Realization Of Chiral Symmetry Research Articles

K 0 → π 0γγ decays in chiral perturbation theory

The decays K L,S → π 0γγ are calculated within the framework of chiral perturbation theory. The amplitude for K L → π 0γγ is found to be finite at the one-loop level yielding a branching ratio of 6.8 × 10 −7. The decay spectra of both decays are very characteristic and provide good tests of the effective chiral symmetry realization of the standard model.

Realizations of chiral symmetry in a spontaneously broken lattice gauge theory

The phase diagram of lattice SU(2) gauge theory with fundamental representation Higgs fields is probed by l= 1 2 and l=1 fermions. Quenched calculations of 〈 ΨΨ〉 l show two distinct regions characterized by broken or unbroken chiral symmetry. The location of the boundary between the two regions depends on the representation l of the fermions. For l= 1 2 fermions the presence is verified of Nambu-Goldstone bosons (“pions”) in the broken region and evidence is found for massless physical fermions in the chirally symmetric region. Effects of boundary conditions and the possibility of observing two particle cuts in finite lattice spectrum calculations are commented on also.

On the realization of chiral symmetry in (1+1) dimensions

By applying non-abelian bosonization to (1+1) dimensional QED, QCD and Gross-Neveu models we shed light on a number of questions: the consistency of 't Hooft's large- N c spectrum with Coleman's theorem on symmetry breaking and with Steinhardt's baryonium spectrum; the secret SU(2) symmetry of the β 2 = 2 π sine-Gordon model; the universal realization of chiral symmetries in (1+1) dimensions.

On Realizations of Chiral Symmetry in QCD(Dynamical Symmetry and Supersymmetry in Nuclear, Particle, and Atomic-Molecular Physics)

On Realizations of Chiral Symmetry in QCD(Dynamical Symmetry and Supersymmetry in Nuclear, Particle, and Atomic-Molecular Physics)

Composite models of quarks and leptons and strong-coupling lattice gauge theories

We extend a previous variational block-spin analysis of the realization of chiral symmetry in a strong-coupling lattice gauge theory to models which have been suggested as possibly describing massless composite fermions. In all cases we find massive fermion composites and spontaneous breaking of chiral symmetry. We also discuss the relevance of this result to the continuum limit.

Dynamical realization of chiral symmetry in quantum chromodynamics

By an examination of the Ward-Takahashi identities and the Dyson-Schwinger equations we are able to establish a causal connection in QCD between the Nambu-Goldstone realization of chiral symmetry and quark confinement. We show that the broken-chiral-symmetry solution leads to a propagator which is an entire function. This is a nonperturbative result driven solely by the instantons. Many remarkable implications of this solution are described.

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.

Goldstone mechanism from gluon dynamics

A single assumption about pure gluon (Yang-Mills) theory is shown to imply the Nambu—Goldstone realization of chiral symmetry in QCD as well as the resolution of its U(1) problem.

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.

A solution to the Goldstein problem and the possibility of dynamical chiral symmetry breaking

The Goldstein equation is carefully analyzed by introducing a cutoff to clarify the physical meaning of the continuous spectrum. The solution belonging to the continuous spectrum is shown to represent the renormalized vertex function. It is also shown that no cutoff-independent discrete spectrum exists, whereas the cutoff-dependent one does. On the basis of these results, the possibility of the Nambu-Goldstone realization of chiral symmetry is examined in the vector gluon model. The appearance of the Nambu-Goldstone boson seems to be impossible at least in the ladder approximation except for the model of Englert et al.

A Dual Picture for Meson Resonances in Terms of Two Limiting Symmetries

On the basis of lightlike chiral algebra, axial charge couplings of meson resonances are studied in terrhs of the two limiting symmetries, SU(6) 8 ®0(3)L and chiral SU(3)®SU(3). By the help of sum rules it is argued that the coexistence of SU(6) and chiral couplings attributes the breaking of one symmetry to the leakage through couplings of the other. Experimental check of this dual picture is made, though it is not conclusive due to the lack of crucial information. The concept of constituent quarks is also discussed in the lightlike formulation. § I. Introduction In previous two articles 1> we investigated a lightlike formulation of the quark model for hadrons. We studied the general structure of axial charge couplings on the non-exoticity assumption, and derived ·SUm rules of Adler-Weisberger type for lightlike chiral contents of hadron resonances. All the arguments were made without recourse to any symmetry higher than SU(3). The aim of this article is to discuss how our approach can be concerned with the symmetry pattern of hadrons. This is an important problem for the lightlike formulation, because lightlike chiral algebra•> is characterized by its commutativity with the stability group Y(r), which does not contain p-. It is our basic standpoine> that the non-symmetry nature of SU(3) 1Q!;;SU(3) 1 essentially arises from the spontaneous breakdown of chiral symmetry. 4> The ap­ proximate realization of chiral symmetry through the Goldstone-Nambu mechanism provides us with a ·theoretical basis for the partially conserved axial-current hypoth­ esis.5> By this hypothesis we can relate axial charge couplings to pseudoscalar octet meson (P8) vertices in terms of the relation 8>

