A chiral bag model with a soft surface : structure and solutions of the Fuzzy and the modified Fuzzy Bag Model

In the present work we propose a new bag model for hadrons, called the modified fuzzy bag model (MFBM). The distinguishing feature of this model is the suppression of the pion field, as it enters the bag, by means of a scalar potential for the pions, while still preserving chiral symmetry. The mechanism of pion suppression in the MFBM is similar to the mechanism of quark suppression in the fuzzy bag model (FBM). The standard chiral transformation for the pion field suffers a natural alteration in the MFBM, and as a result the model is chiral invariant. We present also a discussion of the FBM and study, in the quark sector, the implications of the soft surface of the bag on the expectation value of the mass operator. In the pion-quark sector, we study the effects of the suppression of the pion field on the form factor for the pion-nucleon interaction, on the pion-nucleon coupling constant and on the nucleon axial charge . Calculations of the pion-nucleon form factor exhibit, in particular, an improvement over previous results. The pionic axial current induces, in the MFBM, a nonvanishing and orientation dependent contribution to axial charge. An analysis of the asymptotic behaviour of the axial charge shows that the role of the surface is to increase the difference of the contributions associated to different orientations. Received: 10 March 1997 / Revised version: 14 October 1997     

Dynamical light vector mesons in low-energy scattering of Goldstone bosons

We present a study of Goldstone boson scattering based on the flavor SU(3) chiral Lagrangian formulated with vector mesons in the tensor field representation. A coupled-channel computation is confronted with the empirical s- and p-wave phase shifts, where good agreement with the data set is obtained up to about 1.2 GeV. There are two relevant free parameters only, the chiral limit value of the pion decay constant and the coupling constant characterizing the decay of the rho meson into a pair of pions. We apply a recently suggested approach that implements constraints from micro-causality and coupled-channel unitarity. Generalized potentials are obtained from the chiral Lagrangian and are expanded in terms of suitably constructed conformal variables. The partial-wave scattering amplitudes are defined as solutions of non-linear integral equations that are solved by means of an N/D ansatz.     

Axial polarizability and weak currents in nuclei

The effect of the isobaric excitations on the weak axial coupling constants in nuclei is studied through P.C.A.C. We first establish the Klein-Gordon equation for the virtual pion field in the nucleus; it takes into account pion rescattering. The influence of isobar excitation is contained in the axial polarizability coefficient which is linked to the p-wave π-N scattering volume. The derivation of this equation stresses its analogies with electromagnetism. We give then a basic relation between the axial current and the pionic field. It incorporates the effects of the isobars in the axial polarizability, which leads naturally to an electromagnetic analog. We show that this relation leads in heavy nuclei to a quenching of the axial coupling constant by the Lorentz-Lorenz factor, which may originate from the short range or the Pauli correlations, depending on the range of the π-N forces. Hence this quenching may have a different origin than the existence of short-range correlations and may arise from a Pauli blocking effect. On the other hand, the pseudoscalar coupling constant is found to be strongly suppressed. In finite nuclei, these basic quenchings can be masked by surface effects, the general features of which are studied with the help of a solvable model. This model is further used to obtain the asymptotic pion field which is linked to the effective pion-nucleus coupling constant and can be determined experimentally through π-nucleus dispersion relations. We find that this quantity is quenched, in agreement with recent experimental data.     

The Effects of the Pion String at Heavy ion Collisions

We study the possible signals of the pion string associated with the QCD chiral phase transition in LHC Pb–Pb collision at energy s=5.5 TeV.We follow the Kibble–Zurek mechanism to discuss the production and evolution of the pion string.We will show that if the QCD chiral phase transition really takes place in the LHC Pb-Pb collision process and the phase transition is in the second order,the pion string will be inevitably produced and subsequently decay.The main effect of this phenomenon is that there is a generation of a large number of pions in the final state produced by the decay of the pion string, and these pions are mostly distributed in a low momentum region with p～143MeV; also there are lots of neutral pions distributed in a low momentum region with the mean momentum at p～21MeV.     

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.     

ρ-Meson coupling to the nucleon in the chiral bag model

The vector and tensor couplings of the ρ-meson to the nucleon are calculated by assuming the indirect coupling of the ρ-meson to the nucleon, through the pion cloud of the chiral bag model. Qualitative agreement with experiment is found at reasonable bag radii for both versions of the model: the cloudy bag model with pions in the interior, and the standard model with pions excluded from the bag.     

