$\beta$-Decay Spectrum, Response Function and Statistical Model for Neutrino Mass Measurements with the KATRIN Experiment

TL;DR

This paper develops a comprehensive theoretical and statistical framework for analyzing the beta decay spectrum in the KATRIN experiment to measure the neutrino mass with high precision.

Contribution

It provides detailed analytical models of the beta spectrum, response function, and statistical methods tailored for KATRIN's neutrino mass measurement.

Findings

Analytical expressions for beta decay spectrum near the endpoint.

Quantification of theoretical and experimental correction impacts.

Guidelines for statistical analysis and confidence interval construction.

Abstract

The objective of the Karlsruhe Tritium Neutrino (KATRIN) experiment is to determine the effective electron neutrino mass $m(\nu_\text{e})$ with an unprecedented sensitivity of $0.2\,\text{eV}$ (90\% C.L.) by precision electron spectroscopy close to the endpoint of the $\beta$ decay of tritium. We present a consistent theoretical description of the $\beta$ electron energy spectrum in the endpoint region, an accurate model of the apparatus response function, and the statistical approaches suited to interpret and analyze tritium $\beta$ decay data observed with KATRIN with the envisaged precision. In addition to providing detailed analytical expressions for all formulae used in the presented model framework with the necessary detail of derivation, we discuss and quantify the impact of theoretical and experimental corrections on the measured $m(\nu_\text{e})$. Finally, we outline the statistical methods for parameter inference and the construction of confidence intervals that are appropriate for a neutrino mass measurement with KATRIN. In this context, we briefly discuss the choice of the $\beta$ energy analysis interval and the distribution of measuring time within that range.