Chiral symmetry and the quark model

The construction of chiral-symmetric quark models is investigated. We show that the Nambu-Goldstone realization of chiral symmetry leads naturally to representation mixing of quark states and of their composites. Constructing SU(6) wave functions for hadron states, we obtain a mixing scheme algebraically equivalent to the Melosh transformation. The resulting phenomenology for pionic decays and for weak and electromagnetic vertices is known to be very successful. The present work provides a theoretical basis for these results and opens new avenues for the study of SU(6) symmetry and the investigation of deep-inelastic scattering processes.

Asymptotic freedom and Goldstone realization of chiral symmetry

The feasibility of Goldstone realization of weakly probed chiral symmetries is examined in the case that strong interactions are described by an asymptotically free theory of zero-bare-mass quarks and gauge vector gluons. This investigation is restricted to finding solutions to the homogeneous Bethe-Salpeter equation for the symmetry-breaking part $G$ of the quark propagator $S$, $G(p){\ensuremath{\gamma}}_{5}\ensuremath{\propto}{{S}^{\ensuremath{-}1}(p),{\ensuremath{\gamma}}_{5}}$, in the limit ${p}^{2}\ensuremath{\rightarrow}\ensuremath{-}\ensuremath{\infty}$. Renormalization-group techniques are extremely useful in this limit, and are used extensively. Their naive application implies the leading asymptotic behavior $G(p)\ensuremath{\sim}{(\mathrm{ln}p)}^{\ensuremath{-}A}$, where $A$ is a calculable positive constant. More importantly, it is shown that the Bethe-Salpeter kernel is well approximated by the ladder graph alone, with the effective coupling ${g}^{2}(p)\ensuremath{\sim}{(\mathrm{ln}p)}^{\ensuremath{-}1}$, when the strong interactions are asymptotically free. Two solutions are found for $G$. The asymptotically dominant one, ${G}_{+}(p)\ensuremath{\sim}{(\mathrm{ln}p)}^{\ensuremath{-}A}$, is just what was predicted by straightforward renormalization-group analysis, and does not correspond to Goldstone realization of the symmetry. The other solution has much softer asymptotic behavior, ${G}_{\ensuremath{-}}(p)\ensuremath{\sim}{p}^{\ensuremath{-}2}{(\mathrm{ln}p)}^{A}$. That this solution actually corresponds to the Goldstone mode is established by relating it, through the axial-vector Ward identity, to the Goldstone-boson-quark-antiquark vertex function, whose large-momentum limit is analyzed via the Wilson operator-product expansion.

Phase transitions in vector-gluon models: A solution to the U(3) problem

We have examined the realizations of chiral symmetry in the Abelian vector-gluon model, in the absence of gluon self-energy. The chiral symmetry is broken spontaneously in the vacuum. A vacuum stability condition on the gluon coupling, $g$, and the gluon-fermion mass ratio $\frac{\ensuremath{\mu}}{m}$ of the form ${{f}_{\ensuremath{\pi}}}^{2}({g}^{2},\frac{{\ensuremath{\mu}}^{2}}{{m}^{2}})>0$ is obtained as a necessary condition for a Nambu-Goldstone realization with bound-state Goldstone bosons. Here ${f}_{\ensuremath{\pi}}$ is the decay constant of the bound-state Goldstone boson. It is shown that for those channels that do not communicate with pairs of vector gluons this condition is satisfied in the weak-coupling limit, ${g}^{2}\ensuremath{\rightarrow}0$. For axialvector currents that satisfy anomalous Ward identities and communicate with pairs of gluons we show that the renormalized integral equations for ${{f}_{\ensuremath{\pi}}}^{2}$ do not possess solutions. The failure to find a Goldstone solution for these channels is associated with the fact that these axialvector currents have an anomalous dimension greater than three. Instead of Goldstone bosons one finds that axial-vector-current conservation breaks down and the symmetry is broken explicitly. Hence, there is no Goldstone boson associated with "axial baryonic charge." This also answers in the negative the old question of whether electrodynamics can support a Goldstone mode. We also calculate ${g}_{A}\ensuremath{-}1$ to order ${g}^{2}$ and discuss phase transitions between the Wigner-Weyl mode, the Goldstone mode, and the mode in which the symmetry is explicitly broken. We also speculate on the implications of this work for gauge theories of the strong interactions.

