Data-driven study of the implications of anomalous magnetic moments and lepton flavor violating processes of e , μ , and τ

Abstract

We study anomalous magnetic moments and flavor violating processes of $e$, $\ensuremath{\mu}$, and $\ensuremath{\tau}$ leptons. We use a data driven approach to investigate the implications of the present data on the parameters of a class of models, which has spin-0 scalar and spin-$1/2$ fermion fields. We compare two different cases, which has or does not have a built-in cancelation mechanism. Our findings are as following. Chiral interactions are unable to generate large enough $\mathrm{\ensuremath{\Delta}}{a}_{e}$ and $\mathrm{\ensuremath{\Delta}}{a}_{\ensuremath{\mu}}$ to accommodate the experimental results. Although sizable $\mathrm{\ensuremath{\Delta}}{a}_{e}$ and $\mathrm{\ensuremath{\Delta}}{a}_{\ensuremath{\mu}}$ can be generated from nonchiral interactions, they are not contributed from the same source. Presently, the upper limit of $\ensuremath{\mu}\ensuremath{\rightarrow}e\ensuremath{\gamma}$ decay gives the most severe constraints on photonic penguin contributions in $\ensuremath{\mu}\ensuremath{\rightarrow}e$ transitions, but the situation may change in considering future experimental sensitivities. The $Z$-penguin diagrams can constrain chiral interaction better than photonic penguin diagrams in $\ensuremath{\mu}\ensuremath{\rightarrow}e$ transitions. In most of the parameter space, box contributions to $\ensuremath{\mu}\ensuremath{\rightarrow}3e$ decay are subleading. The present bounds on $\mathrm{\ensuremath{\Delta}}{a}_{\ensuremath{\tau}}$ and ${d}_{\ensuremath{\tau}}$ are unable to give useful constraints on parameters. In $\ensuremath{\tau}\ensuremath{\rightarrow}e$ ($\ensuremath{\mu}$) transitions, the present $\ensuremath{\tau}\ensuremath{\rightarrow}e\ensuremath{\gamma}(\ensuremath{\mu}\ensuremath{\gamma})$ upper limit constrains the photonic penguin contribution better than the $\ensuremath{\tau}\ensuremath{\rightarrow}3e$ $(3\ensuremath{\mu})$ upper limit, and $Z$-penguin amplitudes constrain chiral interaction better than photonic penguin amplitudes. Box contributions to $\ensuremath{\tau}\ensuremath{\rightarrow}3e$ and $\ensuremath{\tau}\ensuremath{\rightarrow}3\ensuremath{\mu}$ decays can sometime be comparable to $Z$-penguin contributions. The ${\ensuremath{\tau}}^{\ensuremath{-}}\ensuremath{\rightarrow}{e}^{\ensuremath{-}}{\ensuremath{\mu}}^{+}{e}^{\ensuremath{-}}$ and ${\ensuremath{\tau}}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{\ensuremath{-}}{e}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ rates are highly constrained by $\ensuremath{\tau}\ensuremath{\rightarrow}e\ensuremath{\gamma}$, $\ensuremath{\mu}\ensuremath{\rightarrow}e\ensuremath{\gamma}$ and $\ensuremath{\tau}\ensuremath{\rightarrow}\ensuremath{\mu}\ensuremath{\gamma}$, $\ensuremath{\mu}\ensuremath{\rightarrow}e\ensuremath{\gamma}$ upper limits, respectively. We compare the current experimental upper limits, future sensitivities and bounds from consistency on various muon and tau LFV processes.