One-loop effective LFV $Zl_kl_m$ vertex from heavy neutrinos within the Mass Insertion Approximation

TL;DR

This paper derives a simple formula for the one-loop lepton flavor violating Z boson vertex in low scale seesaw models with heavy neutrinos, enabling quick estimates of rare decay rates relevant for future collider experiments.

Contribution

It introduces a novel, simplified formula for the effective LFV Z vertex using the mass insertion approximation and large neutrino mass expansion, facilitating phenomenological analysis.

Findings

Derived a simple formula for the LFV Z vertex applicable to inverse seesaw models.

Estimated maximum decay rates for Z → l_k l_m consistent with current experimental bounds.

Found decay rates potentially observable at future lepton colliders.

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 $Z \to l_k {\bar l}_m$ 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.