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Register a new user$beta$-Decay Spectrum, Response Function and Statistical Model for Neutrino Mass Measurements with the KATRIN Experiment
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The objective of the Karlsruhe Tritium Neutrino (KATRIN) experiment is to determine the effective electron neutrino mass $m( u_text{e})$ 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 $m( u_text{e})$. 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.
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The method of quasi-optimal weights is applied to constructing (quasi-)optimal criteria for various anomalous contributions in experimental spectra. Anomalies in the spectra could indicate physics beyond the Standard Model (additional interactions and neutrino flavours, Lorenz violation etc.). In particular the cumulative tritium $beta$-decay spectrum (for instance, in Troitsk-$ u$-mass, Mainz Neutrino Mass and KATRIN experiments) is analysed using the derived special criteria. Using the power functions we show that the derived quasi-optimal criteria are efficient statistical instruments for detecting the anomalous contributions in the spectra.
Bayesian modeling techniques enable sensitivity analyses that incorporate detailed expectations regarding future experiments. A model-based approach also allows one to evaluate inferences and predicted outcomes, by calibrating (or measuring) the consequences incurred when certain results are reported. We present procedures for calibrating predictions of an experiments sensitivity to both continuous and discrete parameters. Using these procedures and a new Bayesian model of the $beta$-decay spectrum, we assess a high-precision $beta$-decay experiments sensitivity to the neutrino mass scale and ordering, for one assumed design scenario. We find that such an experiment could measure the electron-weighted neutrino mass within $sim40,$meV after 1 year (90$%$ credibility). Neutrino masses $>500,$meV could be measured within $approx5,$meV. Using only $beta$-decay and external reactor neutrino data, we find that next-generation $beta$-decay experiments could potentially constrain the mass ordering using a two-neutrino spectral model analysis. By calibrating mass ordering results, we identify reporting criteria that can be tuned to suppress false ordering claims. In some cases, a two-neutrino analysis can reveal that the mass ordering is inverted, an unobtainable result for the traditional one-neutrino analysis approach.
The KArlsruhe TRItium Neutrino (KATRIN) experiment is designed to measure tritium $beta$-decay spectrum with enough precision to be sensitive to neutrino mass down to 0.2eV at 90$%$ Confidence Level. After an initial first tritium run in the summer of 2018, KATRIN is taking tritium data in 2019 that should lead to a first neutrino mass result. The $beta$ spectral shape of the tritium decay is also sensitive to four countershaded Lorentz Violating (LV), oscillation-free operators within the Standard-Model Extension that may be quite large. The status and outlook of KATRIN to produce physics results, including in the LV sector, are discussed.
KATRIN is a very large scale tritium-beta-decay experiment to determine the mass of the neutrino. It is presently under construction at the Forschungszentrum Karlsruhe, and makes use of the Tritium Laboratory built there for the ITER project. The combination of a very large retarding-potential electrostatic-magnetic spectrometer and an intense gaseous molecular tritium source makes possible a sensitivity to neutrino mass of 0.2 eV, about an order of magnitude below present laboratory limits. The measurement is kinematic and independent of whether the neutrino is Dirac or Majorana. The status of the project is summarized briefly in this report.
Assuming 3 neutrino mixing and massive Majorana neutrinos, we analyze the implications of the results of the solar neutrino experiments, including the latest SNO data, which favor the LMA MSW solution of the solar neutrino problem with tan^2 theta_sol < 1, for the predictions of the effective Majorana mass |<m>| in neutrinoless double beta decay. For cos (2 theta_sol) geq 0.26, which follows from the analysis of the new solar neutrino data, we find significant lower limits on |<m>| in the cases of quasi-degenerate and inverted hierarchy neutrino mass spectrum, |<m>| geq 0.035 eV and |<m>| geq 8.5 10^-3 eV, respectively. If the spectrum is hierarchical the upper limit holds |<m>| leq 8.2 10^-3 eV. Correspondingly, not only a measured value of |<m>| eq 0, but even an experimental upper limit on |<m>| of the order of few 10^-2 eV can provide information on the type of the neutrino mass spectrum; it can provide also a significant upper limit on the mass of the lightest neutrino m1. A measured value of |<m>| geq 0.2 eV, combined with data on neutrino masses from the tritium beta-decay experiment KATRIN might allow to establish whether the CP-symmetry is violated in the lepton sector.
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