# ${{\overline{\boldsymbol \nu}}}$ MASS SQUARED (electron based) INSPIRE search

Given troubling systematics which result in improbably negative estimators of $\mathit m{}^{{\mathrm {2(eff)}}}_{{{\mathit \nu}_{{e}}}}{}\equiv\sum_{i}\vert U_{ei}\vert ^2$ ${{\mathit m}^{2}}_{{{\mathit \nu}_{{i}}}}$, in many experiments, we use only KRAUS 2005 , LOBASHEV 1999 , and AKER 2019 for our average.

VALUE (eV${}^{2}$) DOCUMENT ID TECN  COMMENT
$\bf{ -0.9 {}^{+0.8}_{-1.0}}$ OUR AVERAGE
$-1.0$ ${}^{+0.9}_{-1.1}$ 1
 2019
SPEC ${}^{3}\mathrm {H}{{\mathit \beta}}$ decay
$-0.67$ $\pm2.53$ 2
 2011
SPEC ${}^{3}\mathrm {H}{{\mathit \beta}}$ decay
$-0.6$ $\pm2.2$ $\pm2.1$ 3
 2005
SPEC ${}^{3}\mathrm {H}{{\mathit \beta}}$ decay
• • • We do not use the following data for averages, fits, limits, etc. • • •
$-1.9$ $\pm3.4$ $\pm2.2$ 4
 1999
SPEC ${}^{3}\mathrm {H}{{\mathit \beta}}$ decay
$-3.7$ $\pm5.3$ $\pm2.1$ 5
 1999
SPEC ${}^{3}\mathrm {H}{{\mathit \beta}}$ decay
$-22$ $\pm4.8$ 6
 1995
SPEC ${}^{3}\mathrm {H}{{\mathit \beta}}$ decay
$129$ $\pm6010$ 7
 1995
SPEC ${}^{3}\mathrm {H}{{\mathit \beta}}$ decay
$313$ $\pm5994$ 7
 1995
SPEC ${}^{3}\mathrm {H}{{\mathit \beta}}$ decay
$-130$ $\pm20$ $\pm15$ 8
 1995
SPEC ${}^{3}\mathrm {H}{{\mathit \beta}}$ decay
$-31$ $\pm75$ $\pm48$ 9
 1993
SPEC ${}^{3}\mathrm {H}{{\mathit \beta}}$ decay
$-39$ $\pm34$ $\pm15$ 10
 1993
SPEC ${}^{3}\mathrm {H}{{\mathit \beta}}$ decay
$-24$ $\pm48$ $\pm61$ 11
 1992 B
SPEC ${}^{3}\mathrm {H}{{\mathit \beta}}$ decay
$-65$ $\pm85$ $\pm65$ 12
 1991
SPEC ${}^{3}\mathrm {H}{{\mathit \beta}}$ decay
$-147$ $\pm68$ $\pm41$ 13
 1991
SPEC ${}^{3}\mathrm {H}{{\mathit \beta}}$ decay
1  AKER 2019 use the first month of data collected by the KATRIN experiment to determine ${{\mathit m}^{2}}_{{{\mathit \nu}}}$. The result is consistent with a neutrino mass of zero and is used to place a limit on ${\mathit m}_{{{\mathit \nu}}}$.
2  ASEEV 2011 report the analysis of the entire beta endpoint data, taken with the Troitsk integrating electrostatic spectrometer between 1997 and 2002, using a windowless gaseous tritium source. The analysis does not use the two additional fit parameters (see LOBASHEV 99) for a step-like structure near the endpoint. Using only the runs where the tritium gas column density was carefully monitored the need for such parameters was eliminated. Supersedes LOBASHEV 1999 and BELESEV 1995 .
3  KRAUS 2005 is a continuation of the work reported in WEINHEIMER 1999 . This result represents the final analysis of data taken from 1997 to 2001. Problems with significantly negative squared neutrino masses, observed in some earlier experiments, have been resolved in this work.
4  LOBASHEV 1999 report a new measurement which continues the work reported in BELESEV 1995 . The data were corrected for electron trapping effects in the source, eliminating the dependence of the fitted neutrino mass on the fit interval. The analysis assuming a pure beta spectrum yields significantly negative fitted ${{\mathit m}^{2}}_{{{\mathit \nu}}}\approx{}−(20 - 10$) eV${}^{2}$. This problem is attributed to a discrete spectral anomaly of about $6 \times 10^{-11}$ intensity with a time-dependent energy of $5 - 15$ eV below the endpoint. The data analysis accounts for this anomaly by introducing two extra phenomenological fit parameters resulting in a best fit of ${{\mathit m}^{2}}_{{{\mathit \nu}}}=-1.9$ $\pm3.4$ $\pm2.2~$eV${}^{2}$ which is used to derive a neutrino mass limit. However, the introduction of phenomenological fit parameters which are correlated with the derived ${{\mathit m}^{2}}_{{{\mathit \nu}}}~$limit makes unambiguous interpretation of this result difficult.
