# Testing the nature of neutrinos from four-body $\tau$ decays

## TL;DR

This paper investigates four-body tau decays to determine whether neutrinos are Majorana or Dirac particles by analyzing specific decay processes and their branching ratios, proposing experimental detection methods.

## Contribution

It introduces a method to distinguish Majorana from Dirac neutrinos through tau decay processes and calculates relevant branching ratios.

## Key findings

- Calculated branching ratios for tau decays involving neutrinos.
- Proposed experimental approach to detect neutrino nature.
- Demonstrated how lepton number violation indicates Majorana neutrinos.

## Abstract

This paper is designed to discuss four-body lepton number violating tau decay. We study the processes $\tau^+ \to e^+ e^+ \pi^- \nu_\tau$ and $\tau^+ \to e^+ e^+ \pi^- \nu_e$ to determine the nature of neutrino. The first process violates lepton number by two units which can only happen through an internal Majorana. The second one conserves lepton number but violates lepton flavor which can take place with both Majorana neutrino and Dirac neutrino. We calculate their branching ratio $Br$ and differential branching ratio $dBr/dE_\pi$ to distinguish Majorana neutrino vs. Dirac neutrino. We also propose the possibility of experiment to perform this detection.