### Anomalous magnetic moment of the muon

```Brian Plimley • Physics 129 • November 2010
ANOMALOUS MAGNETIC MOMENT
OF THE MUON
Outline
 What is the anomalous magnetic moment?
 Why does it matter?
 Measurements of aµ
 1974-1976: CERN
 1997-2001: BNL
 Conclusions
What is the anomalous
magnetic moment?
 Magnetic moment:
(for a muon)
 Dirac equation predicts g = 2 for e, µ
 Quantum vacuum fluctuations adjust this value
 Anomalous magnetic moment:
(for a muon)
What is the anomalous
magnetic moment?
x
γ
Fundamental diagram:
(consistent with aµ = 0)
µ
Corrections according to Standard Model:γ
SM = Standard Model
EW = electroweak
What is the anomalous
magnetic moment?
x
γ
Fundamental diagram:
(consistent with aµ = 0)
µ
x
γ
γ
µ
µ
γ
QED
electroweak
(1st-order corrections)
γ
γ
Why does it matter?
 Tests theories of fundamental forces in the
Standard Model (QED, weak, QCD)
 Look for new physics beyond the Standard
Model, e.g. supersymmetry (SUSY)
Why does it matter?
 Why muons?
 Electrons also have an anomalous magnetic
moment
 Electrons are much easier to work with
(stable, easy to find)
A rare photo of an electron
Why does it matter?
 The amplitude of weak and hadronic
diagrams scales with the lepton mass:
 So the muon magnetic moment is more
sensitive to these forces by a factor of
(mµ / me)2 ≈ 40 000!
 (QED has been tested very precisely by ae)
Measurements: CERN, 1974-76
 This is the third and most advanced
measurement of aµ at CERN in the 60s and 70s
Measurements: CERN, 1974-76
 Protons on a target produce
pions, which enter the storage
d = 14 m
Eµ ≈ 3 GeV
(pµ = 3.094 GeV/c)
ring and decay into muons
(mostly)
 Muon spins are highly
polarized in the forward
direction
 Muons circle the ring many
times before decaying into
electrons and neutrinos
 Detectors inside ring detect
decay electrons
Measurements: CERN, 1974-76
 Cyclotron frequency:
 Spin precession frequency:
Measurements: CERN, 1974-76
 Spin-cyclotron beat frequency
(anomalous precession frequency):
 Decay electron
preferentially
emitted along spin
axis of muon
Measurements: CERN, 1974-76
[figure from BNL work, 2006]
 Energy threshold selects only electrons
emitted along direction of muon momentum
 Detector
countrate
oscillates at beat
frequency, by
which aµ can be
calculated…
Measurements: CERN, 1974-76
 ωL is the Larmor
frequency (spin
precession of a
muon at rest)
 ωL measured
separately
Measurements: CERN, 1974-76
 CERN results agreed with theory
theory
(after theorists included certain
higher-order Feynman diagrams!)
Total experimental uncertainty in aµ: 10 ppm
Measurements: BNL, 1997-2001
 Same size and energy as CERN,
for good reasons
Measurements: BNL, 1997-2001
 Same technique as CERN experiment, but
with improved technology
 Higher muon fluence
 Pions decay before entering storage ring,




reducing background
Superconducting magnets
et cetera
Measurements: BNL, 1997-2001
 Same
Measurements: BNL, 1997-2001
Calorimeter detectors are a mixture
Measurements: BNL, 1997-2001
 Experimental aµ is 3.4 σ
from the most recent
Standard Model calculation
Conclusions
 The anomalous magnetic moment of the muon is
very useful for testing the fundamental forces of
physics
 Significant discrepancy with theory suggests physics
beyond the Standard Model
 One candidate theory for extension of the Standard
model is supersymmetry (SUSY)
 More work remains to be done
to reduce uncertainties in both
experimental and theoretical
calculations
References
 Content:
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J. Bailey et al, Nuc. Phys. B150 1 (1979)
G.W. Bennett et al, Phys. Rev. D73 072003 (2006)
K. Hagiwara et al, Phys. Lett. B649 173-179 (2007)
J.M. Paley, PhD dissertation (2004)
wikipedia
 Diagrams:
 T.G. Steele et al, Phys. Rev. D44 3610-3619 (1991)
 D.W. Hertzog and W.M. Morse, Annu. Rev. Nucl. Part. Sci. 54 141


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174 (2004)
Brookhaven g-2 project website
University of Glasgow, Particle Physics webpage