$\beta$-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 $m({\nu }_{\text{e}})$ 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.

27 pages, 22 figures, 2 tables

References in corpus (25)

• Evidence for oscillation of atmospheric neutrinos
• Asymptotic formulae for likelihood-based tests of new physics
• A Unified Approach to the Classical Statistical Analysis of Small Signals
• Direct Evidence for Neutrino Flavor Transformation from Neutral-Current Interactions in the Sudbury Neutrino Observatory
• Precision Measurement of Neutrino Oscillation Parameters with KamLAND
• Final Results from phase II of the Mainz Neutrino Mass Search in Tritium $\beta$ Decay
• Limits and Confidence Intervals in the Presence of Nuisance Parameters
• An upper limit on electron antineutrino mass from Troitsk experiment
• Neutrino mass limit from tritium beta decay
• Current Direct Neutrino Mass Experiments
• Focal-plane detector system for the KATRIN experiment
• Assessment of molecular effects on neutrino mass measurements from tritium beta decay
• On the Effective Mass of the Electron Neutrino in Beta Decay
• Kassiopeia: A Modern, Extensible C++ Particle Tracking Package
• Exact relativistic beta decay endpoint spectrum
• Commissioning of the vacuum system of the KATRIN Main Spectrometer
• First transmission of electrons and ions through the KATRIN beamline
• Exact relativistic tritium beta-decay endpoint spectrum in a hadron model
• The KATRIN Pre-Spectrometer at reduced Filter Energy
• The KATRIN Superconducting Magnets: Overview and First Performance Results
• Measurement of the gas-flow reduction factor of the KATRIN DPS2-F differential pumping section
• Calibration of high voltages at the ppm level by the difference of ${}^{83\mathrm{m}}$Kr conversion electron lines at the KATRIN experiment
• Technical design and commissioning of the KATRIN large-volume air coil system
• Electron scattering on hydrogen and deuterium molecules at 14-25 keV by the "Troitsk nu-mass" experiment
• Deconvolution of the energy loss function of the KATRIN experiment

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• Analysis methods for the first KATRIN neutrino-mass measurement
• Improved eV-scale Sterile-Neutrino Constraints from the Second KATRIN Measurement Campaign
• Bound on 3+1 active-sterile neutrino mixing from the first four-week science run of KATRIN
• KATRIN: Status and Prospects for the Neutrino Mass and Beyond
• First operation of the KATRIN experiment with tritium
• Precision measurement of the fundamental vibrational frequencies of tritium-bearing hydrogen molecules: T${}_2$, DT, HT
• KATRIN bound on 3+1 active-sterile neutrino mixing and the reactor antineutrino anomaly
• Bayesian Analysis of a Future Beta Decay Experiment's Sensitivity to Neutrino Mass Scale and Ordering
• Precision measurement of the electron energy-loss function in tritium and deuterium gas for the KATRIN experiment
• Cyclotron Radiation Emission Spectroscopy of Electrons from Tritium Beta Decay and ${}^{83\mathrm{m}}$Kr Internal Conversion
• A comparative study of $0\nu \beta \beta$ decay in symmetric and asymmetric left-right model
• Search for Lorentz-Invariance Violation with the first KATRIN data
• A lab scale experiment for keV sterile neutrino search
• Atomic corrections for the unique first forbidden $\beta$ transition of ${}^{187}$Re
• Sensitivity of Future Tritium Decay Experiments to New Physics
• MeV Sterile Neutrino in light of the Cabibbo-Angle Anomaly
• Feasibility of Liquid-phase Xenon Proportional Scintillation for Low-energy Physics
• First constraints on general neutrino interactions based on KATRIN data
• Measurement of the electric potential and the magnetic field in the shifted analysing plane of the KATRIN experiment
• Searching for a Dark Dimension Right-handed Neutrino in KATRIN
• New Constraint on the Local Relic Neutrino Background Overdensity with the First KATRIN Data Runs
• Comparison of the detector response and calibration function of metallic microcalorimeters for X-ray photons and external electrons
• Measurement of the inhomogeneity of the KATRIN tritium source electric potential by high-resolution spectroscopy of conversion electrons from ${}^{83m}$Kr
• A precision 32 keV angular-selective photoelectron source for calibration measurements at the KATRIN experiment