One-loop effective LFV varvec{Zl_kl_m} vertex from heavy neutrinos within the mass insertion approximation

M. J. Herrero,X. Marcano,R. Morales,A. Szynkman

doi:10.1140/epjc/s10052-018-6281-3

Abstract

In this paper we study the effective lepton flavor violating vertex of an electroweak Z gauge boson and two charged leptons with different flavor, l_k and l_m, that is generated to one-loop in low scale seesaw models with right handed neutrinos whose masses are heavier than the electroweak scale. We first compute the form factor describing this vertex by using the mass insertion approximation, where the flavor non-diagonal entries of the neutrino Yukawa coupling matrix are the unique origin, to one-loop level, of lepton flavor changing processes with charged leptons in the external legs. Then, by considering the proper large right handed neutrino mass expansion of the form factor, we derive a formula for the Z l_k l_m effective vertex which is very simple and useful for fast phenomenological estimates. In the last part of this work we focus on the phenomenological applications of this vertex for simple and accurate estimates of the Z rightarrow l_k {bar{l}}_m decay rates. Concretely, this vertex will allow us to conclude easily on the maximum allowed decay rates by present data in the inverse seesaw model. The found rates are promising, at the reach of future lepton colliders.

Highlights

We consider the Inverse Seesaw model (ISS) [1,2,3,4] as a specific realization of these low scale seesaw models, and work with three pairs of right handed (RH) neutrinos with opposite lepton numbers, which for simplicity are assumed to be quasidegenerate
In this paper we study the effective lepton flavor violating vertex of an electroweak Z gauge boson and two charged leptons with different flavor, lk and lm, that is generated to one-loop in low scale seesaw models with right handed neutrinos whose masses are heavier than the electroweak scale
The effective vertex that we look for summarizes the one-loop effects of the heavy right handed neutrinos, and it is obtained from the result of this large MR expansion, generically, as: VZeffk m = VZeffk m | p12=m2Z = FLMIA| p12=m2Z (MR), (25)

Summary

Introduction

We consider the Inverse Seesaw model (ISS) [1,2,3,4] as a specific realization of these low scale seesaw models, and work with three pairs of RH neutrinos with opposite lepton numbers, which for simplicity are assumed to be quasidegenerate. Regarding the specific LFV processes, we focus here on the particular case of the LFV Z boson decays (LFVZD) to charged leptons with different flavor, Z → km, which have interesting rates in low energy scale seesaw models with heavy neutrinos [3,4,7,8,9,10,11,12,20,25], and in particular in the ISS model, as studied in [20,25] working in the physical basis or in [21] by computing the relevant Wilson coefficients. In the present case of the ISS with right handed neutrinos and neglecting the lepton masses there is just one form factor involved [12], FL. This will be explicitly shown in our forthcoming computation. The definitions of all these loop functions above and their interesting limits for the present paper are collected in Appendices A and D

Check of gauge invariance of the on-shell form factor for LFVZD

Computation of the one-loop effective vertex for LFVZD

H r m 2W

Conclusions

G Z k ni