Those limits given below are for the square root of $\mathit m{}^{{\mathrm {2(eff)}}}_{{{\mathit \nu}_{{e}}}}{}\equiv\sum_{i}\vert U_{ei}\vert ^2$ ${{\mathit m}^{2}}_{{{\mathit \nu}_{{i}}}}$. Limits that come from the kinematics of ${}^{3}\mathrm {H}$ ${{\mathit \beta}^{-}}{{\overline{\mathit \nu}}}$ decay are the square roots of the limits for $\mathit m{}^{{\mathrm {2(eff)}}}_{{{\mathit \nu}_{{e}}}}$. Obtained from the measurements reported in the Listings for “${{\overline{\mathit \nu}}}$ Mass Squared,” below.

VALUE (eV) CL% DOCUMENT ID TECN  COMMENT $\bf{<0.8}$ 90 1 AKER 2022 SPEC ${}^{3}\mathrm {H}{{\mathit \beta}}$ decay • • We do not use the following data for averages, fits, limits, etc. • • $<1.1$ 90 2 AKER 2019 SPEC ${}^{3}\mathrm {H}{{\mathit \beta}}$ decay $<2.05$ 95 3 ASEEV 2011 SPEC ${}^{3}\mathrm {H}{{\mathit \beta}}$ decay $<5.8$ 95 4 PAGLIAROLI 2010 ASTR SN1987A $<2.3$ 95 5 KRAUS 2005 SPEC ${}^{3}\mathrm {H}{{\mathit \beta}}$ decay $<21.7$ 90 6 ARNABOLDI 2003 A BOLO ${}^{187}\mathrm {Re}{{\mathit \beta}}$ decay $<5.7$ 95 7 LOREDO 2002 ASTR SN1987A $<2.5$ 95 8 LOBASHEV 1999 SPEC ${}^{3}\mathrm {H}{{\mathit \beta}}$ decay $<2.8$ 95 9 WEINHEIMER 1999 SPEC ${}^{3}\mathrm {H}{{\mathit \beta}}$ decay $<4.35$ 95 10 BELESEV 1995 SPEC ${}^{3}\mathrm {H}{{\mathit \beta}}$ decay $<12.4$ 95 11 CHING 1995 SPEC ${}^{3}\mathrm {H}{{\mathit \beta}}$ decay $<92$ 95 12 HIDDEMANN 1995 SPEC ${}^{3}\mathrm {H}{{\mathit \beta}}$ decay $15$ ${}^{+32}_{-15}$ HIDDEMANN 1995 SPEC ${}^{3}\mathrm {H}{{\mathit \beta}}$ decay $<19.6$ 95 KERNAN 1995 ASTR SN 1987A $<7.0$ 95 13 STOEFFL 1995 SPEC ${}^{3}\mathrm {H}{{\mathit \beta}}$ decay $<7.2$ 95 14 WEINHEIMER 1993 SPEC ${}^{3}\mathrm {H}{{\mathit \beta}}$ decay $<11.7$ 95 15 HOLZSCHUH 1992 B SPEC ${}^{3}\mathrm {H}{{\mathit \beta}}$ decay $<13.1$ 95 16 KAWAKAMI 1991 SPEC ${}^{3}\mathrm {H}{{\mathit \beta}}$ decay $<9.3$ 95 17 ROBERTSON 1991 SPEC ${}^{3}\mathrm {H}{{\mathit \beta}}$ decay $<14$ 95 AVIGNONE 1990 ASTR SN 1987A $<16$ SPERGEL 1988 ASTR SN 1987A $17\text{ to }40 $ 18 BORIS 1987 SPEC ${}^{3}\mathrm {H}{{\mathit \beta}}$ decay 1  AKER 2022 derive an upper limit on the kinematical neutrino mass using Tritium ${{\mathit \beta}}$-decay and the KATRIN spectrometer. The constraint is based on combining the first two science runs. Supersedes AKER 2019 . 2  AKER 2019 report a neutrino mass limit, derived from the first month of data collected by the KATRIN tritium endpoint experiment. The analysis of the electron kinematics shows no evidence for neutrino mass. The quoted result is based on a frequentist analysis of the data following the method described in LOKHOV 2015 . Using the method of Feldman and Cousins, the derived upper limit is $<$ 0.8 eV at 90$\%$ C.L. Superseded by AKER 2022 . 3  ASEEV 2011 report the analysis of the entire beta endpoint data, taken with the Troitsk integrating electrostatic spectrometer between 1997 and 2002 (some of the earlier runs were rejected), using a windowless gaseous tritium source. The fitted value of ${\mathit m}_{{{\mathit \nu}}}$, based on the method of Feldman and Cousins, is obtained from the upper limit of the fit for ${{\mathit m}^{2}}_{{{\mathit \nu}}}$. Previous analysis problems were resolved by careful monitoring of the tritium gas column density. Supersedes LOBASHEV 1999 and BELESEV 1995 . 4  PAGLIAROLI 2010 is critical of the likelihood method used by LOREDO 2002 . 5  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. Various sources of systematic uncertainties have been identified and quantified. The background has been reduced compared to the initial running period. A spectral anomaly at the endpoint, reported in LOBASHEV 1999 , was not observed. 6  ARNABOLDI 2003A $\mathit et\mathit al.$ report kinematical neutrino mass limit using ${{\mathit \beta}}$-decay of ${}^{187}\mathrm {Re}$. Bolometric AgReO$_{4}$ micro-calorimeters are used. Mass bound is substantially weaker than those derived from tritium ${{\mathit \beta}}$-decays but has different systematic uncertainties. 7  LOREDO 2002 updates LOREDO 1989 . 8  LOBASHEV 1999 report a new measurement which continues the work reported in BELESEV 1995 . This limit depends on phenomenological fit parameters used to derive their best fit to ${{\mathit m}^{2}}_{{{\mathit \nu}}}$, making unambiguous interpretation difficult. See the footnote under ``${{\overline{\mathit \nu}}}~$Mass Squared.'' 9  WEINHEIMER 1999 presents two analyses which exclude the spectral anomaly and result in an acceptable ${{\mathit m}^{2}}_{{{\mathit \nu}}}$. We report the most conservative limit, but the other is nearly the same. See the footnote under ``${{\overline{\mathit \nu}}}~$Mass Squared.'' 10  BELESEV 1995 (Moscow) use an integral electrostatic spectrometer with adiabatic magnetic collimation and a gaseous tritium sources. A fit to a normal Kurie plot above $18300 - 18350$ eV (to avoid a low-energy anomaly) plus a monochromatic line $7 - 15$ eV below the endpoint yields ${{\mathit m}^{2}}_{{{\mathit \nu}}}$ = $-4.1$ $\pm10.9$ eV${}^{2}$, leading to this Bayesian limit. 11  CHING 1995 quotes results previously given by SUN 1993 ; no experimental details are given. A possible explanation for consistently negative values of ${{\mathit m}^{2}}_{{{\mathit \nu}}}$ is given. 12  HIDDEMANN 1995 (Munich) experiment uses atomic tritium embedded in a metal-dioxide lattice. Bayesian limit calculated from the weighted mean ${{\mathit m}^{2}}_{{{\mathit \nu}}}$ = $221$ $\pm4244$ eV${}^{2}$ from the two runs listed below. 13  STOEFFL 1995 (LLNL) result is the Bayesian limit obtained from the ${{\mathit m}^{2}}_{{{\mathit \nu}}}$ errors given below but with ${{\mathit m}^{2}}_{{{\mathit \nu}}}$ set equal to 0. The anomalous endpoint accumulation leads to a value of ${{\mathit m}^{2}}_{{{\mathit \nu}}}$ which is negative by more than 5 standard deviations. 14  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. 15  HOLZSCHUH 1992B (Zurich) result is obtained from the measurement ${{\mathit m}^{2}}_{{{\mathit \nu}}}$ = $-24$ $\pm48$ $\pm61$ (1$\sigma $ errors), in eV${}^{2}$, using the PDG prescription for conversion to a limit in ${\mathit m}_{{{\mathit \nu}}}$. 16  KAWAKAMI 1991 (Tokyo) experiment uses tritium-labeled arachidic acid. This result is the Bayesian limit obtained from the ${{\mathit m}^{2}}_{{{\mathit \nu}}}$ limit with the errors combined in quadrature. This was also done in ROBERTSON 1991 , although the authors report a different procedure. 17  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 $\mathit m{}^{2}$ is only 3$\%$ if statistical and systematic error are combined in quadrature. 18  See also comment in BORIS 1987B and erratum in BORIS 1988 .

