Exact relativistic beta decay endpoint spectrum

TL;DR

This paper derives an exact relativistic formula for the beta decay endpoint spectrum, simplifies it for practical use, and discusses implications for neutrino experiments and future analyses.

Contribution

It provides the first exact relativistic derivation of the beta decay endpoint spectrum in a simple, factorized form, enhancing analysis accuracy.

Findings

Exact relativistic formula derived and simplified

Approximation aligns with KATRIN fit method

Discussion on neutrino oscillation data relevance

Abstract

The exact relativistic form for the beta decay endpoint spectrum is derived and presented in a simple factorized form. We show that our exact formula can be well approximated to yield the endpoint form used in the fit method of the KATRIN collaboration. We also discuss the three neutrino case and how information from neutrino oscillation experiments may be useful in analyzing future beta decay endpoint experiments.