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 ASSAMAGAN 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 DOLGOV 1995 COSM Nucleosynthesis $<0.48$ 3 ENQVIST 1993 COSM Nucleosynthesis $<0.3$ 4 FULLER 1991 COSM Nucleosynthesis $<0.42$ 4 LAM 1991 COSM Nucleosynthesis $<0.50$ 90 5 ANDERHUB 1982 SPEC ${{\mathit m}^{2}}_{{{\mathit \nu}}}$= $-0.14$ $\pm0.20$ $<0.65$ 90 CLARK 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