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

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Anomalous magnetic moment of the muon

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  1. Brian Plimley • Physics 129 • November 2010 Anomalous magnetic moment of the muon

  2. Outline • What is the anomalous magnetic moment? • Why does it matter? • Measurements of aµ • 1974-1976: CERN • 1997-2001: BNL • Conclusions

  3. 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)

  4. 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

  5. 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)

  6. 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)

  7. 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

  8. 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)

  9. Measurements: CERN, 1974-76 • This is the third and most advanced measurement of aµ at CERN in the 60s and 70s

  10. 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)

  11. Measurements: CERN, 1974-76 • Cyclotron frequency: • Spin precession frequency:

  12. Measurements: CERN, 1974-76 • Spin-cyclotron beat frequency (anomalous precession frequency): • Decay electron preferentially emitted along spin axis of muon

  13. 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…

  14. Measurements: CERN, 1974-76 • ωL is the Larmor frequency (spin precession of a muon at rest) • ωL measured separately

  15. 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

  16. Measurements: BNL, 1997-2001 • Same size and energy as CERN, for good reasons

  17. 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

  18. Measurements: BNL, 1997-2001 • Same

  19. Measurements: BNL, 1997-2001 Calorimeter detectors are a mixture of lead and plastic scintillator

  20. Measurements: BNL, 1997-2001 • Experimental aµ is 3.4 σ from the most recent Standard Model calculation

  21. 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

  22. 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

  23. Questions?

  24. Some more figures…

  25. Some more figures… smuon neutralino sneutrino

  26. Some more figures…

  27. Some more figures…

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