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:

WILLMANN 1999 PRL 82 49 New Bounds from Searching for Muonium to Antimuonium Conversion GORDEEV 1997 PAN 60 1164 New Method of Investigating of the Muonium-to-Antimuonium Conversion ABELA 1996 PRL 77 1950 Improved Upper Limit on Muonium to Antimuonium Conversion NI 1993 PR D48 1976 Search for Spontaneous Conversion of Muonium to Antimuonium MATTHIAS 1991 PRL 66 2716 New Search for the Spontaneous Conversion of Muonium to Antimuonium Also PRL 67 932 (erratum) Erratum: MATTHIAS 1991 New Search for the Spontaneous Conversion of Muonium to Antimuonium HUBER 1990B PR D41 2709 Search for Mixing of Muonium (${{\mathit \mu}^{+}}{{\mathit e}^{-}}$) and Antimuonium (${{\mathit \mu}^{-}}{{\mathit e}^{+}}$) BEER 1986 PRL 57 671 Emission of Muonium into Vacuum from a Silica Powder Layer MARSHALL 1982 PR D25 1174 Search for Muonium-to-Antimuonium Conversion