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
had = hadronic (QCD)
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
hadronic
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
Improved quadrupole focusing
Advanced digital electronics
et cetera
Measurements: BNL, 1997-2001
 Same
Measurements: BNL, 1997-2001
Calorimeter detectors are a mixture
of lead and plastic scintillator
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:





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



174 (2004)
Brookhaven g-2 project website
University of Glasgow, Particle Physics webpage
The Particle Adventure
Contemporary Physics Education Project
Questions?
Some more figures…
Some more figures…
smuon
neutralino
sneutrino
Some more figures…
Some more figures…