion fields and in the presence of external sources (Ann. Phys. 297, 27 (2002)). We have made use of the results of J.A. Oller (Phys. Rev. C 65, 025204 (2002)) where the generating functional for the in-medium chiral SU(2) x SU(2) Lagrangian has been derived. Within this approach we develop the so-called standard power counting rules for the calculation of in-medium pion properties if the residual nucleon energies are of the order of the pion mass. In addition, for the case of vanishing residual nucleon energies, a modified scheme (non-standard counting) is introduced. For both schemes the pertinent scales where the chiral expansions have to break down are established as well. We have performed a systematic analysis of n-point in-medium Green functions up to and including next-to-leading order when the standard rules apply. These include the in-medium contributions to quark condensates, pion propagators, pion masses and couplings of the axial-vector, vector and pseudoscalar currents to pions.Received: 30 September 2002, Published online: 22 October 2003PACS: 12.39.Fe Chiral Lagrangians - 11.30.Rd Chiral symmetries - 21.65. + f Nuclear matter     

In-medium chiral perturbation theory

This talk will report about a systematical implementation of a chiral effective field theory in nuclear matter with explicit pion fields and in the presence of external sources[1]. Within the generating functional approach of Ref.[2] the so-called standard power counting rules for the calculation of in-medium pion properties are developed that apply if the residual nucleon energies are of the order of the pion mass. In addition, for the case of vanishing residual nucleon energies, a modified scheme (non-standard counting) is introduced. For both schemes the pertinent scales where the chiral expansions have to break down are established as well. We report about a systematic analysis of n-point in-medium Green functions up to and including next-to-leading order when the standard rules apply. These include the in-medium contributions to quark condensates, pion propagators, pion masses and couplings of the axial-vector, vector and pseudoscalar currents to pions.     

The pion velocity at chiral restoration and the vector manifestation

We study the effects of Lorentz non-invariance on the physical pion velocity at the critical temperature T_c in an effective theory of hidden local symmetry (HLS) with the “vector manifestation” fixed point. We match at a “matching scale” Λ_M the axial-vector current correlator in the HLS with the one in the operator product expansion for QCD, and present the matching condition to determine the bare pion velocity. We find that the physical pion velocity, which is found to be one at T=T_c when starting from the Lorentz invariant bare HLS, remains close to one with the Lorentz non-invariance, v_π(T_c)=0.83–0.99. This result is quite similar to the pion velocity in dense matter.     

Effective chiral symmetry restoration in excited mesons

Results on the spectrum of ${\bar q} q$ mesons in a model with a linear Coulomb-like instantaneous confining potential are presented. The single-quark Green function as well as the dynamical chiral symmetry breaking are obtained from the Dyson-Schwinger (gap) equation. Given the dressed quark propagator, the spectrum of “usual” mesons, i.e., ${\bar q} q$ states with nonexotic quantum numbers J ^PC , is obtained from the Bethe-Salpeter equation. Effective restoration of chiral symmetry at large spins and/or radial excitations is observed and the states fall into approximate linear radial and angular Regge trajectories.     

A holographic model of deconfinement and chiral symmetry restoration

We analyze the finite temperature behavior of the Sakai-Sugimoto model, which is a holographic dual of a theory which spontaneously breaks a U(N_f)_L × U(N_f)_R chiral flavor symmetry at zero temperature. The theory involved is a 4 + 1 dimensional supersymmetric SU(N_c) gauge theory compactified on a circle of radius R with anti-periodic boundary conditions for fermions, coupled to N_f left-handed quarks and N_f right-handed quarks which are localized at different points on the compact circle (separated by a distance L). In the supergravity limit which we analyze (corresponding in particular to the large N_c limit of the gauge theory), the theory undergoes a deconfinement phase transition at a temperature T_d = 1/2πR. For quark separations obeying L > L_c ? 0.97 ∗ R the chiral symmetry is restored at this temperature, but for L < L_c ? 0.97 ∗ R there is an intermediate phase which is deconfined with broken chiral symmetry, and the chiral symmetry is restored at T_χSB ? 0.154/L. All of these phase transitions are of first order.     

Effective restoration of chiral symmetry in excited mesons

A fast restoration of chiral symmetry in excited mesons is demonstrated. A minimal “realistic” chirally symmetric confining model is used, where the only interaction between quarks is the linear instantaneous Lorentz-vector confining potential. Chiral symmetry breaking is generated via the nonperturbative resummation of valence quarks self-energy loops and the meson bound states are obtained from the Bethe–Salpeter equation. The excited mesons fall into approximate chiral multiplets and lie on the approximately linear radial and angular Regge trajectories, though a significant deviation from the linearity of the angular trajectory is observed.     