Anomalous thresholds and the realization of chiral symmetry

We follow the work of some other authors in a study of chiral-symmetry breaking based on the linear $\ensuremath{\sigma}$ model in the semiclassical approximation. By this procedure the masses of the mesons are known in terms of the symmetry-breaking parameters. Therefore, in those terms, we can analyze the system for the possible occurrence of anomalous thresholds corresponding to the bound-state properties of the scalar mesons. We find that when the critical parameter in the symmetric Lagrangian is such that a Goldstone symmetry limit can occur, then the anomalous threshold does not manifest itself by emerging to the physical sheet when mass continuation is performed; instead, the anomalous singularity stays out on the physical sheet and never disappears from it. Conversely, the system has an anomalous threshold with familiar emerging behavior when the critical parameter admits only the normal symmetry limit.

Goldstone Bosons as Bound States in the Quark-Gluon Model

We examine the implications of a Nambu-Goldstone realization of chiral symmetry in the quark-gluon model. The context of this examination is that of a renormalizable, finite theory, so eigenvalue conditions are assumed to be satisfied. We discuss the solutions to the Schwinger-Dyson gap equation for the fermion self-energy $\ensuremath{\Sigma}({p}^{2})$ that exhibit spontaneous breaking of the vacuum symmetry. In the leading-order Bethe-Salpeter approximation the boundary conditions to the homogeneous, linear integral equations stipulate the vacuum symmetry. It is shown how the Goldstone bosons emerge as bound states, as suggested by Nambu and Jona-Lasinio. We also examine the Goldstone alternative in the Bethe-Salpeter equation for fermion-fermion scattering. Explicit symmetry breaking is introduced by additional Abelian vector gluons coupling to hypercharge and isospin besides baryon number. The eigenvalue condition for the fine-structure constant is consequently model-dependent but takes a simple form. We also consider the influence of explicit symmetry breaking on the ground-state mesons and indicate how the solutions to the eigenvalue problem regulate the structure of symmetry breaking.

Algebraic Realization of Chiral Symmetry on the Light Cone

Lightlike charge commutators are used to provide a new derivation of the algebraic realizations of chiral symmetry for pionic processes first found by Dashen, Fubini, and Gell-Mann and by Weinberg, a derivation which avoids the $p\ensuremath{\rightarrow}\ensuremath{\infty}$ limiting procedure. Also, the Gell-Mann-Okubo mass formula is obtained in a way that naturally gives the correct form for both bosons and fermions. In the appendixes, the light-cone commutator structure of some relevant models is discussed.

Chiral Symmetry Realization in the Quark Model

Chiral symmetry realizations of the quark-gluon model are considered in the absence of self-energy insertions for the gluon and photon, so the bare fermion mass vanishes. We exhibit the conditions which realize the chiral symmetry with Nambu-Goldstone bosons as bound states. A formal argument indicates that in this model electromagnetic corrections to the strong interactions are then finite to leading order and possibly all orders.

Conserved Tensor Currents, Isovector Photons, and the Algebraic Realization of Chiral Symmetry. I. The Algebra of Couplings

Weinberg's program for the algebraic realization of chiral symmetry is considered in an enlarged chiral model obtained by adjoining to the usual SU(2) \ifmmode\times\else\texttimes\fi{} SU(2) algebra of currents, isovector and isoscalar tensor currents with equal-time commutation relations given by the quark model. The isovector tensor current is taken to be conserved, thereby permitting the introduction of "isovector photons" into the ordinary model. It is necessary to analyze asymptotically inelastic ($\ensuremath{\pi}+\ensuremath{\alpha}\ensuremath{\rightarrow}\ensuremath{\gamma}+\ensuremath{\beta}$, $\ensuremath{\pi}+\ensuremath{\alpha}\ensuremath{\rightarrow}\ensuremath{\pi}+\ensuremath{\gamma}+\ensuremath{\beta}$, $\ensuremath{\pi}+\ensuremath{\alpha}\ensuremath{\rightarrow}\ensuremath{\pi}+\ensuremath{\gamma}+\ensuremath{\gamma}+\ensuremath{\beta}$) processes as well as elastic ($\ensuremath{\pi}+\ensuremath{\alpha}\ensuremath{\rightarrow}\ensuremath{\pi}+\ensuremath{\beta}$, $\ensuremath{\gamma}+\ensuremath{\alpha}\ensuremath{\rightarrow}\ensuremath{\gamma}+\ensuremath{\beta}$) processes to close the derived algebra of couplings, which is shown to be that of SU(4).

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.