#### ${{\mathit \nu}}$ MASS (tau based)

The limits given below are the square roots of limits for $\mathit m{}^{{\mathrm {2(eff)}}}_{{{\mathit \nu}_{{\tau}}} }{}\equiv\sum_{i}\vert U_{{{\mathit \tau}} i}\vert ^2$ ${{\mathit m}^{2}}_{{{\mathit \nu}_{{i}}}}$.

In some of the ASTR and COSM papers listed below, the authors did not distinguish between weak and mass eigenstates.

VALUE (MeV) CL% EVTS DOCUMENT ID TECN  COMMENT
$\bf{<18.2}$ 95 1
 1998 F
ALEP 1991--1995 LEP runs
• • We do not use the following data for averages, fits, limits, etc. • •
$<28$ 95 2
 2000
CLEO ${\it{}E}^{\it{}ee}_{\rm{}cm}$= $10.6$ GeV
$<27.6$ 95 3
 1998 T
OPAL $1990 - 1995$ LEP runs
$<30$ 95 473 4
 1998
CLEO ${\it{}E}^{\it{}ee}_{\rm{}cm}$ = $10.6$ GeV
$<60$ 95 5
 1997
CLEO ${\it{}E}^{\it{}ee}_{\rm{}cm}$= $10.6$ GeV
$\text{<0.37 or >22}$ 6
 1997
COSM Nucleosynthesis
$<68$ 95 7
 1997
THEO ${\mathit m}_{{{\mathit \tau}}}$, $\tau _{{{\mathit \tau}} }$, ${{\mathit \tau}}$ partial widths
$<29.9$ 95 8
 1996 M
OPAL 1990--1994 LEP runs
$<149$ 9
 1996
THEO ${{\mathit \pi}}$ , ${{\mathit \mu}}$ , ${{\mathit \tau}}$ leptonic decays
$\text{<1 or >25}$ 10
 1996 C
COSM Nucleosynthesis
$<71$ 95 11
 1996
THEO ${\mathit m}_{{{\mathit \tau}}}$, $\tau _{{{\mathit \tau}} }$, B( ${{\mathit \tau}^{-}}$ $\rightarrow$ ${{\mathit e}^{-}}{{\overline{\mathit \nu}}_{{e}}}{{\mathit \nu}_{{\tau}}}$ )
$<24$ 95 25 12
 1995 H
ALEP 1991--1993 LEP runs
$<0.19$ 13
 1995
COSM Nucleosynthesis
$<3$ 14
 1995
ASTR SN 1987A
$\text{<0.4 or >30}$ 15
 1994
COSM Nucleosynthesis
$\text{<0.1 or >50}$ 16
 1994
COSM Nucleosynthesis
$\text{155 - 225}$ 17
 1994
THEO ${{\mathit \pi}}$ ,${{\mathit K}}$ ,${{\mathit \mu}}$ ,${{\mathit \tau}}$ weak decays
$<32.6$ 95 113 18
 1993
CLEO ${\it{}E}^{\it{}ee}_{\rm{}cm}\approx{}$ $10.6$ GeV
$\text{< 0.3 or > 35}$ 19
 1993
COSM Nucleosynthesis
$<0.74$ 20
 1993
COSM Nucleosynthesis
$<31$ 95 19 21
 1992 M
ARG ${\it{}E}^{\it{}ee}_{\rm{}cm}$= $9.4 - 10.6$ GeV
$<0.3$ 22
 1991
COSM Nucleosynthesis
$\text{< 0.5 or > 25}$ 23
 1991
COSM Nucleosynthesis
$<0.42$ 22
 1991
COSM Nucleosynthesis
 1 BARATE 1998F result based on kinematics of 2939 ${{\mathit \tau}^{-}}$ $\rightarrow$ 2 ${{\mathit \pi}^{-}}{{\mathit \pi}^{+}}{{\mathit \nu}_{{\tau}}}$ and 52 ${{\mathit \tau}^{-}}$ $\rightarrow$ 3 ${{\mathit \pi}^{-}}$2 ${{\mathit \pi}^{+}}$ (${{\mathit \pi}^{0}}$ ) ${{\mathit \nu}_{{\tau}}}$ decays. If possible $2.5\%$ excited ${{\mathit a}_{{1}}}$ decay is included in 3-prong sample analysis, limit increases to $19.2$ MeV.
