Triangle Anomalies Research Articles

Anomalies in nonweak interactions

It is shown how the problem of tensor-trace and triangle anomalies can be avoided in the treatment of the nonweak-decay processes σ → 2γ and π0→2γ.

Non-abelian gauge theories and triangle anomalies

Conditions for the validity of (a weak version of) the Adler-Bardeen theorem for non-Abelian gauge theories are obtained. Its validity ensures that those theories in which the coefficient of the triangle anomaly vanishes at the one-loop level are anomaly free and therefore they are renormalizable and unitary. This result is based on the derivation of Slavnov-Taylor identities modified by the presence of anomalous terms and on a renormalization-group-like equation for the anomaly coefficient. In the derivation, the dimensional regularization scheme has been followed.

A New Vectorlike Model of the Weak Interactions

A vectorlike model of the weak interactions with six quark flavors is proposed. The model is based on the gauge theory with the group SU (2) XU (1). It is shown that the model well describes the rise of the ratio of li- to v-induced total cross sections by the charged current. Discussions on the various weak phenomena including the parity violation in atomic physics are given. Gauge theory is interesting as a candidate for the so-called unified theory m particle physics. 1l In the framework of the gauge theory, many kinds of models can be considered. Hovvever, any meaningful model must be free from the triangle anomalies which destroy the renormalizability.'l The anomalies are most naturally removed in the vector like model. 1l Furthermore, the vectorlike model has very interesting properties. For example, we might be able to understand, in the frame­ work of the vectorlike gauge theory, that the left-right asymmetry of nature 1s caused by the spontaneous symmetry breaking. Recently several authors have proposed the models of this kind. 3l One of the characteristic features of their models is that the hadronic neutral current is purely vector type. Therefore their models predict, for instance, O'Nc/ ONc = 1, where Oxc(O'Nc) stands for the inclusive neutrino (antineutrino) cross section by the neu­ tral current. However, experimental data show an apparent departure from their predictions. The most recent data indicate if~c/ O~c<0.61 ± 0.25, where D denotes the averaged nucleon target.') The vectorlike models with the parity violating neutral current have been already proposed.sl,Bl In the model of the Kanazawa group, quark flavors transform as triplets under the weak SU (2), and an artificial angle relation has been assumed in order to guarantee the universality of the charged current. sl The Barnett's model 1 6) is very beautiful and well describes the anomaly in ifcc at high energies with bottom-quark mass ~5 Ge V, where ifcc is the antineutrino-nucleon inclusive cross section by the charged current.7l,lll His model predicts opposite sign for the parity violation in atomic physics compared with the prediction of the conventional GIM modeP0l for Bi atom, if the transformation properties of the lepton sector are reasonably chosen.8l

Generalized gauge for the weak interaction and theΔI=12rule

We show that the local gauge group Sp(4)\ifmmode\times\else\texttimes\fi{}U(1) can be adopted to obtain the standard results for the effective lowest-order weak interaction but with a $\ensuremath{\Delta}I=\frac{1}{2}$ nonleptonic current-current interaction. Some other features of our model are the presence of heavy leptons, the cancellation of triangle anomalies between leptons and quarks if the latter carry charm and color, and, at least in one version, the presence of two extra quarks with the same charge as $u$ and $c$.

Models with more than four quarks

Several models with more than four quarks are reviewed and compared with the four-quark model. They generally have right- and left-handed currents and are of the S${\mathrm{U}}_{2}$ \ifmmode\times\else\texttimes\fi{} ${\mathrm{U}}_{1}$ type. The lepton sectors are also discussed including the possibilities of heavy charged and neutral leptons. The weak phenomenology, triangle anomalies, degenerate quark masses, and radial excitations are examined.

Anomalous currents in gauge field theories

Properties of symmetry currents are examined within the context of renormalizable gauge field theories. The existence of triangle anomalies requires that some of the symmetry currents must have well-defined gauge transformation properties. Exact low-energy theorems for certain matrix elements of the divergences of the currents are established to all orders in perturbation theory.

A chiral SU(4) × SU(4) gauge theory of weak and electromagnetic interactions

A lepton hadron analogy is considered based on the gauge group SU(4) L × SU(4) R × U(1), which is broken entirely spontaneously. The model satisfies the physical requirements of the V-A theory, muon-electron universality, no neutral strangeness changing currents, the Cabibbo structure for the SU(3) currents, and triangle anomalies can be avoided. The contribution of the existing neutral currents to various neutrino processes are calculated.