5  WEINHEIMER 1999 is a continuation of the work reported in WEINHEIMER 1993 . Using a lower temperature of the frozen tritium source eliminated the dewetting of the $\mathit T_{2}$ film, which introduced a dependence of the fitted neutrino mass on the fit interval in the earlier work. An indication for a spectral anomaly reported in LOBASHEV 1999 has been seen, but its time dependence does not agree with LOBASHEV 1999 . Two analyses, which exclude the spectral anomaly either by choice of the analysis interval or by using a particular data set which does not exhibit the anomaly, result in acceptable ${{\mathit m}^{2}}_{{{\mathit \nu}}}~$fits and are used to derive the neutrino mass limit published by the authors. We list the most conservative of the two.
6  BELESEV 1995 (Moscow) use an integral electrostatic spectrometer with adiabatic magnetic collimation and a gaseous tritium sources. This value comes from a fit to a normal Kurie plot above $18300 - 18350$ eV (to avoid a low-energy anomaly), including the effects of an apparent peak $7 - 15$ eV below the endpoint.
7  HIDDEMANN 1995 (Munich) experiment uses atomic tritium embedded in a metal-dioxide lattice. They quote measurements from two data sets.
8  STOEFFL 1995 (LLNL) uses a gaseous source of molecular tritium. An anomalous pileup of events at the endpoint leads to the negative value for ${{\mathit m}^{2}}_{{{\mathit \nu}}}$. The authors acknowledge that the negative value for the best fit of ${{\mathit m}^{2}}_{{{\mathit \nu}}}$ has no physical meaning'' and discuss possible explanations for this effect.
9  SUN 1993 uses a tritiated hydrocarbon source. See also CHING 1995 .
10  WEINHEIMER 1993 (Mainz) is a measurement of the endpoint of the tritium $\beta$ spectrum using an electrostatic spectrometer with a magnetic guiding field. The source is molecular tritium frozen onto an aluminum substrate.
11  HOLZSCHUH 1992B (Zurich) source is a monolayer of tritiated hydrocarbon.
12  KAWAKAMI 1991 (Tokyo) experiment uses tritium-labeled arachidic acid.
13  ROBERTSON 1991 (LANL) experiment uses gaseous molecular tritium. The result is in strong disagreement with the earlier claims by the ITEP group [LUBIMOV 1980 , BORIS 1987 ($+~$BORIS 1988 erratum)] that ${\mathit m}_{{{\mathit \nu}}}$ lies between 17 and 40 eV. However, the probability of a positive ${{\mathit m}^{2}}_{{{\mathit \nu}}}$ is only 3$\%$ if statistical and systematic error are combined in quadrature.
References:
 AKER 2019
PRL 123 221802 An improved upper limit on the neutrino mass from a direct kinematic method by KATRIN
 ASEEV 2011
PR D84 112003 Upper Limit on the Electron Antineutrino Mass from the Troitsk Experiment
 KRAUS 2005
EPJ C40 447 Final Results from Phase II of the Mainz Neutrino Mass Searchin Tritium $\beta$ Decay
 LOBASHEV 1999
PL B460 227 Direct Search for Mass of Neutrino and Anomaly in the Tritium $\beta$ Spectrum
 WEINHEIMER 1999
PL B460 219 High Precision Measurement of the Tritium $\beta$ Spectrum near its Endpoint and Upper Limit on the Neutrino Mass
 BELESEV 1995
PL B350 263 Results of the Troitsk Experiment on the Search for the Electron Antineutrino Rest Mass in Tritium $\beta$ Decay
 HIDDEMANN 1995
JP G21 639 Limits on Neutrino Masses from the Tritium $\beta$ Spectrum
 STOEFFL 1995
PRL 75 3237 Anomalous Structure in the $\beta$ Decay of Gaseous Molecular Tritium
 SUN 1993
CJNP 15 261 An upper Limit for the Electron Antineutrino Mass
 WEINHEIMER 1993
PL B300 210 Improved Limit on the ${{\overline{\mathit \nu}}_{{e}}}$ Rest Mass from Tritium $\beta$ Decay
 HOLZSCHUH 1992B
PL B287 381 Measurement of the Electron Neutrino Mass from Tritium $\beta$ Decay
 KAWAKAMI 1991
PL B256 105 New Upper Bound on the Electron Anti-Neutrino Mass
 ROBERTSON 1991
PRL 67 957 Limit on ${{\overline{\mathit \nu}}_{{e}}}$ Mass from Observation of the $\beta$ Decay of Molecular Tritium