 2 ATHANAS 2000 bound comes from analysis of ${{\mathit \tau}^{-}}$ $\rightarrow$ ${{\mathit \pi}^{-}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}{{\mathit \nu}_{{\tau}}}$ decays.
 3 ACKERSTAFF 1998T use ${{\mathit \tau}}$ $\rightarrow$ 5 ${{\mathit \pi}^{\pm}}{{\mathit \nu}_{{\tau}}}$ decays to obtain a limit of $43.2$ MeV (95$\%$CL). They combine this with ALEXANDER 1996M value using ${{\mathit \tau}}$ $\rightarrow$ 3 ${{\mathit h}^{\pm}}{{\mathit \nu}_{{\tau}}}$ decays to obtain quoted limit.
 4 AMMAR 1998 limit comes from analysis of ${{\mathit \tau}^{-}}$ $\rightarrow$ 3 ${{\mathit \pi}^{-}}$2 ${{\mathit \pi}^{+}}$ ${{\mathit \nu}_{{\tau}}}$ and ${{\mathit \tau}^{-}}$ $\rightarrow$ 2 ${{\mathit \pi}^{-}}{{\mathit \pi}^{+}}$2 ${{\mathit \pi}^{0}}{{\mathit \nu}_{{\tau}}}$ decay modes.
 5 ANASTASSOV 1997 derive limit by comparing their ${\mathit m}_{{{\mathit \tau}}}$ measurement (which depends on ${\mathit m}_{{{\mathit \nu}_{{\tau}}}}$) to BAI 1996 ${\mathit m}_{{{\mathit \tau}}}$ threshold measurement.
 6 FIELDS 1997 limit for a Dirac neutrino. For a Majorana neutrino the mass region $<0.93$ or $>$31 MeV is excluded. These bounds assume $\mathit N_{{{\mathit \nu}} }<$4 from nucleosynthesis; a wider excluded region occurs with a smaller $\mathit N_{{{\mathit \nu}} }$ upper limit.
 7 SWAIN 1997 derive their limit from the Standard Model relationships between the tau mass, lifetime, branching fractions for ${{\mathit \tau}^{-}}$ $\rightarrow$ ${{\mathit e}^{-}}{{\overline{\mathit \nu}}_{{e}}}{{\mathit \nu}_{{\tau}}}$ , ${{\mathit \tau}^{-}}$ $\rightarrow$ ${{\mathit \mu}^{-}}{{\overline{\mathit \nu}}_{{\mu}}}{{\mathit \nu}_{{\tau}}}$ , ${{\mathit \tau}^{-}}$ $\rightarrow$ ${{\mathit \pi}^{-}}{{\mathit \nu}_{{\tau}}}$ , and ${{\mathit \tau}^{-}}$ $\rightarrow$ ${{\mathit K}^{-}}{{\mathit \nu}_{{\tau}}}$ , and the muon mass and lifetime by assuming lepton universality and using world average values. Limit is reduced to 48 MeV when the CLEO ${{\mathit \tau}}$ $~$mass measurement (BALEST 1993 ) is included; see CLEO's more recent ${\mathit m}_{{{\mathit \nu}_{{\tau}}}}$ limit (ANASTASSOV 1997 ). Consideration of mixing with a fourth generation heavy neutrino yields sin$^2{{\mathit \theta}_{{L}}} <0.016$ (95$\%$CL).
 8 ALEXANDER 1996M bound comes from analyses of ${{\mathit \tau}^{-}}$ $\rightarrow$ 3 ${{\mathit \pi}^{-}}$2 ${{\mathit \pi}^{+}}{{\mathit \nu}_{{\tau}}}$ and ${{\mathit \tau}^{-}}$ $\rightarrow$ ${{\mathit h}^{-}}{{\mathit h}^{-}}{{\mathit h}^{+}}{{\mathit \nu}_{{\tau}}}$ decays.
 9 BOTTINO 1996 assumes three generations of neutrinos with mixing, finds consistency with massless neutrinos with no mixing based on 1995 data for masses, lifetimes, and leptonic partial widths.
 10 HANNESTAD 1996C limit is on the mass of a Majorana neutrino. This bound assumes $\mathit N_{{{\mathit \nu}} }<4$ from nucleosynthesis. A wider excluded region occurs with a smaller $\mathit N_{{{\mathit \nu}} }$ upper limit. This paper is the corrected version of HANNESTAD 1996 ; see the erratum: HANNESTAD 1996B.