S-matrix elements in the presence of shadow states, the Bjorken limit and shadow quarks

When a scattering reaction occurs, it is usually assumed that the complete set of collision states is entirely composed of travelling waves, hense any constituent, in principle, is observable. Should, however, either quarks, regulator photons or lepton satellites be standing wave states, i.e. only shadow states, we would not expect to have observed them. In this paper we discuss the new terms which modify the usual dispersion relations and the Low equation and argue that present two-body experiments do not provide strong tests for their presence. In the Bjorken limit these piecewise analytic terms vanish. Yet, in a shadow indefinite-metric theory, the logarithmic terms breaking this limit are still absent. The triangle anomalies, therefore, should only be taken seriously in low energy reactions. A stronger constraint on the presence of shadow states can be provided by verification of the Callen-Gross sum rule. By means of a simple version of the Kuti-Weisskopf model, containing valence quarks and quark-antiquark pairs, we demonstrate explicitly how quarks can be shadow states. In an appendix, in formal scattering theory with shadow states, the correct formal solutions for the exact asymptotic states, both physical and shadow, are obtained.

Weak-Boson Triangle Anomalies

The causal methods of source theory are used to calculate the triangle anomalies of weak bosons (${W}^{\ifmmode\pm\else\textpm\fi{}}$ and $Z$) in a unified gauge theory of weak and electromagnetic interactions (not involving heavy leptons). The pseudoelectric form factors for these particles are also presented.

Second-Order Corrections to Triangle Anomalies in an Abelian Gauge Theory

We consider an Abelian gauge theory of weak interactions which is arranged so that in lowest order there are no anomalies in the divergence of the axial-vector current. This is done by having two fermions whose couplings to the axial-vector current are equal in magnitude but opposite in sign. We then show that while the second-order corrections to the anomaly are nonzero for each of the fermions, their sum vanishes, ensuring that the theory is anomaly-free through second order.

Second-Order Radiative Corrections to the Triangle Anomaly. II

In a preceding paper, we have calculated the radiative correction to the "triangle anomaly," using source-theoretical techniques. Here we apply the same methods to a different causal arrangement, and obtain the same result, giving a total anomaly through order $\ensuremath{\alpha}$ proportional to $1+\frac{\ensuremath{\alpha}}{2\ensuremath{\pi}}$. In order to obtain this result, we found it necessary to compute (for ${m}_{\ensuremath{\pi}}=0$) the first radiative corrections to the ${\ensuremath{\pi}}^{0}$ photoproduction amplitudes, which are presented here for the first time.

Second-Order Radiative Corrections to the Triangle Anomaly. I

Lowest-order radiative corrections to the pion-photon-photon vertex are calculated in the pseudoscalar $\ensuremath{\pi}N\overline{N}$ theory. Causal analysis of two- and three-particle exchange processes is used, in the context of Schwinger's source theory, to calculate the spectral weight function for the vertex function. Evaluated at zero momentum transfer squared, this vertex function gives the so-called triangle anomaly in the relation between the pseudoscalar and axial-vector couplings, in second order. Unlike previous authors, we find a nonzero result, giving a total anomaly through this order proportional to $1+\frac{\ensuremath{\alpha}}{2\ensuremath{\pi}}$. This discrepancy is due to the fact that we have normalized the pseudoscalar form factor at zero momentum transfer squared, rather than at $\frac{3{m}^{2}}{\mathrm{ln}(\frac{{\ensuremath{\mu}}^{2}}{{m}^{2}})}$, where $\ensuremath{\mu}$ is the fictitious photon mass. Independent of the choice of normalization point, there exist radiative corrections to the low-energy theorem for ${\ensuremath{\pi}}^{0}$ decay.

Gauge Theories Without Anomalies

Theories with spontaneously broken gauge symmetry but without triangle anomalies can yield renormalizable models of weak and electromagnetic interactions. We identify and discuss the class of anomaly-free gauge theories.

Absence of Second-Order Correction to the Triangle Anomaly in Quantum Electrodynamics

Absence of Second-Order Correction to the Triangle Anomaly in Quantum Electrodynamics

Triangle anomalies from Einstein manifolds

The triangle anomalies in conformal field theory, which can be used to determine the central charge a, correspond to the Chern-Simons couplings of gauge fields in AdS5 under the gauge/gravity correspondence. We present a simple geometrical formula for the Chern-Simons couplings in the case of type IIB supergravity compactified on a five-dimensional Einstein manifold X. When X is a toric Sasaki-Einstein manifold, we show that the gravity result is in perfect agreement with the corresponding quiver gauge theory. This article is based on the work [1] by the speaker, S. Benvenuti and L. A. Pando Zayas.