# Interference effects in LNV and LFV semileptonic decays: the Majorana hypothesis

## TL;DR

This paper investigates how interference effects among multiple sterile Majorana fermions can significantly alter the expected rates of lepton number violating and conserving semileptonic decays, impacting interpretations of experimental results.

## Contribution

It introduces the first detailed analysis of interference effects in semileptonic decays involving multiple sterile fermions, highlighting their impact on decay rates and experimental interpretations.

## Key findings

- Interference can enhance or suppress decay modes depending on CP phases.
- Non-observation of a mode does not necessarily imply absence of Majorana neutrinos.
- Interference effects are significant in interpreting future kaon decay experiments.

## Abstract

In the case where the Standard Model is extended by one heavy Majorana fermion, the branching fractions of semileptonic meson decays into same-sign and opposite-sign dileptons are expected to be of the same order. As we discuss here, this need not be the case in extensions by at least two sterile fermions, due to the possible destructive and constructive interferences that might arise. Depending on the $CP$ violating phases, one can have an enhancement of the lepton number violating modes and suppression of the lepton number conserving ones (and vice-versa). We explore for the first time the interference effects in semileptonic decays, and illustrate them for a future observation of kaon decays at NA62. We also argue that a non-observation of a given mode need not be interpreted in terms of reduced active-sterile mixings, but that it could instead be understood in terms of interference effects due to the presence of several sterile states; in particular, for different-flavour final state charged leptons, observing a lepton number conserving process and not a lepton number violating one does not rule out that the mediators are Majorana fermions.