1. B. Lee Roberts, NuFact WG4: 24 June 2005 - p. 1/36 Muon (g-2) Past, Present and Future B. Lee Roberts Department of Physics Boston University roberts@bu.eduroberts@bu.edu http://physics.bu.edu/roberts.html

2. B. Lee Roberts, NuFact WG4: 24 June 2005 - p. 2/36 (in modern language) 673 (1924)

3. B. Lee Roberts, NuFact WG4: 24 June 2005 - p. 3/36 Dirac + Pauli moment Schwinger term

4. B. Lee Roberts, NuFact WG4: 24 June 2005 - p. 4/36 The Muon Trio: Lepton Flavor Violation Muon MDM (g-2) chiral changing Muon EDM

5. B. Lee Roberts, NuFact WG4: 24 June 2005 - p. 5/36 Muon (g-2) : Four Past Experiments CERN 1 - 1950s –SC  precessed in a gradient field CERN 2 - 1960s –Dedicated Storage Ring, p  = 1.28 GeV/c protons from PS injected into the storage ring CERN 3 - 1970s –Dedicated Storage Ring used  injection +  →  decay to give the kick, The “magic”  p   3.09 GeV/c, BNL E821 –Superconducting “superferric” storage ring magic , direct muon injection, fast non-ferric kicker

6. B. Lee Roberts, NuFact WG4: 24 June 2005 - p. 6/36 Spin Precession Frequencies:  in B field spin difference frequency =  s -  c

7. B. Lee Roberts, NuFact WG4: 24 June 2005 - p. 7/36 Use an E field for vertical focusing spin difference frequency =  s -  c 0

8. B. Lee Roberts, NuFact WG4: 24 June 2005 - p. 8/36 Spin Precession Frequencies:  in B field with both an MDM and EDM The EDM causes the spin to precess out of plane. The motional E - field, β X B, is much stronger than laboratory electric fields.

9. B. Lee Roberts, NuFact WG4: 24 June 2005 - p. 9/36 Muon (g-2): Store  ± in a storage ring magnetic field averaged over azumuth in the storage ring

10. B. Lee Roberts, NuFact WG4: 24 June 2005 - p. 10/36 Muon (g-2) Present precision: ± 0.5 ppm

11. B. Lee Roberts, NuFact WG4: 24 June 2005 - p. 11/36 Theory and Experiment Using these hadronic contributions K. Hagiwara, et al., Phys. Rev. D69, 093003 (2004) M. Davier et al., Eur. Phys. J. C 31, 503 (2003), A Höcker, hep-ph/0410081

12. B. Lee Roberts, NuFact WG4: 24 June 2005 - p. 12/36  a  with standard model ~2.7  With this discrepancy, a compelling case can be made to do better, and resolve whether this “discrepancy” is significant or not.

13. B. Lee Roberts, NuFact WG4: 24 June 2005 - p. 13/36 Can we do a more precise measurement? Yes –E969 at BNL has scientific approval to reach 0.2ppm –At a more intense muon facility we could do better. Will Theory Improve? Yes First, let’s look at the pieces which might contribute to a potential discrepancy.

14. B. Lee Roberts, NuFact WG4: 24 June 2005 - p. 14/36 Why might this be interesting? what sources of new physics are there?

15. B. Lee Roberts, NuFact WG4: 24 June 2005 - p. 15/36 a μ is sensitive to a wide range of new physics muon substructure anomalous couplings SUSY (with large tanβ ) many other things (extra dimensions, etc.)

16. B. Lee Roberts, NuFact WG4: 24 June 2005 - p. 16/36 SUSY connection between a , D μ, μ → e

17. B. Lee Roberts, NuFact WG4: 24 June 2005 - p. 17/36 SUSY, dark matter, (g-2)   CMSSM

18. B. Lee Roberts, NuFact WG4: 24 June 2005 - p. 18/36  E969 =  now

19. B. Lee Roberts, NuFact WG4: 24 June 2005 - p. 19/36  E969 

20. B. Lee Roberts, NuFact WG4: 24 June 2005 - p. 20/36 SM value dominated by hadronic issues: Lowest order hadronic contribution ( ~ 60 ppm) Hadronic light-by-light contribution ( ~ 1 ppm) The error on these two contributions will ultimately limit the interpretation of a more precise muon (g-2) measurement.

21. B. Lee Roberts, NuFact WG4: 24 June 2005 - p. 21/36 Lowest Order Hadronic contribution from e + e - annihilation

22. B. Lee Roberts, NuFact WG4: 24 June 2005 - p. 22/36 Magnitude of the errors present hadronic uncertainty ~0.6 ppm present experimental uncertainty 0.5 ppm theory: better R measurements –KLOE –BaBar –SND and CMD2 at Novosibirsk –More work on the strong interaction experiment: E969 @ BNL or elsewhere How could we do better?

23. B. Lee Roberts, NuFact WG4: 24 June 2005 - p. 23/36 Recent News from Novosibirsk SND has just released their results for the cross section e + e - →  +  - over the . –Error on dispersion integral 50% higher than CMD2 –Good agreement with CMD2 –Completely independent from CMD2 Preprint should be on the web soon

24. B. Lee Roberts, NuFact WG4: 24 June 2005 - p. 24/36 How much could the theory improve? In their “Annual Reviews” articleDavier and Marciano guess a factor of 2 or so for argument let’s assume theory uncertainty will get to – 0.3 to 0.1 ppm Experiment –E969 at BNL (if it runs) could achieve a factor of 2.5 for a total error of 0.2 ppm –future experiment could reach 0.06 ppm How much could experiment improve?

