# Revisiting the flavor violating decays of the Tau and Mu leptons in the Standard Model with massive neutrinos

### Submission summary

 As Contributors: Gerardo Hernández-Tomé Preprint link: scipost_201811_00016v1 Date accepted: 2019-01-09 Date submitted: 2018-11-14 Submitted by: Hernández-Tomé, Gerardo Submitted to: SciPost Physics Proceedings Proceedings issue: The 15th International Workshop on Tau Lepton Physics (Amsterdam, 2018-09) Domain(s): Theoretical Subject area: Quantum Physics

### Abstract

The flavor violating leptonic decays of the $\tau$ and $\mu$ leptons into three lighter charged leptons are revisited in the framework the Standard Model with massive neutrinos. In contrast to the previous prediction, we have found strongly suppressed rates for the $\tau^-\to \mu^- \ell^+ \ell^-$ ($\ell=\mu, e$) decays. Our results are in good agreement with the approximation of neglecting masses and momenta of the external particles in the loop integrals made in the first computation for the $\mu^- \to e^-e^+ e^-$ decay.

### Submission & Refereeing History

Submission scipost_201811_00016v1 on 14 November 2018

## Reports on this Submission

### Anonymous Report 1 on 2018-12-12 Invited Report

• Cite as: Anonymous, Report on arXiv:scipost_201811_00016v1, delivered 2018-12-12, doi: 10.21468/SciPost.Report.737

### Report

This contribution reports on a recalculation of all the processes of the kind L− → l−l′−l′+ within the Standard Model with massive neutrinos. Main aim of this calculation is to verify the claim in ref. [9] of BR(τ− → μ−l+l−) ≥ 10−14 within the same model. Ref. [9] calculates this process by performing an expansion around the momentum transfer q^2 = 0. This contribution points out that, being q^2 much larger than the neutrino mass squared, the expansion in ref. [9] amounts to evaluating the amplitude outside the physical region.

The main results of this contributions are summarized in table 2, confirming that, due to the smallness of the (m_neutrino / m_W)^4 ratio, all processes of the kind L− → l−l′−l′+ are hopelessly small within the SM, and any measurement would be a clear sign of new physics.

Before accepting the contribution, I would like to ask whether the relevant paper, ref. [23], has meanwhile been published in a journal.

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Author Gerardo Hernández-Tomé on 2018-12-13 (in reply to Report 1 on 2018-12-12)

Dear referee, thanks for reading our manuscript. Regarding your question, we have recently received a report by EPJC editor asking only for minor style changes. We sent our answer yesterday. We hope our work will be published soon.