$L\to l{l}^{\prime }{l}^{\prime }\hat{I}{½}_l\hat{I}{½}_L$ in the SM and beyond

Abstract

We study the $L\to l{l}^{\prime }{l}^{\prime }\hat{I}{½}_l\hat{I}{½}_L$ decays ($L=\ddot{I}„,\hat{I}¼$; $l,l^{\prime }=\hat{I}¼,e$) in the Standard Model (SM) and in the effective field theory (EFT) description of the weak charged current at low energy, both for polarized and unpolarized $L$, keeping the $l,l^{\prime }$ mass dependence. We clarify the discrepancy between two previous SM calculations of the decay rate improving their precision. The recent $3.5\ddot{I}ƒ$ anomaly found in $\ddot{I}„\to e{\hat{I}}^3\bar{\hat{I}}{½}_e\hat{I}{½}_{\ddot{I}}„$ could be checked using our precise prediction for the $\ddot{I}„\to eee\bar{\hat{I}}{½}_e\hat{I}{½}_{\ddot{I}}„$ decays, which shall be measured analyzing already existing data from the first generation B-factories. It is shown how measurements of the di-$l^{\prime }$ mass distribution (with appropriate cuts) and $T$-asymmetries are able to reveal the corresponding lepton flavor violating (LFV) processes without neutrinos in the final state.

5 pages, two figures, contribution to the Proceedings of the PhiPsi15 Workshop, Sep. 23-26, 2015, Hefei, China. To be published by the Journal of University of Science and Technology of China