 11 SOBIE 1996 derive their limit from the Standard Model relationship between the tau mass, lifetime, and leptonic branching fraction, and the muon mass and lifetime, by assuming lepton universality and using world average values.
 12 BUSKULIC 1995H bound comes from a two-dimensional fit of the visible energy and invariant mass distribution of ${{\mathit \tau}}$ $\rightarrow$ 5 ${{\mathit \pi}}$ (${{\mathit \pi}^{0}}$ ) ${{\mathit \nu}_{{\tau}}}$ decays. Replaced by BARATE 1998F.
 13 DOLGOV 1995 removes earlier assumptions (DOLGOV 1993 ) about thermal equilibrium below $\mathit T_{{\mathrm {QCD}}}$ for wrong-helicity Dirac neutrinos (ENQVIST 1993 , FULLER 1991 ) to set more stringent limits. DOLGOV 1996 argues that a possible window near 20$~$MeV is excluded.
 14 SIGL 1995 exclude massive Dirac or Majorana neutrinos with lifetimes between $10^{-3}$ and $10^{8}$ seconds if the decay products are predominantly ${{\mathit \gamma}}$ or ${{\mathit e}^{+}}{{\mathit e}^{-}}$ .
 15 DODELSON 1994 calculate constraints on ${{\mathit \nu}_{{\tau}}}$ mass and lifetime from nucleosynthesis for 4 generic decay modes. Limits depend strongly on decay mode. Quoted limit is valid for all decay modes of Majorana neutrinos with lifetime greater than about 300$~$s. For Dirac neutrinos limits change to $<0.3$ or $>33$.
 16 KAWASAKI 1994 excluded region is for Majorana neutrino with lifetime $>1000~$s. Other limits are given as a function of ${{\mathit \nu}_{{\tau}}}$ lifetime for decays of the type ${{\mathit \nu}_{{\tau}}}$ $\rightarrow$ ${{\mathit \nu}_{{\mu}}}{{\mathit \phi}}$ where ${{\mathit \phi}}$ is a Nambu-Goldstone boson.
 17 PERES 1994 used PDG 1992 values for parameters to obtain a value consistent with mixing. Reexamination by BOTTINO 1996 which included radiative corrections and 1995 PDG parameters resulted in two allowed regions, $\mathit m_{3}<70$ MeV and 140 MeV $\mathit m_{3}<149$ MeV.
 18 CINABRO 1993 bound comes from analysis of ${{\mathit \tau}^{-}}$ $\rightarrow$ 3 ${{\mathit \pi}^{-}}$2 ${{\mathit \pi}^{+}}{{\mathit \nu}_{{\tau}}}$ and ${{\mathit \tau}^{-}}$ $\rightarrow$ 2 ${{\mathit \pi}^{-}}{{\mathit \pi}^{+}}$2 ${{\mathit \pi}^{0}}{{\mathit \nu}_{{\tau}}}$ decay modes.
 19 DOLGOV 1993 assumes neutrino lifetime $>100~$s. For Majorana neutrinos, the low mass limit is $0.5$ MeV. KAWANO 1992 points out that these bounds can be overcome for a Dirac neutrino if it possesses a magnetic moment. See also DOLGOV 1996 .
 20 ENQVIST 1993 bases limit on the fact that thermalized wrong-helicity Dirac neutrinos would speed up expansion of early universe, thus reducing the primordial abundance. FULLER 1991 exploits the same mechanism but in the older calculation obtains a larger production rate for these states, and hence a lower limit. Neutrino lifetime assumed to exceed nucleosynthesis time, $\sim{}1~$s.
 21 ALBRECHT 1992M reports measurement of a slightly lower ${{\mathit \tau}}$ mass, which has the effect of reducing the ${{\mathit \nu}_{{\tau}}}$ mass reported in ALBRECHT 1988B. Bound is from analysis of ${{\mathit \tau}^{-}}$ $\rightarrow$ 3 ${{\mathit \pi}^{-}}$2 ${{\mathit \pi}^{+}}{{\mathit \nu}_{{\tau}}}$ mode.