In-medium isovector piN amplitude from low-energy pion scattering

Differential cross sections for elastic scattering of 21.5 MeV positive and negative pions by Si, Ca, Ni, and Zr have been measured as part of a study of the pion-nucleus potential across the threshold. The "anomalous" repulsion in the s-wave term was observed, as is the case with pionic atoms. The extra repulsion can be accounted for by a chiral-motivated model where the pion decay constant is modified in the medium. Unlike in pionic atoms, the anomaly cannot be removed by merely introducing an empirical on-shell energy dependence.     

Pion interaction in nuclear matter and chiral symmetry restoration

This paper is devoted to the interplay between p-wave, s-wave pion-nucleon/nucleus interaction and in-medium pion-pion interaction with special emphasis on the role of the nuclear pionic scalar density driving a large amount of chiral symmetry restoration. In particular we show that the πNN coupling constant and the Goldberger-Treiman relation are preserved in the nuclear medium under certain conditions. We also discuss the related problem of the in-medium pion-pion strength function.     

The chirally improved quark propagator and restoration of chiral symmetry

The chirally improved (CI) quark propagator in Landau gauge is calculated in two flavor lattice Quantum Chromodynamics. Its wave-function renormalization function Z(p²)$Z(p^2)$ and mass function M(p²)$M(p^2)$ are studied. To minimize lattice artifacts, tree-level improvement of the propagator and tree-level correction of the lattice dressing functions is applied. Subsequently the CI quark propagator under Dirac operator low-mode removal is investigated. The dynamically generated mass in the infrared domain of the mass function is found to dissolve continuously as a function of the reduction level and strong suppression of Z(p²)$Z(p^2)$ for small momenta is observed.     

Pion scalar density and chiral symmetry restoration at finite temperature and density

This paper is devoted to the evaluation of the pionic scalar density at finite temperature and baryonic density. We express the latter effect in terms of the nuclear response evaluated in the random phase approximation. We discuss the density and temperature evolution of the pionic density which governs the quark condensate evolution. Numerical evaluations are performed. Received: 7 December 1999 / Accepted: 8 May 2000     

Confinement,chiral symmetry breaking,and the pion in a chromo-dielectric model of quantum chromodynamics

We study a chirally symmetric effective model of quantum chromodynamics, where the long-range parts of the (non-abelian) gluon self-interactions are assumed to give rise to a color-dielectric field. In particular we show how in this model confinement and the Goldstone pion arise naturally and simultaneously from dynamical chiral symmetry breaking. We also provide justification for successful chiral bag models, including for example the cloudy bag model.     

Precision spectroscopy of pionic 1s states of Sn nuclei and evidence for partial restoration of chiral symmetry in the nuclear medium

Deeply bound 1s states of pi(-) in (115,119,123)Sn were preferentially observed using the Sn(d,3He) pion-transfer reaction under the recoil-free condition. The 1s binding energies and widths were precisely determined and were used to deduce the isovector parameter of the s-wave pion-nucleus potential to be b1=-(0.115+/-0.007)m(-1)(pi). The observed enhancement of |b(1)| over the free piN value (b(free)1/b1=0.78+/-0.05) indicates a reduction of the chiral order parameter, f*pi(rho)2/f2pi approximately 0.64, at the normal nuclear density, rho=rho(0).     

More about chiral symmetry restoration at finite temperature in the planar limit

In the planar limit, in the deconfined phase, the Euclidean Dirac operator has a spectral gap around zero. We show that functions of eigenvalues close to the spectral edge, which are independent of common rescalings and shifts gauge configuration by gauge configuration, have distributions described by a Gaussian Hermitian matrix model. However, combinations of eigenvalues that are scale and shift invariant only on the average, do not match this matrix model.     

Electromagnetic probes of strongly interacting matter: probes of chiral symmetry restoration?

The QCD sum rule approach to in-medium modifications of the ω meson in nuclear matter is reviewed with emphasis of its relation to 4-quark condensates and chiral symmetry restoration. Possible implications of the CBTAPS experiment for the reaction γA → A′ω(→ π⁰γ) are sketched and the particularly important role of di-electron probes, accessible with HADES, is highlighted. A brief update of a parametrization of the previous dilepton and photon probes from CERES and WA98 of heavy-ion collisions at CERN-SPS energies is presented.