Realization Of Chiral Symmetry Research Articles

Spectrum of the fixed point Dirac operator in the Schwinger model

Recently, properties of the fixed point action for fermion theories have been pointed out indicating realization of chiral symmetry on the lattice. We check these properties by numerical analysis of the spectrum of a parametrized fixed point Dirac operator investigating also microscopic fluctuations and fermion condensation.

Chiral Lagrangian for strange hadronic matter

A generalized Lagrangian for the description of hadronic matter based on the linear $SU(3)_L \times SU(3)_R$ $\sigma$-model is proposed. Besides the baryon octet, the spin-0 and spin-1 nonets, a gluon condensate associated with broken scale invariance is incorporated. The observed values for the vacuum masses of the baryons and mesons are reproduced. In mean-field approximation, vector and scalar interactions yield a saturating nuclear equation of state. We discuss the difficulties and possibilities to construct a chiral invariant baryon-meson interaction that leads to a realistic equation of state. It is found that a coupling of the strange condensate to nucleons is needed to describe the hyperon potentials correctly. The effective baryon masses and the appearance of an abnormal phase of nearly massless nucleons at high densities are examined. A nonlinear realization of chiral symmetry is considered, to retain a Yukawa-type baryon-meson interaction and to establish a connection to the Walecka-model.

QCD hamiltonian approach for the glueball spectrum

A new, comprehensive relativistic many-body approach utilizing the Coulomb gauge QCD Hamiltonian is advanced for hadron physics. The formalism properly incoporates renormalization for regularizing divergences and also manifests the Nambu-Goldstone realization of chiral symmetry. Using standard many-body techniques, calculations for the constitutuent quark, gluon condensates and masses and gluon spectrum are found to be in good agreement with QCD sum-rules and quenched lattice gauge results.

Pion Observables in the Extended NJL Model with Vector and Axial-Vector Mesons

The momentum-space bosonization method of a Nambu and Jona-Lasinio type model with vector and axial-vector mesons is applied toππscattering. Unlike the case in earlier published papers, we obtain theππscattering amplitude using the linear and nonlinear realizations of chiral symmetry and fully taking into account the momentum dependence of meson vertices. We show the full physical equivalence between these two approaches. The chiral expansion procedure in this model is discussed in detail. Chiral expansions of the quark mass, pion mass and constantfπare obtained. The low-energyππphase shifts are compared to the available data. We also study the scalar form factor of the pion.

Low-energy hadronic interactions beyond the current algebra approach

Within chiral perturbation theory at the quark level (CHPT) q with linear realization of chiral U(3) × U(3) symmetry the new low-energy AP 3-interaction, produced by convergent box-constituent-quark-loop diagrams, is obtained, and its contributions to processes of low-energy interactions of low-lying mesons are investigated. The new interaction goes beyond the framework of the low-energy current algebra approach and effective chiral Lagrangians with linear realization of chiral symmetry, constructed at the hadronic level.

Full QCD hadron spectroscopy with two flavors of dynamical Kogut-Susskind quarks on the lattice.

A full lattice QCD simulation is carried out with two flavors of Kogut-Susskind staggered dynamical quarks using lattices of a size ranging from ${4}^{4}$ to ${20}^{4}$ at the gauge coupling constant $\ensuremath{\beta}=\frac{6}{{g}^{2}}=5.7$ with the quark mass of ${m}_{q}=0.01 \mathrm{and} 0.02$ in lattice units. Primary emphasis is given to the study of finite-lattice-size effects in the hadron mass spectrum. It is found that hadron masses suffer from substantial finite-size effects even for a lattice size of the order of 2 fm, showing the importance of a quantitative control of the effect for a comparison with the experimental spectrum at the accuracy of a few percent level. The finite-size correction is found to be well described by a power law in the lattice size, rather than an exponential form predicted by analytic formulas derived for point particles. It is suggested that the effect arises from the size of hadrons squeezed on a finite lattice. Finite-size effects on the realization of chiral symmetry are also studied. The behavior of the pion mass, the chiral condensate, and the mass splitting between parity partners all support a spontaneous breakdown of chiral symmetry for a large lattice size. Prediction from chiral Lagrangians on the size dependence of the chiral condensate does not describe the simulation results well, however, at least for the quark mass employed for the present study. Calculation of the pion decay constant with various relations derived from current algebra and partial conservation of axial-vector current gives ${f}_{\ensuremath{\pi}}=94(8)\ensuremath{-}105(9)$ MeV, with a method-dependent uncertainty contained within 10%. An examination is also made of the question of the dependence of hadron masses on hadron operators. Meson masses are basically operator independent, while baryon masses exhibit some operator dependence, necessitating further studies to resolve systematic uncertainties of this origin in the determination of the hadron mass spectrum.

