1. Brian Plimley Physics 129 November 2010

2. Outline  What is the anomalous magnetic moment?  Why does it matter?  Measurements of a µ  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)

4. What is the anomalous magnetic moment? γ Fundamental diagram: (consistent with a µ = 0) x γ µ Corrections according to Standard Model: had = hadronic (QCD) EW = electroweak SM = Standard Model

5. What is the anomalous magnetic moment? Fundamental diagram: (consistent with a µ = 0) QEDelectroweakhadronic x γ µ x γ µ γ µ γγ γ (1 st -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 (m µ / m e ) 2 ≈ 40 000!  (QED has been tested very precisely by a e )

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

10. Measurements: CERN, 1974-76 d = 14 m E µ ≈ 3 GeV (p µ = 3.094 GeV/c)  Protons on a target produce pions, which enter the storage 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

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  Energy threshold selects only electrons emitted along direction of muon momentum  Detector countrate oscillates at beat frequency, by which a µ can be calculated… [figure from BNL work, 2006]

14. Measurements: CERN, 1974-76  ω L is the Larmor frequency (spin precession of a muon at rest)  ω L 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 a µ : 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 muon fluence  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 a µ 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 webpageParticle Physics webpage  The Particle Adventure The Particle Adventure  Contemporary Physics Education Project Contemporary Physics Education Project

23. Questions?

24. Some more figures…

25. smuon sneutrinoneutralino

26. Some more figures…