1. B. Lee Roberts, Fermilab – 9 November 2009 - p. 1/28 The Physics Case for a Dedicated Muon EDM Experiment in the Project X Era Lee Roberts BU (in collaboration with Jim Miller (BU), Gerco Onderwater (KVI) and Yannis Semertzidis (BNL) ) roberts @bu.edu http://physics.bu.edu/show/roberts + -

2. B. Lee Roberts, Fermilab – 9 November 2009 - p. 2/28 Outline Introduction to dipoles search for electric dipole moments –overview –experimental considerations for a  EDM Conclusions

3. B. Lee Roberts, Fermilab – 9 November 2009 - p. 3/28 I wish to acknowledge up front that I have borrowed heavily from articles in the new World Scientific book http://www.worldscibooks.com/physics/7273.html Especially the articles by Czarnecki and Marciano, and Roberts, Miller and Semertzidis. Disclaimer: Disclaimer: The physics presented here is compelling. The experimental details for  EDM at Project X are preliminary, and illustrate the possibilities Clearly much work is needed.

4. B. Lee Roberts, Fermilab – 9 November 2009 - p. 4/28 The Dirac Equation predicted electron magnetic moment However, experimentally g > 2; need to add a Pauli term where a is the anomaly, dimension 5 operator (only from loops)

5. B. Lee Roberts, Fermilab – 9 November 2009 - p. 5/28 What if we introduced the additional Pauli-like term Parameterize the effect of new physics on a and d by: where the EDM is defined as Electric Dipole Moment, EDM

6. B. Lee Roberts, Fermilab – 9 November 2009 - p. 6/28 Electromagnetic Form Factors: ( q = momentum transfer, Q = charge) (anapole moment which we ignore in this talk)

7. B. Lee Roberts, Fermilab – 9 November 2009 - p. 7/28 Magnetic and Electric Dipole Interactions Muon Magnetic Dipole Momoment a  Muon EDM

8. B. Lee Roberts, Fermilab – 9 November 2009 - p. 8/28 Connection between MDM, EDM and the lepton flavor violating transition moment  → e SUSY slepton mixing MDM, EDM

9. B. Lee Roberts, Fermilab – 9 November 2009 - p. 9/28 Electric Dipole Moment: P T If CPT is valid, an EDM would imply CP. Of course, we need new sources of CP to explain why we’re here. (BAU) Transformation Properties

10. B. Lee Roberts, Fermilab – 9 November 2009 - p. 10/28 The search for electric dipole moments: non- SM CP Phys. Rev. 78 (1950) torque

11. B. Lee Roberts, Fermilab – 9 November 2009 - p. 11/28 Principle of the “traditional” EDM measurements B0B0 EB0B0 B0B0 E Animation by J. Karamath E=100kV/m Back

12. B. Lee Roberts, Fermilab – 9 November 2009 - p. 12/28 New Result! 199 Hg - PRL 102, 101601 (2009) Back

13. B. Lee Roberts, Fermilab – 9 November 2009 - p. 13/28 The present EDM limits are orders of magnitude from the standard-model value ParticlePresent EDM limit (e-cm) SM value (e-cm) References: n PRL 97, 131801 (2006) p, 199 Hg PRL 102, 101601 (2009) e - PRL 88, 071805 (2002)  PRD 80, 052008 (2009)

14. B. Lee Roberts, Fermilab – 9 November 2009 - p. 14/28 10 -28 Left - Right MSSM  ~  Multi Higgs MSSM  ~ 1 10 -24 10 -22 10 -26 10 -30 10 -32 10 -34 10 -36 e EDM (e.cm) E. Hinds’ e-EDM experiment at Imperial College with YbF molecules seems to be ahead in the race for d e Standard Model d e < 1.6 x 10 -27 e.cm Commins (2002) Excluded region (Tl atomic beam) with thanks to Ed Hinds n The SUSY CP problem! The strong CP problem! 199 Hg  p

15. B. Lee Roberts, Fermilab – 9 November 2009 - p. 15/28 a μ implications for the muon EDM assuming same New Physics participates (recall that (  today =255(80) X10 -11 ) Either d µ is of order 10 –22 e cm, or the CP phase is strongly suppressed! Assuming that

16. B. Lee Roberts, Fermilab – 9 November 2009 - p. 16/28 Spin Frequencies:  in B field with MDM & EDM The motional E - field, β X B, is (~GV/m). 0

17. B. Lee Roberts, Fermilab – 9 November 2009 - p. 17/28 Total frequency Plane of the spin precession tipped by the angle  Number above (+) and below (-) the mid-plane will vary as:

18. B. Lee Roberts, Fermilab – 9 November 2009 - p. 18/28 E821 Data: up-going / down-going tracks vs. time, (modulo f a ): BNL traceback measurement was entirely statistics limited –1 station –Late turn-on time –Small acceptance –Ran 2 out of 3 years (g-2) signal: # Tracks vs time, modulo g-2 period, in phase. EDM Signal: Average vertical angle modulo g-2 period. Out-of- phase by 90° from g-2; this is the EDM signal (g-2) EDM Fermilab g-2 should do 100 X better