References:

AKER 2022 NATP 18 160 Direct neutrino-mass measurement with sub-electronvolt sensitivity AKER 2019 PRL 123 221802 An improved upper limit on the neutrino mass from a direct kinematic method by KATRIN Also PR D104 012005 Analysis methods for the first KATRIN neutrino-mass measurement ASEEV 2011 PR D84 112003 Upper Limit on the Electron Antineutrino Mass from the Troitsk Experiment PAGLIAROLI 2010 ASP 33 287 Neutrino Mass Bound in the Standard Scenario for Supernova Electronic Antineutrino Emission KRAUS 2005 EPJ C40 447 Final Results from Phase II of the Mainz Neutrino Mass Searchin Tritium $\beta $ Decay ARNABOLDI 2003A PRL 91 161802 Bolometric Bounds on the Antineutrino Mass LOREDO 2002 PR D65 063002 Bayesian Analysis of Neutrinos Observed from Supernova SN1987a 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 CHING 1995 IJMP A10 2841 A Possible Explanation of the Negative Values of $\mathit m{}^{2}$ (${{\mathit \nu}_{{e}}}$) Obtained from the $\beta $ Spectrum Shape Analyses HIDDEMANN 1995 JP G21 639 Limits on Neutrino Masses from the Tritium $\beta $ Spectrum KERNAN 1995 NP B437 243 Update Limits on the Electron Neutrino Mass and Large Angle Oscillations from SN1987a STOEFFL 1995 PRL 75 3237 Anomalous Structure in the $\beta $ Decay of Gaseous Molecular Tritium 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 AVIGNONE 1990 PR D41 682 Quasi Model Independent Analysis of the Kamiokande-II Neutrino Events from SN1987a SPERGEL 1988 PL B200 366 The Mass of the ${{\mathit \nu}_{{e}}}$: Monte Carlo Studies of SN1987a Observations BORIS 1987 PRL 58 2019 Neutrino Mass from the $\beta $ Spectrum in the Decay of Tritium Also PRL 61 245 (erratum) Erratum to BORIS 1987 . Neutrino Mass from the $\beta $ Spectrum in the Decay of Tritium