Effective neutrino masses in KATRIN and future tritium beta-decay experiments

TL;DR

This paper compares different approximations of effective neutrino masses in tritium beta-decay experiments, evaluates their validity under various experimental conditions, and uses Bayesian methods to incorporate current data for posterior analysis.

Contribution

It provides a detailed comparison of relativistic and non-relativistic effective mass definitions and presents Bayesian posterior distributions using current experimental data.

Findings

Relativistic spectrum calculations improve accuracy at high energy resolutions.

Certain approximations are valid only within specific energy resolution ranges.

Bayesian analysis yields posterior distributions consistent with current experimental constraints.

Abstract

Past and current direct neutrino mass experiments set limits on the so-called effective neutrino mass, which is an incoherent sum of neutrino masses and lepton mixing matrix elements. The electron energy spectrum which neglects the relativistic and nuclear recoil effects is often assumed. Alternative definitions of effective masses exist, and an exact relativistic spectrum is calculable. We quantitatively compare the validity of those different approximations as function of energy resolution and exposure in view of tritium beta decays in the KATRIN, Project 8 and PTOLEMY experiments. Furthermore, adopting the Bayesian approach, we present the posterior distributions of the effective neutrino mass by including current experimental information from neutrino oscillations, beta decay, neutrinoless double-beta decay and cosmological observations. Both linear and logarithmic priors for the smallest neutrino mass are assumed.