Radiative $\mu$ and $\tau$ leptonic decays at NLO

Abstract

We present the differential rates and branching ratios of the radiative decays $\tau \to l\bar{\nu }\nu \gamma$, with $l=e$ or $\mu$, and $\mu \to e\bar{\nu }\nu \gamma$ in the Standard Model at next-to-leading order. Radiative corrections are computed taking into account the full depencence on the mass $m_l$ of the final charged leptons, which is necessary for the correct determination of the branching ratios. Only partial agreement is found with previous calculations performed in the $m_l\to 0$ limit. Our results agree with the measurements of the branching ratios $\mathcal{B}(\mu \to e\bar{\nu }\nu \gamma )$ and $\mathcal{B}(\tau \to \mu \bar{\nu }\nu \gamma )$ for a minimum photon energy of 10 MeV in the $\mu$ and $\tau$ rest frames, respectively. Babar's recent precise measurement of the branching ratio $\mathcal{B}(\tau \to e\bar{\nu }\nu \gamma )$, for the same photon energy threshold, differs from our prediction by 3.5 standard deviations.

13 pages, 1 figure, results included as ancillary files

References in corpus (9)

• The automated computation of tree-level and next-to-leading order differential cross sections, and their matching to parton shower simulations
• Big-Bang Nucleosynthesis
• Tenth-Order Electron Anomalous Magnetic Moment --- Contribution of Diagrams without Closed Lepton Loops
• MEG Upgrade Proposal
• W-propagator corrections to muon and tau leptonic decays
• Measurement of the radiative decay of polarized muons in the MEG experiment
• Muon decay spin asymmetry
• Measurement of the branching fractions of the radiative leptonic tau decays tau -> e gamma nu anti-nu and tau -> mu gamma nu anti-nu at BaBar
• New results in rare allowed muon and pion decays

Cited by in corpus (19)

• New Developments in FeynCalc 9.0
• Technical design of the phase I Mu3e experiment
• QED at NNLO with McMule
• $\tau$ dipole moments via radiative leptonic $\tau$ decays
• Fully differential NLO predictions for the rare muon decay
• Measurement of the radiative decay of polarized muons in the MEG experiment
• Fully differential NLO predictions for the radiative decay of muons and taus
• Five-body leptonic decays of muon and tau leptons
• Next-to-leading order prediction for the decay $\mu \to e(e^{+}{e}^{-})\nu \bar{\nu }$
• The effective field theory of low scale see-saw at colliders
• Michel parameters in radiative muon decay
• Measurement of the tau Michel parameters $\bar{\eta }$ and $\xi \kappa$ in the radiative leptonic decay ${\tau }^{-}\to {\ell }^{-}{\nu }_{\tau }{\bar{\nu }}_{\ell }\gamma$
• Michel parameters for $\tau$ decays $\tau \to l\nu \bar{\nu }(l=e,\mu )$ in a general two Higgs doublet model with $\mu -\tau$ flavor violation
• A theory vade mecum for PSI experiments
• Superfactory of bottomed hadrons Belle II
• Dirac-Majorana neutrinos distinction in four-body decays
• Effective-field theories for charged lepton flavour violation
• Can a Nonstandard Invisible Pair Mimic the Michel Distribution?
• Testing $WW\gamma$ vertex in radiative muon decay