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Final Results from phase II of the Mainz Neutrino Mass Search in Tritium $β$ Decay

Ch. Kraus, B. Bornschein, L. Bornschein, J. Bonn, B. Flatt, A. Kovalik, B. Ostrick, E. W. Otten, J. P. Schall, Th. Thümmler, Ch. Weinheimer

TL;DR

The Mainz phase II experiment significantly improved the tritium β-spectrum endpoint measurement by achieving a tenfold rise in signal-to-background and rigorous control of systematic uncertainties, enabling a final assessment of the electron antineutrino mass. Through a detailed forward-model analysis that accounts for transmission, energy loss, source charging, backscattering, and detector response, the study reports $m^2(\nu_e)=(-0.6\pm2.2_{stat}\pm2.1_{syst})$ eV$^2$/c$^4$ and sets an upper limit $m(\nu_e)\leq 2.3$ eV/$c^2$ (95% C.L.). The work demonstrates precise background suppression via cryotraps and rf techniques, stable HV operation, and meticulous data handling across 1997–2001, informing design choices for next-generation experiments like KATRIN. Overall, the results narrow the absolute neutrino mass scale in a model-independent way and validate the MAC-E-Filter approach for high-precision endpoint spectroscopy.

Abstract

The paper reports on the improved Mainz experiment on tritum $β$ spectroscopy which yields a 10 times' higher signal to background ratio than before. The main experimental effects and systematic uncertainties have been investigated in side experiments and possible error sources have been eliminated. Extensive data taking took place in the years 1997 to 2001. A residual analysis of the data sets yields for the square of the electron antineutrino mass the final result of $m^2(ν_e)=(-0.6 \pm 2.2_{\rm{stat}} \pm 2.1_{\rm{syst}})$ eV$^2$/c$^4$. We derive an upper limit of $m(ν_e)\leq 2.3$ eV/c$^2$ at 95% confidence level for the mass itself.

Final Results from phase II of the Mainz Neutrino Mass Search in Tritium $β$ Decay

TL;DR

The Mainz phase II experiment significantly improved the tritium β-spectrum endpoint measurement by achieving a tenfold rise in signal-to-background and rigorous control of systematic uncertainties, enabling a final assessment of the electron antineutrino mass. Through a detailed forward-model analysis that accounts for transmission, energy loss, source charging, backscattering, and detector response, the study reports eV/c and sets an upper limit eV/ (95% C.L.). The work demonstrates precise background suppression via cryotraps and rf techniques, stable HV operation, and meticulous data handling across 1997–2001, informing design choices for next-generation experiments like KATRIN. Overall, the results narrow the absolute neutrino mass scale in a model-independent way and validate the MAC-E-Filter approach for high-precision endpoint spectroscopy.

Abstract

The paper reports on the improved Mainz experiment on tritum spectroscopy which yields a 10 times' higher signal to background ratio than before. The main experimental effects and systematic uncertainties have been investigated in side experiments and possible error sources have been eliminated. Extensive data taking took place in the years 1997 to 2001. A residual analysis of the data sets yields for the square of the electron antineutrino mass the final result of eV/c. We derive an upper limit of eV/c at 95% confidence level for the mass itself.

Paper Structure

This paper contains 15 sections, 21 equations, 11 figures, 1 table.

Table of Contents

  1. Introduction
  2. $\boldsymbol \beta$-spectrum and neutrino mass measured by an integrating electrostatic filter.
  3. ${\boldsymbol \beta}$-spectrum in T$\bf _2$ decay
  4. Sensitivity of the ${\boldsymbol \beta}$-spectrum to ${\boldsymbol m}^{\boldsymbol 2}({\boldsymbol \nu}_e)$
  5. Improvements of the Mainz MAC-E-Filter
  6. The new source section
  7. Electrode and HV system
  8. Spectrometer vacuum and conditioning
  9. $\boldsymbol \beta$-detection and data acquisition
  10. Measurements in phase II, 1997-2001
  11. Spectrometer background
  12. Discussion of Runs Q1 to Q12
  13. Analysis of data
  14. Raw data selection
  15. The fit function and the response function

Figures (11)

  • Figure 1: Tritium $\beta$ spectrum close to the endpoint $E_0$. The dotted and the dashed line correspond to $m(\nu_e)=0$, the solid one to $m(\nu_e)=10$ eV/c$^2$. In case of the dashed and the solid line only the decay into the electronic ground state of the daughter is considered. For $m(\nu_e)$=10 eV/c$^2$ the missing decay rate in the last 10 eV below $E_0$ (shaded region) is a fraction of 2$\cdot10^{-10}$ of the total decay rate, scaling as $m^3(\nu_e)$.
  • Figure 2: Excitation spectrum of the daugther ($^3$HeT)$^+$ in $\beta$- decay of molecular tritium Saenz.
  • Figure 3: The improved Mainz MAC-E-Filter is shown schematically. The distance between source and detector is about 6 m and the diameter of the spectrometer vessel is 1 m. From left to right: Frozen T$_2$ source housed in the tilted solenoid S1; guiding solenoids S2, S3; the vessel with altogether 27 electrodes; refocussing solenoid S4, S5 housing the detector. The shown magnetic field lines confine the flux tube within which the $\beta$ particles are guided.
  • Figure 4: Scheme of the tritium source with setup for growing the T$_2$ film and controlling its thickness by ellipsometry
  • Figure 5: Control of film growth by ellipsometry for D$_2$ (open circles) and T$_2$ (full circles). On the axes are given the corresponding shifts of light extinguishing ($\alpha$, $\beta$)- pairs. The lines are fits to the data. The loop closes at the first interference order.
  • ...and 6 more figures