19. B. Lee Roberts, Fermilab – 9 November 2009 - p. 19/28 Frozen Spin: Storage ring p  d  EDM Experiments (not at magic  ) With  a = 0, the EDM causes the spin to steadily precess out of the plane. 0 Use a radial E-field to turn off the  a precession  first suggested by Y. Semertzidis, see: PRL 93  aa 

20. B. Lee Roberts, Fermilab – 9 November 2009 - p. 20/28 “Frozen spin” technique to measure EDM Turn off the (g-2) precession with radial E Up-Down detectors measure EDM asymmetry Look for an up-down asymmetry building up with time Side detectors measure (g-2) precession cancellation –To prove the spin is frozen

21. B. Lee Roberts, Fermilab – 9 November 2009 - p. 21/28 Proposed PSI muon EDM storage ring (Could also run at the European Spallation Neutron Source being built in Lund) “one muon at a time” by A. Streun hep-ex/0606034v3 June 2009

22. B. Lee Roberts, Fermilab – 9 November 2009 - p. 22/28 J-PARC LOI L22, January 2003 Lattice n.b. The E and B fields have to be a the same place to avoid the geometric phase. (Berry’s phase, rotations do not commute) In addition, the local cancellation of  a (point to point) must be good, for the same reason.

23. B. Lee Roberts, Fermilab – 9 November 2009 - p. 23/28 Building designed by FESS for (g-2) could house an EDM ring after (g-2) is finished. AP0 g-2

24. B. Lee Roberts, Fermilab – 9 November 2009 - p. 24/28 High-bay hall is 70’ X 80’ (21.3 m X 24 m)

25. B. Lee Roberts, Fermilab – 9 November 2009 - p. 25/28 Errors and possible parameters for Fermilab Need to optimize the parameters The building could handle a ring of ≤ 6.5 m bending radius (+ straight sections) –0.6 to 0.65 GeV/c momentum –5 MV/m E field On the next slide we compare the 3 suggested opportunities.

26. B. Lee Roberts, Fermilab – 9 November 2009 - p. 26/28 Parameters of a Fermilab dedicated EDM ring compared to other suggestions. Fermilab not yet optimized. (Preliminary) E (MV/m) B (T) p  (Mev/c)  (  s) PAR 0 (m) 2.20.255004.810.60.50.36.5 0.640.251251.63.50.30.50.4 50.456005.812.70.90.34.2 JPARC PSI Pr-X No attempt yet has been made to optimize a ring for the Fermilab program. Clearly things can be improved, but already we see that it is competitive with other possibilities. Both the beam and ring details are extremely important.

27. B. Lee Roberts, Fermilab – 9 November 2009 - p. 27/28 Muon EDM Limits: Present and Future E821 Factory Need: NA 2 ≃ 10 16 for d  ≃ 10 -23 e ·cm new (g-2) ? PSI ? Dedicated storage rings Back Proj. X/

28. B. Lee Roberts, Fermilab – 9 November 2009 - p. 28/28 Summary and Conclusions The non-observation of an EDM remains a mystery, and is beginning to press BSM theories such as SUSY. The muon, because of its long lifetime, and copious production by high intensity pion beams, presents a unique opportunity to search for the EDM of a second- generation particle. A dedicated search for a muon EDM which could be done in the Project X era would permit a sensitivity several orders of magnitude beyond the present limit. The beam required would have high polarization, and would need a pulsed time structure.

29. B. Lee Roberts, Fermilab – 9 November 2009 - p. 29/28

30. B. Lee Roberts, Fermilab – 9 November 2009 - p. 30/28 Review: a  Experiment

31. B. Lee Roberts, Fermilab – 9 November 2009 - p. 31/28 Muons: –born polarized –die with information on where their spin was at the time of decay –highest energy e - carry spin information Self-analyzing Muon Decay N A NA 2 =0.4

32. B. Lee Roberts, Fermilab – 9 November 2009 - p. 32/28 EDMs in Hadronic Systems, p, n, d, 199 Hg QCD vacuum state can be parameterized by: P T Physical quantity is the sum of  and the overall phase of the quark matrix, which is constrained by the non-observation of a neutron EDM. We have the form factors F 2n,p (0) and F 3n,p (0) (the aMDM and EDM) which we can write as isovector and isoscalar contributions: strong CP problem! Back

33. B. Lee Roberts, Fermilab – 9 November 2009 - p. 33/28 Parasitic Muon EDM Measurement using straw tube arrays The EDM tips the precession plane, producing an up-down oscillation with time (out of phase with  a ) Measure upward-going vs. downward-going decay electrons vs. time with straw tube arrays E821 straw-tube array arXiv:0811.1207v1 Back