Anomalous Ward Identities Research Articles

The η′ meson disobeys the Zweig rule up to infinite color

The pseudoscalar flavor singlet meson associated with the anomalous chiral Ward identity in QCD, based on the gauge group SU( N c) and N fl (massless) quark flavors, which we denote by η′( N c, N fl), obtains a nonzero mass fro the gauge field configuration with nontrivial winding number, with fixed ratio to the mass of the ϱ meson say, in the limit N c → ∞. This proposition is related to the local bosonic current algebra.

Vector mesons, anomalies and the KSFR relation

It is shown that the physics of the anomalous σπππ vertex is consistent with the KSFR relation which relates properties of the ϱ meson to the pion decay constant. The derivation is based on anomalous Ward identities. This result shows that it is possible to formulate consistent models in which all vector-isovector processes proceed via the ϱ meson.

DERIVATION OF ANOMALIES USING THE ITÔ STOCHASTIC CALCULUS

Itô’s stochastic calculus is used to derive a number of anomalous Ward identities. The general features of the method are described and similarities with Fujikawa’s path integral approach are pointed out. The stochastic calculus provides an easily understood origin for anomalies within the framework of the stochastic quantization scheme.

Meaning of anomalous commutators and descent equation in chiral gauge theories.

The anomalous Ward identity ${\ensuremath{\partial}}_{0}$${G}^{a}$=i(${D}_{\ensuremath{\mu}}$${j}^{\ensuremath{\mu}}$${)}^{a}$ which was found by Fujikawa via path integration is discussed in the Hamiltonian framework. We obtain an answer to the following question: Why do electric fields become noncommutative as found by Jo through the Bjorken-Johnson-Low method? We also obtain a meaning for the descent procedure of Faddeev which yields the Schwinger term in the algebra of the Gauss-law constraint operators.

Effective action and meson spectrum in quantum chromodynamics

The low-energy meson spectrum of spin 0 and 1+ mesons in one-flavour massive QCD is studied. An invariance property expressed by the anomalous chiral Ward identity is used to set up a low-energy expansion for the symmetric effective action. The propagator matrix corresponding to a certain set of operators is calculated and used to study the meson spectrum in the sector under consideration. The spectrum includes two 0− mesons, one 0+ meson and one 1+ meson.

WARD IDENTITIES, TWO PHOTON DECAYS AND OFF-SHELL CORRECTIONS

Off-shell corrections are considered in the low energy theorems for π0, η, η′ and l→2γ decays to solve the anomalous Ward identities. The l→2γ prove to be sensitive to both SU(3) breaking and off-shell corrections.

Meson-gluonium mixing and the glueball candidate⇌i(1,460)

The mixing of the glueball candidate⇌i(1,460) with η and η′ is studied in a chiral symmetry breaking framework. Using the solutions of anomalous Ward identities for flavourU(3)×U(3), we find that the octet-singlet mixing angle is quite large and that our results are consistent with a large glueball component in⇌i(1,460) with moderate gluonium mixing in η and η′.

Skyrmion-baryon phenomenology in the effective gauged chiral-SU(2) action approach

The phenomenology of the baryon-skyrmion is examined within the gauged chiral-SU(2) action approach developed recently by Brihaye, Pak and Rossi. The effective action incorporates the ρ, ω and A 1 vector mesons and obeys all (normal and anomalous) Ward identities of QCD, consistently with vector meson dominance. The approach realizes the chiral × hypercharge symmetry SU(2) L × SU(2) R × U(1) Y as a local gauge symmetry, modified by the addition of degenerate vector meson mass terms (breaking the symmetry from local to global) and of a gauged Wess-Zumino anomalous action, breaking the symmetry to SU(2) V × U(1) Y. We offer a general didactic presentation of the method and emphasize those aspects relating to the higher-order couplings and to the identification of currents. Detailed numerical investigations are carried out for the chiral soliton with respect to the classical field theory problem as well as the semi-classical quantization of isorotational zero modes. We treat first a truncated version where only ρ and ω are present and consider next, in classical approximation only, the complete version with ρ, ω and A 1 present. The results obtained are globally satisfactory, better for the classical mass and isoscalar observables than for the spin and isovector observables (Δ − N mass difference, μ v and g A). For a precise matching of predictions with experiment one cannot dispense with a readjustment of physical parameters F π and g. However, the amplitude of the readjustment needed are relatively mild (−15% for F π and 40% for g with respect to the meson phenomenology) and the improved fit to the nucleon properties is superior to that of the conventional Skyrme model.

Nonet symmetry, anomalous Ward identities and meson-gluonium mixing

TheSU(3) flavour structure of ι(1460) is exploited to seek consistency between vector meson dominance and anomalous Ward identities. Our analysis shows that a minimum of 10 to 20% breaking in nonet symmetry is necessary to get an overall fit with the radiative rates of low-lying η and η′.

