Nonlinear Realization Of Chiral Symmetry Research Articles

Holographic model for the baryon octet

By adopting the nonlinear realization of chiral symmetry, a holographic model for the baryon octet is proposed. The mass spectra of the baryon octet and their low-lying excited states are calculated, which show good consistency with experiments. The couplings of pion to nucleons are derived in two gauges and are shown to be equivalent with each other. It also shows that only derivative couplings of pion to nucleons appear in this holographic model. The coupling constant is then calculated.

Realistic implementation of massive Yang-Mills theory forρanda1mesons

We revisit the massive Yang-Mills approach to implement axial-/vector mesons into the chiral pion Lagrangian. Employing the non-linear realization of chiral symmetry, we compute vector and axial-vector spectral functions. This includes, for the first time, a resummation of the $\rho$ propagator in the $a_1$ selfenergy while maintaining a partially conserved axial-vector current (PCAC). A realistic $\rho$ propagator, combined with a recent idea of a chirally invariant continuum in the vector and axial-vector channels, turns out be critical to obtain a quantitative description of hadronic $\tau$-decay data which has not been achieved before in local-gauge approaches to the chiral lagrangian. The thus obtained model provides a realistic basis to rigorously address the long-standing question of chiral symmetry restoration in the context of dilepton data in heavy-ion collisions.

The general relativity with conformal units

General Relativity rewritten in conformal units identifies conformal intervals with the real observational distances. This identification gives a base to explain all epochs of the Universe evolution including Ia supernova luminosity long distance-redshift relation by the dominance of the Casimir vacuum energy of all physical fields. A set of arguments is discussed in favor that SNe Ia data in the conformal units can be an evidence of the conformal twistor structure of the space-time as a nonlinear realization of the affine group, like the nonlinear realization of chiral symmetry and phenomenological Lagrangian is evidence of the quark structure of hadrons.

COMPACT STARS IN HADRON AND QUARK-HADRON MODELS

We investigate strongly interacting dense matter and neutron stars using a flavor-SU(3) approach based on a nonlinear realization of chiral symmetry. We study chiral symmetry restoration and the equation of state of stellar matter and determine neutron star properties using different sets of degrees of freedom. Finally, we include quarks in the model approach. We show the resulting phase diagram as well as hybrid star solutions for this model.

Nonlinear realization of chiral symmetry on the lattice

We formulate lattice theories in which chiral symmetry is realized nonlinearly on the fermion fields. In this framework the fermion mass term does not break chiral symmetry. This property allows us to use the Wilson term to remove the doubler fermions while maintaining exact chiral symmetry on the lattice. Our lattice formulation enables us to address non-perturbative questions in effective field theories of baryons interacting with pions and in models involving constituent quarks interacting with pions and gluons. We show that a system containing a non-zero density of static baryons interacting with pions can be studied on the lattice without encountering complex action problems. In our formulation one can also decide non-perturbatively if the chiral quark model of Georgi and Manohar provides an appropriate low-energy description of QCD. If so, one could understand why the non-relativistic quark model works.

Axial current conservation in nonrelativistic nuclear physics: The nonlinearσmodel

We analyze partially conserved axial current in the nonlinear realization of chiral symmetry in nuclear physics. We construct the two-nucleon (meson-exchange) axial currents and associated pion emission and absorption operators and compare them with those derived earlier in the linear $\ensuremath{\sigma}$ model. We show the absence of necessity of meson-exchange currents in the nonlinear model, in contrast with the linear one.

Many pion decays ofρ(770)andω(782)mesons in chiral theory

The decays rho(770) to 4 pi and omega(782) to 5pi are considered in detail in the approach based on the Weinberg Lagrangian obtained upon the nonlinear realization of chiral symmetry, added with the term induced by the anomalous Lagrangian of Wess and Zumino. The partial widths and excitation curves of the decays rho^0 to 2 pi^+ 2 pi^-, pi^+ pi^- 2 pi^0, rho^{+-} to 2 pi^{+-} pi^{-+} pi^0, rho^(+-} to pi^(+-} 3 pi^0 are evaluated for e^+e^- annihilation, photoproduction and tau lepton decays. The results of calculations are compared with the recent CMD-2 data on the decay rho^0 to 2 pi^+ 2 pi^- observed in e^+e^- annihilation. The omega to 5 pi decay widths and excitation curves in e^+e^- annihilation are obtained. The angular distributions for various combinations of the final pions in the decays rho to 4 pi and omega to 5 pi are written. The perspectives of the experimental study of the above decays in e^+e^- annihilation, tau lepton decays and photoproduction are discussed.

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.

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.

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.

Nonlinear realization of chiral symmetry in the MIT bag model

Using the method of nonlinear realization of the chiral symmetry developed in the past for the description of the pion hadron interactions, we construct a lagrangian model in which quarks are confined and the chiral symmetry is exact. The model allows to study questions connected with soft pion emission and at the same time to make use of the explicit wave functions of the MIT bag. Three quantities are studied in more details:GA/GV for nucleon,gπN andgπNΔ. Results for all of them suggest that nonstrange quarks may have a nonnegligible mass in the bag.

Duffin-Kemmer formulation of gauge theories

Gauge theories, including the Yang-Mills theory as well as Einstein's general relativity, are reformulated in first-order differential forms. In this generalized Duffin-Kemmer formalism, gauge theories take very simple forms with only cubic interactions. Moreover, every local gauge transformation, e.g., that of Yang and Mills or Einstein, etc., has an essentially similar form. Other examples comprise a gauge theory akin to the Sugawara theory of currents and the nonlinear realization of chiral symmetry. The octonion algebra is found possibly relevant to the discussion of the Yang-Mills theory.

Scalar-Conformal Derivatives and Chiral-Conformal Lagrangians

In a previous paper a scalar-conformal derivative (SCD) was derived. In this paper we investigate the properties of SCD, showing that when the kinetic energy is expressed in terms of SCD, the trace of the canonical energy-momentum tensor is soft (zero for conformal Lagrangians). For Lagrangians which are both chirally and conformally invariant, the SCD can be reduced to a simple derivative by using the relation ${\ensuremath{\chi}}^{2}={\ensuremath{\pi}}^{2}+{\ensuremath{\sigma}}^{2}$ when the chiral symmetry is realized linearly. In the nonlinear realization of chiral symmetry, for chirally and conformally invariant Lagrangians, the SCD is in agreement with Isham et al. Also, the breaking of a nonlinearly realized chiral symmetry is discussed. When chiral symmetry is broken, one finds that the mass of the $\ensuremath{\pi}$ field is proportional to the mass of the $\ensuremath{\chi}$ field. The proportionality constant is shown to be related to the normalization one chooses for the chiral covariant derivative.

On the non-local realization of chiral symmetry

It is shown that there exists a non-local, non-hermitian, effective Lagrangian giving in the tree approximation a description of scattering phenomena correct at all energies. Because such a Lagrangian cannot be invariant under the ordinary local, non-linear realization of chiral symmetry a non-local realization of chiral SU 2 × SU 2 is introduced and its consequences are studied.