$$\upbeta $$-Decay spectrum, response function and statistical model for neutrino mass measurements with the KATRIN experiment

Abstract

The objective of the Karlsruhe Tritium Neutrino (KATRIN) experiment is to determine the effective electron neutrino mass m(ν e) with an unprecedented sensitivity of 0.2eV/c 2 (90% C.L.) by precision electron spectroscopy close to the endpoint of the β-decay of tritium. We present a consistent theoretical description of the β-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 β-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(ν 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 β-energy analysis interval and the distribution of measuring time within that range.

First operation of the KATRIN experiment with tritium

“…Finally, radiative corrections are included in the differential β-electron spectrum. The response function is slightly modified due to the dependence of the path length (and therefore effective column density) on the pitch angle of the β-electrons [29]. This effect is not taken into account in this analysis.…”

“…1 A very detailed description of the full spectrum and instrument response calculation can be found in Ref. [29].…”

“…(2)] of electrons in the source [29]. In good approximation, the column density can assumed to be constant in radius [29].…”

“…(2)] of electrons in the source [29]. In good approximation, the column density can assumed to be constant in radius [29]. Of relevance for the KATRIN analysis are (1) unaccountedfor variations of the total number of tritium atoms N tot during a scan and (2) the precise knowledge of the scattering probabilities P s , and therefore the product of ρd • σ inel , where σ inel is the cross-section for inelastic scattering of electrons off molecular deuterium (dominant isotopologue during the FT campaign).…”

Improved Upper Limit on the Neutrino Mass from a Direct Kinematic Method by KATRIN

“…[16]. In this Letter, we report on the first neutrino mass result from the Karlsruhe Tritium Neutrino experiment KATRIN [17][18][19][20], which is targeted to advance the sensitivity on m ν by 1 order of magnitude down to 0.2 eV (90% C.L.) after five years.…”