# Measuring the heavy neutrino oscillations in rare W boson decays at the Large Hadron Collider

## TL;DR

This paper explores the potential to detect heavy neutrino oscillations through lepton number violating W boson decays at the LHC, focusing on scenarios with neutrino masses between 1 and 10 GeV.

## Contribution

It introduces a method to measure heavy neutrino oscillations via LNV decay signatures at the LHC, considering nearly degenerate neutrinos within a specific mass range.

## Key findings

- Possible to observe LNV oscillation modulation at the LHC under realistic conditions.
- Identifies the decay process involving heavy neutrinos as a promising signature.
- Analyzes the impact of neutrino mass degeneracy on detection prospects.

## Abstract

Majorana neutrinos in the seesaw model can have sizable mixings through which they can be produced at the Large Hadron Collider (LHC) and show a remarkable Lepton Number Violating (LNV) signature. In this article we study the LNV decay of the W boson via two almost degenerate heavy on-shell Majorana neutrinos $N_j$, into three charged leptons and a light neutrino. We consider the scenario where the heavy neutrino masses are within $1$ GeV $\leq M_N \leq 10$ GeV. We evaluated the possibility to measure a LNV oscillation process in such a scenario, namely, the modulation of the quantity $d \Gamma/d L$ for the process at the LHC where $W^{\pm} \to \mu^{\pm} N \to \mu^{\pm} \tau^{\pm} W^{\mp *}$ $ \to \mu^{\pm} \tau^{\pm} e^{\mp} \nu_e$. $L$ is the distance within the detector between the two vertices of the process. We found out some realistic conditions under which such a modulation could be probed at the LHC.