#### ${{\mathit \mu}}$ MAGNETIC MOMENT ANOMALY

The parity-violating decay of muons in a storage ring is observed. The difference frequency $\omega _{\mathit a}$ between the muon spin precision and the orbital angular frequency (${{\mathit e}}$ /${\mathit m}_{{{\mathit \mu}}}\mathit c)\langle{}\mathit B\rangle{}$ is measured, as is the free proton NMR frequency $\omega _{{{\mathit p}} }$, thus determining the ratio $\mathit R=\omega _{\mathit a}/\omega _{{{\mathit p}} }$. Given the magnetic moment ratio $\lambda =\mu _{{{\mathit \mu}} }/\mu _{{{\mathit p}} }$ (from hyperfine structure in muonium), ($\mathit g−$2)/2 = $\mathit R/(\lambda −\mathit R$).

#### ${{\mathit \mu}_{{\mu}}}$ /(${{\mathit e}}$ $\hbar{}/2{{\mathit m}_{{\mu}}}$ )$−$1 = (${{\mathit g}_{{\mu}}}$ $−$2)/2

VALUE ($10^{-10}$) DOCUMENT ID TECN CHG  COMMENT
$11659206.1$ $\pm4.1$ 1
 2021
MUG2 $\pm{}$ Combined FNAL and BNL values
• • We do not use the following data for averages, fits, limits, etc. • •
$11659204.0$ $\pm5.4$
 2021
MUG2 + Storage ring
$11659208.0$ $\pm5.4$ $\pm3.3$
 2006
MUG2 $\pm{}$ Average ${{\mathit \mu}^{+}}$ and ${{\mathit \mu}^{-}}$
$11659208$ $\pm6$
 2004
MUG2 $\pm{}$ Average ${{\mathit \mu}^{+}}$ and ${{\mathit \mu}^{-}}$
$11659214$ $\pm8$ $\pm3$
 2004
MUG2 - Storage ring
$11659203$ $\pm6$ $\pm5$
 2004
MUG2 + Storage ring
$11659204$ $\pm7$ $\pm5$
 2002
MUG2 + Storage ring
$11659202$ $\pm14$ $\pm6$
 2001
MUG2 + Storage ring
$11659191$ $\pm59$
 2000
MUG2 +
$11659100$ $\pm110$ 2
 1979
CNTR + Storage ring
$11659360$ $\pm120$ 2
 1979
CNTR - Storage ring
$11659230$ $\pm85$ 2
 1979
CNTR $\pm{}$ Storage ring
$11620000$ $\pm5000$
 1962
CNTR +
 1 ABI 2021 combined their value with the previous independent BNL measurement of BENNETT 2006 . ABI 2021 also report that the difference of this combination with the standard model value of ($11659181.0$ $\pm4.3$) $\times 10^{-10}$ (AOYAMA 2020 ) has a significance of 4.2 ${{\mathit \sigma}}$ .
 2 BAILEY 1979 values recalculated by HUGHES 1999 using the COHEN 1987 ${{\mathit \mu}}$ /${{\mathit p}}$ magnetic moment. The improved MOHR 1999 value does not change the result.
References:
 ABI 2021
PRL 126 141801 Measurement of the Positive Muon Anomalous Magnetic Moment to 0.46 ppm
 BENNETT 2006
PR D73 072003 Final Report of the E821 Muon Anomalous Magnetic Moment Measurement at BNL
 BENNETT 2004
PRL 92 161802 Measurement of the Negative Muon Anomalous Magnetic Moment to 0.7 ppm
 BENNETT 2002
PRL 89 101804 Measurement of the Positive Muon Anomalous Magnetic Moment to 0.7 ppm
 BROWN 2001
PRL 86 2227 Precise Measurement of the Positive Muon Anomalous Magnetic Moment
 BROWN 2000
PR D62 091101 Improved Measurement of the Positive Muon Anomalous Magnetic Moment
 BAILEY 1979
NP B150 1 Final Report on the CERN Muon Storage Ring Including the Anomalous Magnetic Moment and the Electric Dipole Moment of the Muon, and a Direct Test of Relativistic Time Dilation
 CHARPAK 1962
PL 1 16 A New Measurement of the Anomalous Magnetic Moment of the Muon