Pauli couplings and chiral anomalies in realistic Kaluza-Klein theories

The anomalous chiral Ward identity for the gauge fields in a class of realistic Kaluza-Klein models is obtained. Particular attention is paid to the six-dimensional model of Randjbar-Daemi et al (1983), including Pauli couplings and the reduction of appropriate topological terms.

The iota (1440), anomalous Ward identities, and topological susceptibility for QCD.

Anomalous Ward identities for QCD are comprehensively analyzed taking into account contributions of all known pseudoscalar mesons, including the iota(1440 MeV) which is a possible glueball candidate. Implications for the standard resolution of the U(1) problem are examined by imposing the important and crucial constraint of positivity for the topological susceptibility. The pure Yang-Mills susceptibility: a quantity relevant in quenched lattice calculations: is shown to increase quite considerably in the presence of the iota, while the total susceptibility is reduced and may even vanish. Allowed ranges for the axial couplings are delineated and two classes of solution emerge: one corresponding to an iota with suppressed singlet axial coupling; the other to a large eta'-like coupling. It may be possible to discriminate between these two alternatives by measurements of the branching ratio for iota..-->..KK-bar..pi..: values near 100% give suppressed couplings; values below 50% unsuppressed ones.

How effective massless fermions modify the anomalous decays of the goldstone bosons

We consider the consequences of the anomalous Ward identities when both Goldstone bosons and massless fermions appear as low-energy degress of freedom in confining theories. A general procedure for evaluating the anomalous vertices of the Goldstone bosons is given. We show that these vertices can be described in a compact way. The emerging structures have an intrinsic geometrical meaning. Some particular features occuring when the massless fermions are superpartners of the Goldstone bosons are illustrated on the example of supersymmetric QCD.

O(mq/N) effects in the Ward identities approach to the pseudoscalar nonet

Anomalous Ward identities are investigated in the combined chiral and large-N limit of QCD, up to non-leading O(mq/N) terms, taking into account chiral symmetry breaking effects in the η′ axial vector couplings. The bound θ > 16° for the η - η′ mixing angle is obtaned. Gasser and Leutwyler results on the O(mq2) corrections to the η mass are used to determine the size of the O(mq/N) terms, which are found to be reasonably small. Problems with the anomaly predictions for η, η′ → γγ are pointed out. Some aspects of the non-smoothness of the large-N expansion in presence of SU3 breaking effects are clarified.

The triangle anomaly in the light-cone gauge

It is shown that the triangle anomaly can be evaluated in the light-cone gauge and that the result obtained is consistent with the usual covariant one. We use two different procedures: (i) Eliminating the nonphysical fields from the covariant anomalous Ward identity. (ii) Carrying out a chiral transformation on the light-cone Lagrangian. The use of both dimensional and Pauli-Villars regularisations are discussed.

Chiral anomalies in the stochastic quantization scheme

Stochastic quantization scheme with an invariant stochastic regularization is applied to models of chiral fermions in even-dimensional spacetime. In spite of the manifest preservation of chiral gauge symmetries by stochastic regularization of the stochastic averages, the anomalous chiral Ward identities are correctly reproduced in a covariant form after removing the regularization.

How large is the η-η′ mixing angle?

New experimental results on Γ ( η → γγ) seem to require a large η-η′ mixing angle Θ. Using anomalous Ward identities and 1/ N arguments, we show that0 Θ > 16°, and that values of Θ as large as 28° are theoretically admissible, and in reasonable agreement with the new data. A satisfactory prediction for Γ( J/ ψ → η′ γ) is also obtained in the range 16° < Θ < 25°.

On the definition of topological susceptibility via lattice-anomalous ward identities and its perturbative tail

We consider the lattice definition of the topological charge density suggested by the U(1)A anomalous Ward identity. We prove that the associated topological susceptibility has no perturbative tail in the “chiral limit” (zero renormalized quark mass) by studying the infrared properties of perturbative lattice QCD.

Solutions of anomalous Ward identities in a QCD framework. II

Solutions of anomalous Ward identities in a QCD framework. II

The Gauge Invariant Wess-Zumino Action Functional, Chiral Anomalies and Topology

The gauge invariant Wess-Zumino action functional in dimensional space is obtained by properly constructing the manifestly gauge invariant -forms which satisfy the Abelian anomalous Ward identity in dimensional space. Apart from its simplicity, directness, the construction clearly embodies the connections between the gauge invariant Wess-Zumino action functional, chiral anomalies and topology.

Solutions of anomalous Ward identities in a QCD framework

The anomalous Ward identities are solved in the framework of QCD. An important outcome of this calculation is the possibility of an extremely small width for ι→γγ decay mode.