The effective Lagrangian for the ${{\mathit \mu}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \mu}^{-}}{{\mathit e}^{+}}$ conversion is assumed to be

$\cal L$ = 2${}^{−1/2}$ $\mathit G_{\mathit C}$ [${{\overline{\mathit \psi}}_{{{\mu}}}}{{\mathit \gamma}_{{{\lambda}}}}$ (1 $−$ ${{\mathit \gamma}}_{5}$) ${{\mathit \psi}_{{{e}}}}$] [${{\overline{\mathit \psi}}_{{{\mu}}}}{{\mathit \gamma}_{{{\lambda}}}}$ (1 $−$ ${{\mathit \gamma}}_{5}$) ${{\mathit \psi}_{{{e}}}}$] $+$ h.c.

The experimental result is then an upper limit on $\mathit G_{\mathit C}/\mathit G_{\mathit F}$, where $\mathit G_{\mathit F}$ is the Fermi coupling constant.

VALUE CL% EVTS DOCUMENT ID TECN CHG  COMMENT $\bf{<0.0030}$ 90 1 1 WILLMANN 1999 SPEC + ${{\mathit \mu}^{+}}$ at 26 GeV/$\mathit c$ • • We do not use the following data for averages, fits, limits, etc. • • $<0.14$ 90 1 2 GORDEEV 1997 SPEC + JINR phasotron $<0.018$ 90 0 3 ABELA 1996 SPEC + ${{\mathit \mu}^{+}}$ at 24 MeV $<6.9$ 90 NI 1993 CBOX LAMPF $<0.16$ 90 MATTHIAS 1991 SPEC LAMPF $<0.29$ 90 HUBER 1990 B CNTR TRIUMF $<20$ 95 BEER 1986 CNTR TRIUMF $<42$ 95 MARSHALL 1982 CNTR 1  WILLMANN 1999 quote both probability $\mathit P_{{{\mathit M}} {{\overline{\mathit M}}}}<8.3 \times 10^{-11}$ at 90$\%$CL in a $0.1~$T field and $\mathit R_{\mathit g}$= $\mathit G_{\mathit C}/\mathit G_{\mathit F}$. 2  GORDEEV 1997 quote limits on both $\mathit f=\mathit G_{{{\mathit M}} {{\mathit M}}}/\mathit GF$ and the probability $\mathit W_{{{\mathit M}} {{\mathit M}}}<4.7 \times 10^{-7}$ (90$\%$ CL). 3  ABELA 1996 quote both probability $\mathit P_{{{\mathit M}} {{\overline{\mathit M}}}}$ $<8 \times 10^{-9}$ at 90$\%$ CL and $\mathit R_{\mathit g}$ = $\mathit G_{\mathit C}/\mathit G_{\mathit F}$.

Conservation Laws:

LEPTON FAMILY NUMBER

References