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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 a µ 1974-1976: CERN 1997-2001: BNL Conclusions. What is the anomalous magnetic moment?. Magnetic moment:

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Brian Plimley • Physics 129 • November 2010

Anomalous magnetic moment of the muon


Outline l.jpg
Outline

  • What is the anomalous magnetic moment?

  • Why does it matter?

  • Measurements of aµ

    • 1974-1976: CERN

    • 1997-2001: BNL

  • Conclusions


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What is the anomalous magnetic moment?

  • Magnetic moment:

  • Dirac equation predicts g = 2 for e, µ

  • Quantum vacuum fluctuations adjust this value

  • Anomalous magnetic moment:

(for a muon)

(for a muon)


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What is the anomalous magnetic moment?

x

Fundamental diagram:

(consistent with aµ = 0)

γ

µ

Corrections according to Standard Model:

γ

SM = Standard Model

had = hadronic (QCD)

EW = electroweak


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What is the anomalous magnetic moment?

Fundamental diagram:

(consistent with aµ = 0)

x

x

γ

µ

γ

γ

µ

γ

γ

µ

QED

electroweak

hadronic

γ

(1st-order corrections)


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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)


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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


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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)


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Measurements: CERN, 1974-76

  • This is the third and most advanced measurement of aµ at CERN in the 60s and 70s


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Measurements: CERN, 1974-76

  • Protons on a target produce pions, which enter the storage ring and decay into muons (mostly)

  • Muon spinsare highly polarized in the forward direction

  • Muons circle the ring many times before decaying into electrons and neutrinos

  • Detectors inside ring detect decay electrons

d = 14 m

Eµ ≈ 3 GeV

(pµ = 3.094 GeV/c)


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Measurements: CERN, 1974-76

  • Cyclotron frequency:

  • Spin precession frequency:


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Measurements: CERN, 1974-76

  • Spin-cyclotron beat frequency (anomalous precession frequency):

  • Decay electron preferentially emitted along spin axis of muon


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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…


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Measurements: CERN, 1974-76

  • ωL is the Larmor frequency (spin precession of a muon at rest)

  • ωL measured separately


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Measurements: CERN, 1974-76

  • CERN results agreed with theory (after theorists included certain higher-order Feynman diagrams!)

theory

Total experimental uncertainty in aµ: 10 ppm


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Measurements: BNL, 1997-2001

  • Same size and energy as CERN, for good reasons


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Measurements: BNL, 1997-2001

  • Same technique as CERN experiment, but with improved technology

    • Higher muonfluence

    • Pions decay before entering storage ring, reducing background

    • Superconducting magnets

    • Improved quadrupole focusing

    • Advanced digital electronics

    • et cetera



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Measurements: BNL, 1997-2001

Calorimeter detectors are a mixture of lead and plastic scintillator


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Measurements: BNL, 1997-2001

  • Experimental aµ is 3.4 σ from the most recent Standard Model calculation


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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


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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




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Some more figures…

smuon

neutralino

sneutrino




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