Properties of the nucleon in the nuclear medium within a chiral quark-meson theory

The modifications of the nucleon structure due to the presence of an external baryon medium are investigated in a chiral quark meson theory. To that end the Nambu-Jona-Lasinio (NJL) model is combined with the projected chiral soliton model. The medium effects are incorporated using the medium modified values of the pion decay constant and the pion and sigma masses at finite density. These values are evaluated within the NJL model. Using functional integral techniques the latter is solved in a quark continuum at finite density. The effective meson values serve to fix the parameters of the linear chiral sigma model which is solved in a variational projected mean field approach in order to obtain the nucleon properties. All nucleon properties show modifications in the medium except for the pion nucleon coupling constant. The proton radius shows an increase of 19% and the nucleon mass a decrease of 17% if the medium reaches nuclear matter density. The magnetic moments and axial vector coupling constant are less modified. All form factors show remarkable reduction at finite transfer momenta.     

Chiral symmetry and diffractive neutral pion photo- and electroproduction

We show that diffractive production of a single neutral pion in photon-induced reactions at high energy is dynamically suppressed due to the approximate chiral symmetry of QCD. These reactions have been proposed as a test of the odderon-exchange mechanism. We show that the odderon contribution to the amplitude for such reactions vanishes exactly in the chiral limit. This result is obtained in a nonperturbative framework and by using PCAC relations between the amplitudes for neutral pion and axial vector current production.     

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     

Pion Loops in Chiral Perturbation Theory and Light-Front Dynamics

From the approximate chiral symmetry of QCD, it is known that the pion loops in chiral perturbation theory play a vital role in understanding the nucleon’s long-range structure. We demonstrate the equivalence of the light-front, equal-time and covariant formulations for the interactions of nucleons with pions in chiral perturbation theory. In particular, we discuss the self-energy Σ of a nucleon dressed by pion loops with the pseudovector πNN coupling. It is shown that the leading nonanalytic behavior of Σ is equivalent whichever formulations are used for the derivation. We also discuss the relation between the mass shift and the wavefunction renormalization as well as the difference between the pseudovector and pseudoscalar theories.     

Hard pions and axial meson exchange currents in nuclear physics

Starting from the hard meson method we develop a consistent approach to the problem of the axial meson exchange currents (MEC). This method incorporates the current algebra and PCAC together with the vector dominance and allows one to study the pion as well as heavy-meson exchanges on an equal footing. Using a minimal, chiral and approximately gauge-invariant phenomenological Lagrangian (PL) model for the A_1ρπ system we construct the two-nucleon axial MEC operator in the tree approximation. This operator automatically possesses the correct chiral SU(2) × SU(2) transformation properties and has the smoothest momentum dependence which is allowed within the combined current algebra and vector dominance approaches. In the given model, we consider the non-Born part of the amplitude N + J^A → n + π and demonstrate that in the soft pion limit, it exactly coincides with the PCAC prediction.     

Chiral anomaly and nucleon properties in the Nambu-Jona-Lasinio model with vector mesons

We consider the extended SU(3) Nambu and Jona-Lasinio model with explicit vector couplings in the presence of external fields. We study the chiral anomaly in this model and its implications on the properties of the nucleon described as a chiral soliton of three valence quarks bounded in mesonic background fields. For the model to reproduce the QCD anomaly it is necessary to subtract suitable local and polynomial counterterms in the external and dynamical vector and axial-vector fields. We compute the counterterms explicitly in a vector-gauge-invariant regularization, and obtain modifications to the total effective action and vector and axial currents. We study the numerical influence of those counterterms in the two-flavour version of model with dynamical σ, π, , A and ω mesons. We find that, for time-independent hedgehog configurations, the numerical effects in the nucleon mass, the isoscalar nucleon radius and the axial coupling constant are negligibly small.     

Solution of a symmetry conserving chiral soliton model for nucleon and delta

The linear chiral soliton model is solved for nucleon and delta by constructing Fock states in the coherent pair approximation with correct spin and isospin properties. The quark configurations are those arising from theSU(2)×SU(2) coupling of three quarks in 1s-orbits. The overall Fock state is formed by the vector coupling of the quark configurations with the pion coherent state and thus avoids the use of the hedgehog ansatz. The sigma field is treated in the mean field approximation. Equations of motion for the quark, sigma and pion fields are solved in the static approximation. Soliton solutions are found with properties that are in reasonable agreement with those observed for the nucleon and delta including the axial vector coupling constant. With only components having zero and one unpaired pion in the coherent pair approximation the nucleon mass is found to be larger than that using the projected hedgehog approach.     

