Isospin Violation in Chiral Perturbation Theory and the Decays $η\ra π\ell ν$ and $τ\ra ηπν$

Abstract

I discuss isospin breaking effects within the standard model. Chiral perturbation theory presents the appropriate theoretical framework for such an investigation in the low--energy range. Recent results on the electromagnetic contributions to the masses of the pseudoscalar mesons and the $K_{\ell 3}$ amplitudes are reported. Using the one--loop formulae for the ${\eta }_{\ell 3}$ form factors, rather precise predictions for the decay rates of $\eta \to \pi \ell \nu$ can be obtained. Finally, I present an estimate of the $τ\ra ηπν$ branching ratio derived from the dominant meson resonance contributions to this decay.

10 pages, latex, one figure available upon request

References in corpus (4)

• On the Foundations of Chiral Perturbation Theory
• Virtual Photons in Chiral Perturbation Theory
• The Masses of the Light Quarks
• Masses of the Light Quarks

Cited by in corpus (57)

• Chiral perturbation theory
• Physics Opportunities with the 12 GeV Upgrade at Jefferson Lab
• Kaon Decays in the Standard Model
• Flavor Physics in the Quark Sector
• Hadronic light-by-light scattering contribution to the muon g-2: an effective field theory approach
• QCD Isospin Breaking in Meson Masses, Decay Constants and Quark Mass Ratios
• Electromagnetic Corrections for Pions and Kaons : Masses and Polarizabilities
• Virtual Photons in Low Energy pi-pi Scattering
• Isospin Violation and the Magnetic Moment of the Muon
• Radiative tau decay and the magnetic moment of the muon
• Virtual photons in SU(2) chiral perturbation theory and electromagnetic corrections to $\pi \pi$ scattering
• pi/K -> e nu branching ratios to O(e^2 p^4) in Chiral Perturbation Theory
• Precision tests of fundamental physics with $\eta$ and ${\eta }^{\prime }$ mesons
• Electromagnetic corrections in the anomaly sector
• Isospin Breaking in K -> Pi Pi Decays
• Four-point correlator constraints on electromagnetic chiral parameters and resonance effective Lagrangians
• Virtual photons in baryon chiral perturbation theory
• Charge-dependent nucleon-nucleon potential from chiral effective field theory
• Electromagnetic Corrections to the decays $\eta \to 3\pi$
• On the Corrections to Dashen's Theorem
• Predictions on the second-class current decays ${\tau }^{-}\to {\pi }^{-}{\eta }^{(\prime )}{\nu }_{\tau }$
• The Dalitz decay pi0 -> e+ e- gamma revisited
• Effective-field theory analysis of the ${\tau }^{-}\to {\pi }^{-}{\pi }^0{\nu }_{\tau }$ decays
• The Kl3 scalar form factors in the standard model
• Electromagnetism in nonleptonic weak interactions
• Resonance Contributions to the Electromagnetic Low Energy Constants of Chiral Perturbation Theory
• Electromagnetic corrections to gamma pi(+) -> pi(0) pi(+)
• First Observation of $\tau \to 3\pi \eta {\nu }_{\tau }$ and $\tau \to f_1\pi {\nu }_{\tau }$ Decays
• Precise determination of the low-energy hadronic contribution to the muon $g-2$ from analyticity and unitarity: An improved analysis
• The decays ${\rho }^{-}\to \eta {\pi }^{-}$ and ${\tau }^{-}\to \eta ({\eta }^{\prime }){\pi }^{-}\nu$ in the NJL model
• Measurement of the tau -> 3pi eta nu Branching Fraction and a Search for a Second-Class Current in the tau -> eta'(958) pi nu Decay
• Estimate of the branching fraction ${\tau }^{-}\to \eta {\pi }^{-}{\nu }_{\tau }$, the $a_0^{-}(980)$, and non-standard weak interactions
• On meson dominance in the `second class' tau \to eta pi nu_tau decay
• Large-$N_c$ analysis of two-nucleon neutrinoless double beta decay and charge-independence-breaking contact terms
• Isospin breaking corrections to low-energy pi-K scattering
• Estimate of the Branching Fraction of tau --> pi eta' nu_tau
• On the branching ratio of the "second class" tau --> eta' pi nu_tau decay
• Electromagnetic low-energy constants in ChPT
• Observation of the doubly radiative decay ${\eta }^{\prime }\to \gamma \gamma {\pi }^0$
• Isospin violation in pion-kaon scattering
• ${\tau }^{-}\to {\eta }^{(\prime )}{\pi }^{-}{\nu }_{\tau }\gamma$ decays as backgrounds in the search for second class currents
• Explicit generating functional for pions and virtual photons
• Two-loop representations of low-energy pion form factors and pi-pi scattering phases in the presence of isospin breaking
• Contributions of order $\mathcal{O}(m_{\mathrm{quark}}^2)$ to $K_{\ell 3}$ form factors and unitarity of the CKM matrix
• Isospin Breaking in $K_{\ell 4}$ Decays of the Neutral Kaon
• Search for $\eta$ and ${\eta }^{\prime }\to {\pi }^{+}{e}^{-}{\bar{\nu }}_e+c.c.$ decays in $\jpsi \to ϕη$ and $\varphi {\eta }^{\prime }$
• Search for the decay ${\eta }^{\prime }\to \gamma \gamma \eta$
• G-parity breaking in ${\tau }^{-}\to {\eta }^{(\prime )}{\pi }^{-}{\nu }_{\tau }$ decays induced by the ${\eta }^{(\prime )}\gamma \gamma$ form factor
• Review of Rare and Forbidden $\tau$ Decays
• Towards the (Mexican) discovery of second class currents at Belle-II
• ${\tau }^{-}\to {\pi }^{-}\eta {\nu }_{\tau }$ decay induced by QED one-loop effects
• Dispersive evaluation of the second-class amplitude $\tau \to \eta \pi {\nu }_{\tau }$ in the standard model
• Hadronic and radiative decays of the tau lepton
• The second-class current decays $\tau \to \pi \eta ({\eta }^{\prime }){\nu }_{\tau }$ in the NJL model including the interaction of mesons in the final state
• Chiral Perturbation Theory with Photons and Leptons
• Reducing Hadronic Uncertainty in Low-Energy Neutral-Current Processes
• Electromagnetic Corrections to Low-Energy pi-pi Scattering