#### LIMIT ON MUONIUM $\rightarrow$ ANTIMUONIUM CONVERSION

Forbidden by lepton family number conservation.

#### $\mathit R_{\mathit g}$ = $\mathit G_{\mathit C}$ $/$ $\mathit G_{\mathit F}$

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
 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
 1997
SPEC + JINR phasotron
$<0.018$ 90 0 3
 1996
SPEC + ${{\mathit \mu}^{+}}$ at 24 MeV
$<6.9$ 90
 1993
CBOX LAMPF
$<0.16$ 90
 1991
SPEC LAMPF
$<0.29$ 90
 1990 B
CNTR TRIUMF
$<20$ 95
 1986
CNTR TRIUMF
$<42$ 95
 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