Finite nuclei in relativistic models with a light chiral scalar meson.

Relativistic chiral models with a light scalar meson appear to provide an economical marriage of successful relativistic mean-field theories and chiral symmetry. The scalar meson serves as both the chiral partner of the pion and the mediator of the intermediate-range nucleon-nucleon ([ital NN]) attraction. However, while some of these models can reproduce the empirical nuclear matter saturation point, they fail to reproduce observed properties of finite nuclei, such as spin-orbit splittings, shell structure, charge densities, and surface energetics. These deficiencies imply that this realization of chiral symmetry is incorrect. An alternative scenario, which features a heavy chiral scalar and dynamical generation of the [ital NN] attraction, is discussed.

About the realization of chiral symmetry in QCD2

Two dimensional massless Quantum Chromodynamics presents many features which resemble those of the true theory. In particular the spectrum consists of mesons and baryons arranged in flavor multiplets without parity doubling. We analyze the implications of chiral symmetry, which is not spontaneously broken in two dimensions, in the spectrum and in the quark condensate. We study how parity doubling, an awaited consequence of Coleman's theorem, is avoided due to the dimensionality of space-time and confinement. We prove that a chiral phase transition is not possible in the theory.

THE POLARIZED PHOTON STRUCTURE FUNCTION $g_1^\gamma $ AS A PROBE OF CHIRAL SYMMETRY REALIZATIONS

The first moment of the polarized photon structure function [Formula: see text] is determined by the anomalous three-current axial-vector-vector (AVV) correlation function. Its dependence on the off-shell momentum κ2 of the target photon is a direct probe of the way chiral symmetry is realized in the AVV function. A careful account is given of the effect of different realizations of chiral symmetry on the AVV correlation function with special emphasis on the delicate chiral limit, where the occurrence of singularities in the invariant amplitudes makes the relation with the first moment of [Formula: see text] more subtle. The behavior of [Formula: see text] as κ2 is increased through the thresholds associated with the different quarks and leptons is described.

GENESIS AND EVOLUTION OF THE SKYRME MODEL FROM 1954 TO THE PRESENT

Not widely known facts on the genesis of the Skyrme model are presented in a historical survey, based on Skyrme's earliest papers and on his own published remembrance. We consider the evolution of Skyrme's model description of nuclear matter from the "Mesonic Fluid" model up to its final version, known as the baryon model. We pay special tribute to some well-known ideas in contemporary particle physics which one can find in Skyrme's earlier papers, such as: Nuclear Democracy, the Solitonic Mechanism, the Nonlinear Realization of Chiral Symmetry, Topological Charges, Fermi–Bose Transmutations, etc. It is curious to note in the final version of the Skyrme model gleams of Kelvin's "Vortex Atoms" theory. In conclusion we make a brief analysis of the validity of Skyrme's conjectures in view of recent results and pinpoint some questions which still remain.

On semileptonicB-decays into longitudinally polarized ρ-mesons

The heavy quark limit can not be taken directly for the decayB→ρev if the ρ meson is longitudinally polarized. We employ some recent ideas of a special realization of chiral symmetry to relate the above process to the decayB→πev in the heavy quark limit, which corresponds to the chiral limit in this so called vector realization of chiral symmetry.

Linear σ model in one-quark-loop order and the low-energy theorem for the a 1 → π( ππ) s-wave decay

Within the framework of the linear σ model with SU (2) × SU(2) realization of chiral symmetry we prove a low-energy theorem for the a 1 → π( ππ) s-wave decay amplitude. this theorem demonstrates the vanishing of the overall amplitude at the zero momentum of any interacting pion in a manner compatible with experimental data.

The spectrum of bosonized QCD2 in the chiral limit

By studying an equivalent non-abelian bosonic theory we resolve the spectrum of Quantum Chromodynamics in one space-one time dimensions for massless quarks. The emphasis is placed in the non chiral sector described by colored meson fields. Two and four point functions of these fields are explicitly calculated in the large N limit. Some of the relevant issues: chiral symmetry realization, phases, baryon spectrum, topology etc…, are revisited.

