Anomalous $\eta /{\eta }^{\prime }$ Decays: The Triangle and Box Anomalies

Abstract

We examine the decay modes $η/\etp\ra π^+ π^- γ$ within the context of the Hidden Local Symmetry (HLS) Model. Using numerical information derived in previous fits to $VP\gamma$ and $V{e}^{+}{e}^{-}$ decay modes in isolation and the $\rho$ lineshape determined in a previous fit to the pion form factor, we show that all aspects of these decays can be predicted with fair accuracy. Freeing some parameters does not improve the picture. This is interpreted as a strong evidence in favor of the box anomaly in the $η/\etp$ decays, which occurs at precisely the level expected. We also construct the set of equations defining the amplitudes for $η/\etp\ra π^+ π^- γ$ and $ η/\etp \ra \ggam $ at the chiral limit, as predicted from the anomalous HLS Lagrangian appropriately broken. This provides a set of four equations depending on only one parameter, instead of three for the traditional set. This is also shown to match the (two--angle, two--decay--constant) $η-\etp$ mixing scheme recently proposed and is also fairly well fulfilled by the data. The information returned from fits also matches expectations from previously published fits to the $VP\gamma$ decay modes in isolation.

47 pages

References in corpus (11)

• Measurement of e+e- -> pi+pi- cross section with CMD-2 around rho-meson
• The decay pi0 to gamma gamma to next to leading order in Chiral Perturbation Theory
• Electromagnetic corrections in the anomaly sector
• Rho Meson Properties in the Chiral Theory Framework
• Mixing of Pseudoscalar Mesons
• Can One See the Number of Colors?
• Allowed Eta Decay Modes and Chiral Symmetry
• Isospin Symmetry Breaking within the HLS Model: A Full ($\rho ,\omega ,\varphi$) Mixing Scheme
• Study of the $\pi \pi$ mass spectra in the process $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}{\pi }^0$ at $\sqrt[]{s}\simeq 1020$ MeV
• Study of the decay phi --> pi+pi-pi0 with the KLOE detector
• The Pion Form Factor Within the Hidden Local Symmetry Model

Cited by in corpus (16)

• Physics with the KLOE-2 experiment at the upgraded DA$\varphi$NE
• Study of the eta-eta' system in the two mixing angle scheme
• Model-independent approach to eta -> pi+ pi- gamma and eta' -> pi+ pi- gamma
• Upgraded Breaking Of The HLS Model: A Full Solution to the tau-e+e- and phi Decay Issues And Its Consequences On g-2 VMD Estimates
• The Dipion Mass Spectrum In e+e- Annihilation and tau Decay: A Dynamical (rho0, omega, phi) Mixing Approach
• A Global Treatment Of VMD Physics Up To The $\varphi$: I. $e^{+}{e}^{-}$ Annihilations, Anomalies And Vector Meson Partial Widths
• Exclusive Measurement of the eta --> pi+ pi- gamma Decay
• Measurement of Γ(η-> π^+π^-γ)/Γ(η-> π^+π^-π^0) with the KLOE Detector
• Measurements of Branching Ratios for $\eta$ Decays into Charged Particles
• Glueballs, Hybrids, Pentaquarks : Introduction to Hadron Spectroscopy and Review of Selected Topics
• $\eta -{\eta }^{\prime }$ Mixing Angle from Vector Meson Radiative Decays
• Multiple solutions in extracting physics information from experimental data
• Can VMD improve the estimate of the muon g-2 ?
• Account for axial vector mesons in the $\eta \to {\pi }^{+}{\pi }^{-}\gamma$ and ${\eta }^{\prime }\to {\pi }^{+}{\pi }^{-}\gamma$ decays
• ${\eta }^{{(}^{\prime })}\to {\pi }^{+}{\pi }^{-}{\gamma }^{(\ast )}$ in large-$N_c$ chiral perturbation theory
• Light hadron, Charmonium(-like) and Bottomonium(-like) states