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

Limits given below are for the square root of $\mathit m{}^{{\mathrm {2(eff)}}}_{{{\mathit \nu}_{{\mu}}} }{}\equiv\sum_{i}\vert U_{{{\mathit \mu}} i}\vert ^2$ ${{\mathit m}^{2}}_{{{\mathit \nu}_{{i}}}}$.

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

OUR EVALUATION is based on OUR AVERAGE for the ${{\mathit \pi}^{\pm}}$ mass and the ASSAMAGAN 1996 value for the muon momentum for the ${{\mathit \pi}^{+}}$ decay at rest. The limit is calculated using the unified classical analysis of FELDMAN 1998 for a Gaussian distribution near a physical boundary. WARNING: since $\mathit m{}^{{\mathrm {2(eff)}}}_{{{\mathit \nu}_{{\mu}}} }$ is calculated from the differences of large numbers, it and the corresponding limits are extraordinarily sensitive to small changes in the pion mass, the decay muon momentum, and their errors. For example, the limits obtained using JECKELMANN 1994 , LENZ 1998 , and the weighted averages are 0.15, 0.29, and 0.19 MeV, respectively.

VALUE (MeV) CL% DOCUMENT ID TECN  COMMENT
 $\bf{ <0.19}$ OUR EVALUATION
$<0.17$ 90 1
 1996
SPEC ${{\mathit m}^{2}}_{{{\mathit \nu}}}$ = $-0.016$ $\pm0.023$
• • We do not use the following data for averages, fits, limits, etc. • •
$<0.15$ 2
 1995
COSM Nucleosynthesis
$<0.48$ 3
 1993
COSM Nucleosynthesis
$<0.3$ 4
 1991
COSM Nucleosynthesis
$<0.42$ 4
 1991
COSM Nucleosynthesis
$<0.50$ 90 5
 1982
SPEC ${{\mathit m}^{2}}_{{{\mathit \nu}}}$= $-0.14$ $\pm0.20$
$<0.65$ 90
 1974
ASPK ${{\mathit K}_{{\mu3}}}$ decay
 1 ASSAMAGAN 1996 measurement of ${{\mathit p}_{{\mu}}}$ from ${{\mathit \pi}^{+}}$ $\rightarrow$ ${{\mathit \mu}^{+}}{{\mathit \nu}}$ at rest combined with JECKELMANN 1994 Solution$~$B pion mass yields ${{\mathit m}^{2}}_{{{\mathit \nu}}}$ = $-0.016$ $\pm0.023$ with corresponding Bayesian limit listed above. If Solution$~$A is used, ${{\mathit m}^{2}}_{{{\mathit \nu}}}$ = $-0.143$ $\pm0.024$ MeV${}^{2}$. Replaces ASSAMAGAN 1994 .
 2 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.
 3 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.
 4 Assumes neutrino lifetime $>1~$s. For Dirac neutrinos only. See also ENQVIST 1993 .
 5 ANDERHUB 1982 kinematics is insensitive to the pion mass.
References:
 ASSAMAGAN 1996
PR D53 6065 Upper Limit of the ${{\mathit \nu}_{{\mu}}}$ Mass and Charged Pion Mass from Momentum Analysis of a Surface Muon Beam
 DOLGOV 1995
PR D51 4129 Bounds on Dirac Neutrino Masses from Nucleosynthesis
 ENQVIST 1993
PL B301 376 Cosmological Neutrino Mass Limit Revisited
 FULLER 1991
PR D43 3136 New Cosmological Limit on Neutrino Mass
 LAM 1991
PR D44 3345 Cosmological Bound on Dirac Neutrino Mass via ${{\mathit \gamma}}$ ${{\mathit \gamma}}$ $\rightarrow$ ${{\mathit \pi}^{0}}$ $\rightarrow$ ${{\mathit \nu}}{{\overline{\mathit \nu}}}$
 ANDERHUB 1982
PL 114B 76 Determination of an Upper Limit of the Mass of the Muonic Neutrino from the Pion Decay in Flight
 CLARK 1974
PR D9 533 Neutrino Mass Limits from the ${{\mathit K}_L^0}$ $\rightarrow$ ${{\mathit \pi}^{\pm}}{{\mathit \ell}^{\mp}}{{\mathit \nu}}$ Decay Spectra