25. B. Lee Roberts, NuFact WG4: 24 June 2005 - p. 25/36 E969 at BNL Scientific approval in September 2004 –at present: no funds for construction or running Goal: total error = 0.2 ppm –lower systematic errors –more beam

26. B. Lee Roberts, NuFact WG4: 24 June 2005 - p. 26/36 Strategy of the improved experiment More muons – E821 was statistics limited  stat = 0.46 ppm,  syst = 0.3 ppm –Backward-decay, higher-transmission beamline –Double the quadrupoles in the  decay line –New, open-end inflector –Upgrade detectors, electronics, DAQ Improve knowledge of magnetic field B –Improve calibration, field monitoring and measurement Reduce systematic errors on ω a –Improve the electronics and detectors –New parallel “ integration ” method of analysis

27. B. Lee Roberts, NuFact WG4: 24 June 2005 - p. 27/36 Improved transmission into the ring Inflector Inflector aperture Storage ring aperture E821 Closed EndP969 Proposed Open End

28. B. Lee Roberts, NuFact WG4: 24 June 2005 - p. 28/36 Pedestal vs. Time Near sideFar side E821: forward decay beam Pions @ 3.115 GeV/c Decay muons @ 3.094 GeV/c This baseline limits how early we can fit data

29. B. Lee Roberts, NuFact WG4: 24 June 2005 - p. 29/36 E969: backward decay beam Pions @ 5.32 GeV/c Decay muons @ 3.094 GeV/c No hadron-induced prompt flash Approximately the same muon flux is realized x 1 more muons Expect for both sides

30. B. Lee Roberts, NuFact WG4: 24 June 2005 - p. 30/36 E969: Systematic Error Goal Field improvements will involve better trolley calibrations, better tracking of the field with time, temperature stability of room, improvements in the hardware Precession improvements will involve new scraping scheme, lower thresholds, more complete digitization periods, better energy calibration Systematic uncertainty (ppm)1998199920002001E969 Goal Magnetic field –  p 0.50.40.240.170.1 Anomalous precession –  a 0.80.3 0.210.1

31. B. Lee Roberts, NuFact WG4: 24 June 2005 - p. 31/36 Beyond E969? It’s not clear how far we can push the present technique. To get to 0.06 ppm presents many challenges. Perhaps a new storage ring design, and a smaller aperture. –detectors for another factor of 4 will be very challenging. At a neutrino factory we certainly we can get more muons

32. B. Lee Roberts, NuFact WG4: 24 June 2005 - p. 32/36 A new idea (F.J.M. Farley) Sector focused storage ring, which uses polarized protons to measure ∫ B. dℓ No need to know   /  p Need to know ∫B. dℓ to 20 ppb!!!!! (while E821 already achieved: Can run well above the magic , so that there are more (g-2) cycles per lifetime. Many details to be worked out.

33. B. Lee Roberts, NuFact WG4: 24 June 2005 - p. 33/36 As always, there are questions … Will E969 be funded and reach 0.2 ppm? How far can theory be improved? a observation from history....

34. B. Lee Roberts, NuFact WG4: 24 June 2005 - p. 34/36 Where we came from:

35. B. Lee Roberts, NuFact WG4: 24 June 2005 - p. 35/36 Today with e + e - based theory: All E821 results were obtained with a “blind” analysis. world average

36. B. Lee Roberts, NuFact WG4: 24 June 2005 - p. 36/36 Summary (g-2)  provides a precise check of the standard model, and accesses new physics in a way complementary to other probes. (g-2)  is dependent on a standard model value, part of which must be taken from data (e + e - → hadrons ) The hadronic contribution will eventually set the limit on useful precision, but substantial improvement can be made beyond the present situation.

37. B. Lee Roberts, NuFact WG4: 24 June 2005 - p. 37/36

38. B. Lee Roberts, NuFact WG4: 24 June 2005 - p. 38/36 Fourier Transform: residuals to 5-parameter fit beam motion across a scintillating fiber – ~15 turn period

39. B. Lee Roberts, NuFact WG4: 24 June 2005 - p. 39/36 Effects of the CBO on e - spectrum CBO causes modulation of N, amplitude ~0.01 CBO causes modulation of observed energy distribution which in turn causes oscillation in A ( E ),  (E), with amplitudes ~0.001, ~1 mrad.

40. B. Lee Roberts, NuFact WG4: 24 June 2005 - p. 40/36 Functional form of the time spectrum A 1 and A 2 → artificial shifts in  a up to 4 ppm in individual detectors when not accounted for.

41. B. Lee Roberts, NuFact WG4: 24 June 2005 - p. 41/36 Other Systematic Effects:  a muon losses gain changes and pedistal shifts pulse pileup

42. B. Lee Roberts, NuFact WG4: 24 June 2005 - p. 42/36 E821: Systematic Errors Systematic uncertainty (ppm) 1998199 9 2000200 1 Spin precession –  a 0.80.3 0.21 Systematic uncertainty (ppm) 19981999200 0 200 1 Magnetic field –  p 0.50.40.240.17 Muon spin precession Magnetic field