The spectrum of bosonized QCD2 in the chiral limit

By studying an equivalent non-abelian bosonic theory we resolve the spectrum of Quantum Chromodynamics in one space-one time dimensions for massless quarks. The emphasis is placed in the non chiral sector described by colored meson fields. Two and four point functions of these fields are explicitly calculated in the large N limit. Some of the relevant issues: chiral symmetry realization, phases, baryon spectrum, topology etc …, are revisited.

Vector model phenomenology

We review the vector model, a low-energy effective theory of QCD based upon a novel realization of chiral symmetry incorporating vector mesons. After discussing some of the problems with the lowest-order phenomenological results of this model, we compute the leading log corrections to the theory's tree level predictions. The corrections are found to significantly improve the agreement between values for several physical meson observables from the vector model and experiment.

The mesonic spectrum of bosonized QCD 2 in the chiral limit

By studying an equivalent non-abelian bosonic theory we resolve the mesonic spectrum of quantum chromodynamics in one space-one time dimension for massless quarks. The emphasis is placed in the non-chiral sector described be colored meson fields. Two and four point functions of these fields are explicitly calculated in the large N limit. Some of the relevant issues: chiral symmetry realization, phases, anomaly saturation, etc…, are revisited.

Vector realization of chiral symmetry

I discuss a new realization of chiral SU(3) × SU(3) symmetry which, in a sense, encompasses both the Wigner-Weyl mode and the Nambu-Goldstone mode. The chiral symmetry is unbroken, but there are Goldstone bosons. Furthermore, the light vector mesons, as well as the pseudoscalar mesons, are intimately involved because the chiral partners of the pseudoscalars are the longitudinal components of the vectors.

New realization of chiral symmetry.

I identify a new realization of chiral SU(3)\ifmmode\times\else\texttimes\fi{}SU(3) symmetry which, in a sense, encompasses both the Wigner-Weyl mode and the Nambu-Goldstone mode. The chiral symmetry is unbroken, but there are Goldstone bosons. Furthermore, the light vector mesons, as well as the pseudoscalar mesons, are intimately involved because the chiral partners of the pseudoscalars are the longitudinal components of the vectors. I discuss the connection of this realization with vector dominance, the Kawarabayashi-Suzuki-Riazuddin-Fayyazuddin relation, and the large-N approximation.

Hyperon resonances in the chiral bag model

We calculate the masses of low-lying negative-parity ..lambda../sup */ and ..sigma../sup */ in a chiral bag model with broken SU(2)/direct product/SU(2) realization of chiral symmetry. All relevant one-gluon-exchange and effective quark-quark one-pion-exchange diagrams are evaluated. We show why the spin-flavor contents of the hyperon resonances are different from that of a nonrelativistic quark model. In particular, we find that the ..lambda..(1405) has almost no flavor-singlet component. The prescription used to project out the translational mode of the bag is tested for the simplest case.

Skyrme model of nucleons with vector and scalar mesons

Abstract A systematic investigation is carried out for the two-flavor Skyrme model of the nucleon incorporating the vector and scalar mesons. The effective lagrangian for the coupled system of pseudoscalar and vector mesons, including the anomalous-parity terms, is discussed first. We examine the two main versions which are distinguished by the role fulfilled by vector meson dominance (VMD). In the first version, corresponding to a linear realization of chiral symmetry for the vector mesons, VMD is assumed by construction and exploited to derive an effective lagrangian for the πρω (or πρωA) system consistent with the low-energy soft-pion constraints. We discuss the issues related to the presence of a second soliton solution in the baryon B = 1 sector and the sensitivity of nucleon properties on the VMD subtraction counterterms, the higher order derivative couplings and the approximate elimination of the axials. The second version corresponds to the non-linear realization of chiral symmetry for vectors, where the axials are eliminated by gauge fixing. We examine the nucleon phenomenology of this model and discuss the violations of VMD taking place in the transition from the vacuum to the soliton sector. The role of scalars is analyzed in terms of the coupled system of pseudoscalars, vectors and scalars with an effective lagrangian based on the gauged chiral symmetry approach. We study two models which are characterized by the complementary gluonium and quarkonium aspects of scalars, respectively. The first is based on a dilaton description and the second on a linear σ-model description.