 22 Assumes neutrino lifetime $>1~$s. For Dirac neutrinos. See also ENQVIST 1993 .
 23 KOLB 1991 exclusion region is for Dirac neutrino with lifetime $>1~$s; other limits are given.
References:
 ATHANAS 2000
PR D61 052002 Limit on ${{\mathit \nu}_{{\tau}}}$ Mass from ${{\mathit \tau}^{-}}$ $\rightarrow$ ${{\mathit \pi}^{-}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}{{\mathit \nu}_{{\tau}}}$
 ACKERSTAFF 1998T
EPJ C5 229 An Upper Limit for the ${{\mathit \nu}_{{\tau}}}$ Mass from ${{\mathit \tau}}$ $\rightarrow$ 5 ${{\mathit \pi}^{\pm}}{{\mathit \nu}_{{\tau}}}$ Decays
 AMMAR 1998
PL B431 209 A Limit on the Mass of the ${{\mathit \nu}_{{\tau}}}$
 BARATE 1998F
EPJ C2 395 An Upper Limit on the ${{\mathit \tau}}$ Neutrino Mass from Three and Five Prong ${{\mathit \tau}}$ Decays
 ANASTASSOV 1997
PR D55 2559 Experimental Test of Lepton Universality in ${{\mathit \tau}}$ Decay
 Also
PR D58 119903 (erratum) Erratum: ANASTASSOV 1997 Experimental Test of Lepton Universality in ${{\mathit \tau}}$ Decay
 FIELDS 1997
ASP 6 169 Nucleosynthesis Limits on the Mass of Long Lived ${{\mathit \nu}_{{\tau}}}$ 's and ${{\mathit \nu}_{{\mu}}}$ 's
 SWAIN 1997
PR D55 1 Constraints on the ${{\mathit \tau}}$ Neutrino Mass and Mixing from Precise Measurements of ${{\mathit \tau}}$ Decay Rates
 ALEXANDER 1996M
ZPHY C72 231 Upper Limit on the ${{\mathit \nu}_{{\tau}}}$ Mass from ${{\mathit \tau}}$ $\rightarrow$ 3 ${{\mathit \nu}_{{\tau}}}$ Decays
 BOTTINO 1996
PR D53 6361 Limits on the Neutrino Mass and Mixing Angle from Pion and Lepton Decays
PR D54 7894 Nucleosynthesis and the Mass of ${{\mathit \nu}_{{\tau}}}$ Revisited
 SOBIE 1996
ZPHY C70 383 An Upper Limit on the ${{\mathit \nu}_{{\tau}}}$ Mass from Leptonic ${{\mathit \tau}}$ Decays
 BUSKULIC 1995H
PL B349 585 An Upper Limit for the ${{\mathit \nu}_{{\tau}}}$ Mass from ${{\mathit \tau}^{\pm}}$ $\rightarrow$ 5 ${{\mathit \pi}}{{\mathit x}}{{\mathit \pi}^{0}}$ ${{\mathit \nu}_{{\tau}}}$ Decays
 DOLGOV 1995
PR D51 4129 Bounds on Dirac Neutrino Masses from Nucleosynthesis
 SIGL 1995
PR D51 1499 Massive ${{\mathit \nu}_{{\tau}}}$ and SN1987a
 DODELSON 1994
PR D49 5068 Primordial Nucleosynthesis with a Decaying
 KAWASAKI 1994
NP B419 105 Big Bang Nucleosynthesis Constraints on the ${{\mathit \nu}_{{\tau}}}$ Mass
 PERES 1994
PR D50 513 Some Consequences in Weak Processes of Three Generations Mixing in the Leptonic Sector
 CINABRO 1993
PRL 70 3700 A Limit of the ${{\mathit \tau}}$ Neutrino Mass
 DOLGOV 1993
PRL 71 476 New Upper Limits on the Tau-Neutrino Mass from Primordial Helium Considerations
 ENQVIST 1993
PL B301 376 Cosmological Neutrino Mass Limit Revisited
 ALBRECHT 1992M
PL B292 221 A Measurement of the ${{\mathit \tau}}$ Mass
 FULLER 1991
PR D43 3136 New Cosmological Limit on Neutrino Mass
 KOLB 1991
PRL 67 533 Constraints from Primordial Nucleosynthesis to the Mass of the ${{\mathit \tau}}$ Neutrino
 LAM 1991
PR D44 3345 Cosmological Bound on Dirac Neutrino Mass via ${{\mathit \gamma}}$ ${{\mathit \gamma}}$ $\rightarrow$ ${{\mathit \pi}^{0}}$ $\rightarrow$ ${{\mathit \nu}}{{\overline{\mathit \nu}}}$