Classical pion fields in the presence of a source

A classical pion field that is similar to a disoriented chiral condensate is considered in the presence of an external source. The field is similar to the condensate in that the isotopic orientation of the field in the whole space is determined by a single vector. Within the nonlinear sigma model, classical solutions are considered both in the chiral limit, where the pions are massless, and in the case of a finite pion mass. In either case, the classical filed is similar to the Coulomb field of a charged particle; however, the nonlinear pion interaction results in the existence of several solutions. In the massless case and in the case where the source is sufficiently small, there are a great number of classical solutions characterized by finite discrete energies. In the more realistic case of heavy ions, there are no stable solutions of this type; however, long-lived quasistationary states, which slowly decay, emitting very soft pions, can be formed. The structure and the energies of these solutions are studied numerically.     

Pion propagation near the QCD chiral phase transition

We point out that, in analogy with spin waves in antiferromagnets, all parameters describing the real-time propagation of soft pions at temperatures below the QCD chiral phase transition can be expressed in terms of static correlators. This allows, in principle, the determination of the soft pion dispersion relation on the lattice. Using scaling and universality arguments, we determine the critical behavior of the parameters of pion propagation. We predict that, when the critical temperature is approached from below, the pole mass of the pion drops despite the growth of the pion screening mass. This fact is attributed to the decrease of the pion velocity near the phase transition.     

Effects of Composite Pions on the Chiral Condensate within the PNJL Model at Finite Temperature

We investigate the effect of composite pions on the behaviour of the chiral condensate at finite temperature within the Polyakov-loop improved NJL model. To this end we treat quark-antiquark correlations in the pion channel (bound states and scattering continuum) within a Beth–Uhlenbeck approach that uses medium-dependent phase shifts. A striking medium effect is the Mott transition which occurs when the binding energy vanishes and the discrete pion bound state merges the continuum. This transition is triggered by the lowering of the continuum edge due to the chiral restoration transition. This in turn also entails a modification of the Polyakov-loop so that the SU(3) center symmetry gets broken at finite temperature and dynamical quarks (and gluons) appear in the system, taking over the role of the dominant degrees of freedom from the pions. At low temperatures our model reproduces the chiral perturbation theory result for the chiral condensate while at high temperatures the PNJL model result is recovered. The new aspect of the current work is a consistent treatment of the chiral restoration transition region within the Beth–Uhlenbeck approach on the basis of mesonic phase shifts for the treatment of the correlations.     

Elastic neutrino proton scattering and the structure of the neutral current

Optimal constraints on the structure of a general V, A hadronic neutral current are derived from neutrino proton scattering and compared with corresponding results from inclusive neutrino scattering and single pion production by neutrinos. For an arbitrary axial component of the neutral current, restrictions for the vector coupling constants are obtained. It is shown that the most general neutral current which can be related to charged weak and electromagnetic currents accounts for all existing data on neutrino hadron scattering. The neutral current coupling constants are determined for the pure isovector model, the Salam-Weinberg model and the bottom-quark model. All three models lead to practically the same isovector couplings but they differ in the strength of the isoscalar current.     

Current algebra derivation of temperature dependence of hadron couplings with currents

The vector and the axial-vector meson couplings with the vector and the axial-vector currents respectively at finite temperature were obtained by calculating all the relevant one-loop Feynman graphs with vertices obtained from the effective chiral Lagrangian. On the other hand, the same couplings were also derived by applying the method of current algebras and the hypothesis of partial conservation of axial-vector currents. The latter method appears to miss certain terms; in the case of the vector meson coupling with the vector current, for example, a term containing the ρωπ coupling is missed. A similar situation would also appear for the nucleon coupling with the nucleon current. In this note we resolve these differences.     

Studying pion effects in the quark propagator

Within the framework of Schwinger-Dyson and Bethe-Salpeter equations we investigate the importance of pions for the quark-gluon interaction. To this end we choose a truncation for the quark-gluon vertex that includes intermediate pion degrees of freedom and adjust the interaction such that unquenched lattice results for various current quark masses are reproduced. After extrapolation to the physical point we find a considerable contribution of the pion back reaction to the quark mass function as well as to the chiral condensate.     

The origin of the pion mass

We discuss the origin of the pion mass using a simple model of the QCD vacuum as a condensate of overlapping quark-antiquark pairs. We analyze the relationship between local conservation of the axial current and the nonzero current quark mass. Away from the chiral limit, we find that the pion mass comes from a change in the geometry of the overlap of condensed pairs.