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THE MUON ANOMALOUS MAGNETIC MOMENT
Updated July 2009 by A. H¨
ocker (CERN), and W.J. Marciano
(BNL).
The Dirac equation predicts a muon magnetic moment,
±
M
=
g
μ
e
2
m
μ
±
S
, with gyromagnetic ratio
g
μ
= 2. Quantum
loop efects lead to a small calculable deviation From
g
μ
=2
,
parameterized by the anomalous magnetic moment
a
μ
≡
g
μ
−
2
2
.
(1)
That quantity can be accurately measured and, within the
Standard Model (SM) Framework, precisely predicted. Hence,
comparison oF experiment and theory tests the SM at its quan
tum loop level. A deviation in
a
exp
μ
From the SM expectation
would signal efects oF new physics, with current sensitivity
reaching up to mass scales oF
O
(TeV) [1,2].
±or recent and
very thorough muon
g
−
2 reviews, see ReFs. [3,4].
The E821 experiment at Brookhaven National Lab (BNL)
studied the precession oF
μ
+
and
μ
−
in a constant external
magnetic ²eld as they circulated in a con²ning storage ring. It
Found [6]
1
a
exp
μ
+
= 11 659 204(6)(5)
×
10
−
10
,
a
exp
μ
−
= 11 659 215(8)(3)
×
10
−
10
,
(2)
where the ²rst errors are statistical and the second systematic.
Assuming CPT invariance and taking into account correlations
between systematic errors, one ²nds For their average [6]
a
exp
μ
= 11 659 208
.
9(5
.
4)(3
.
3)
×
10
−
10
.
(3)
These results represent about a Factor oF 14 improvement over
the classic CERN experiments oF the 1970’s [7].
The SM prediction For
a
SM
μ
is generally divided into three
parts (see ±ig. 1 For representative ±eynman diagrams)
a
SM
μ
=
a
QED
μ
+
a
EW
μ
+
a
Had
μ
.
(4)
1
The original results reported by the experiment have been
updated in Eqs. (2) and (3) to the newest value For the abso
lute muontoproton magnetic ratio
λ
=3
.
183345137(85) [5].
The change induced in
a
exp
μ
with respect to the value oF
λ
=
3
.
18334539(10) used in ReF. [6] amounts to +0
.
92
×
10
−
10
.
CITATION: K. Nakamura
et al.
(Particle Data Group), JPG
37
, 075021 (2010) (URL: http://pdg.lbl.gov)
July 30, 2010
14:34
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γ
γ
μμ
γ
Z
γ
WW
ν
γ
γγ
had
Figure 1:
Representative diagrams contribut
ing to
a
SM
μ
. From left to right: ±rst order QED
(Schwinger term), lowestorder weak, lowest
order hadronic.
The QED part includes all photonic and leptonic (
e, μ, τ
)loops
starting with the classic
α/
2
π
Schwinger contribution. It has
been computed through 4 loops and estimated at the 5loop
level [8]
a
QED
μ
=
α
2
π
+0
.
765857410(27)
³
α
π
´
2
+24
.
05050964(43)
³
α
π
´
3
+ 130
.
8055(80)
³
α
π
´
4
+ 663(20)
³
α
π
´
5
+
···
(5)
Employing
α
−
1
= 137
.
035999084(51), determined [8,9] from the
electron
a
e
measurement, leads to
a
QED
μ
= 116 584 718
.
09(0
.
15)
×
10
−
11
,
(6)
where the error results from uncertainties in the coeﬃcients of
Eq. (5) and in
α
.
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