1. Proposal to measure the muon electric dipole moment with a compact storage ring at PSI Thomas Schietinger in collaboration with K. Kirch, A. Adelmann, A. Streun, G. Onderwater* PSI, July 4 th 2007 *Rijksuniversiteit Groningen

2. Thomas Schietinger PSI, 4 July 2007 Measuring the muon EDM at PSI 2 Contents ● Introduction: lepton dipole moments ● Muon spin precession in B and E fields ● (g–2) µ and µEDM at storage rings ● A new method to measure µEDM: the “frozen spin” technique ● Motivations to go below the current limit (10 –19 e cm) ● A possible layout for PSI ● Sensitivity estimate ● Status of the project

3. Thomas Schietinger PSI, 4 July 2007 Measuring the muon EDM at PSI 3 Lepton dipole moments Define g and as unit-free quantities describing magnetic and electric dipole moments, respectively: For a Dirac particle (i.e. lepton): g = 2 (+ corrections) and = 0 (+ super-tiny corrections from CP-violating interactions ) Hamiltonian: ⇒ convenient to define:

4. Thomas Schietinger PSI, 4 July 2007 Measuring the muon EDM at PSI 4 Lepton g –2 versus The corrections to g = 2 in principle contain all of physics! – Muon more sensitive to physics from higher-mass scales than electron by a factor of (m µ /m e ) 2 = 42 000! – Therefore, at the level of current experimental precision: ● (g–2) e contains all of QED (use it to determine ) ● (g–2) µ contains all of QED, electroweak and strong (and new physics up to ~500 GeV scale) – (g–2) even more sensitive, but much harder to measure! The corrections to = 0 contain almost no physics! – EDMs are “protected” by P and T symmetries – Only CP-violating interactions can give ≠ 0. – The muon vs. electron enhancement is only m µ /m e = 206

5. Thomas Schietinger PSI, 4 July 2007 Measuring the muon EDM at PSI 5 (g –2) µ contains all of physics! Courtesy L. Roberts and J. Miller QED, electroweak, strong,… … + new physics?

6. Thomas Schietinger PSI, 4 July 2007 Measuring the muon EDM at PSI 6 Lepton EDMs ● EDMs in elementary particles (also nuclei, atoms and some molecules) violate P and T symmetries, therefore violate CP if CPT is conserved. – No contributions from QED and strong interactions, only higher- order electroweak! ● Current efforts are mainly focused on neutral particles (neutron, atoms). ● But lepton EDMs are theoretically much cleaner. – + + – T P + – M. Pospelov, A. Ritz: Electric dipole moments as probes of new physics, Annals of Physics 318 (2005) 119

7. Thomas Schietinger PSI, 4 July 2007 Measuring the muon EDM at PSI 7 contains almost no physics! Fourth order electroweak? F. Hoogeveen: The Standard Model Prediction for the Electric Dipole Moment of the Electron, Nucl. Phys. B 241 (1990) 322 … + new physics?

8. Thomas Schietinger PSI, 4 July 2007 Measuring the muon EDM at PSI 8 contains almost no physics! Fourth order electroweak? No! F. Hoogeveen: The Standard Model Prediction for the Electric Dipole Moment of the Electron, Nucl. Phys. B 241 (1990) 322 … + new physics? Much greater sensitivity to new, CP-violating physics! Even these diagrams cannot give any contribution to EDM! M.E. Pospelov, I.B. Khriplovich : Electric dipole moment of the W boson and the electron in the Kobayashi- Maskawa model, Sov. J. Nucl. Phys. 53 (1991) 638 Abstract: In the Kobayashi-Maskawa model the W boson and the electron do not have electric dipole moments in the two- and three-loop approximations, respectively.

9. Thomas Schietinger PSI, 4 July 2007 Measuring the muon EDM at PSI 9 The Matter-Antimatter imbalance The Big Bang produced equal amounts of matter and antimatter We now know with high confidence that only matter is left in today's universe !

10. Thomas Schietinger PSI, 4 July 2007 Measuring the muon EDM at PSI 10 The Matter-Antimatter imbalance ⇒ Some (CP-violating!) interaction at some scale must have caused this asymmetry! Y0Y0 n +... ? 60% 40% (The known CP violation from weak interaction is by far not enough to produce the effect.) Very strong motivation to look for EDMs! The Big Bang produced equal amounts of matter and antimatter We now know with high confidence that only matter is left in today's universe

11. Thomas Schietinger PSI, 4 July 2007 Measuring the muon EDM at PSI 11 Measuring lepton dipole moments e µ Storage Rings Store muons in a ring, observe response to E and B fields Colliders Exploit dependence of pair production kinematics on dipole moments Penning Traps / Atomic Physics Look for T-violation in heavy paramagnetic atoms (EDM); electrons and positrons in Penning traps (MDM)

12. Thomas Schietinger PSI, 4 July 2007 Measuring the muon EDM at PSI 12 Muon spin precession in B field Muon spin precession in the presence of a uniform B field, perpendicular to the muon momentum: Larmor precession (classical) Thomas precession (relativistic) Compare to cyclotron frequency (momentum precession): Gift Nr. 1 from Nature: get direct access to a µ (i.e. g–2) by measuring the spin precession relative to the momentum! Difference: frequency with which the spin precesses relative to the momentum:

13. Thomas Schietinger PSI, 4 July 2007 Measuring the muon EDM at PSI 13 Muon spin precession in B and E field Muon spin precession in the presence of B and E field, perpendicular to each other and to the muon momentum: E B -spin -trajectory Example: B-field pointing down, E-field radially outward: a : spin precession in orbital plane (“g–2” precession) e : spin precession out of orbital plane = a + e tilts the precession plane out of the orbital plane ae

14. Thomas Schietinger PSI, 4 July 2007 Measuring the muon EDM at PSI 14 Muon spin precession in B and E field ae Strategy for (recent) g–2 measurement at storage rings: ● run at “magic ”, = 29.3 (p= 3.1 GeV) ⇒ no effect from electric fields, can use electric focusing (need for uniform B field precludes magnetic focusing) ● assume small for measurement of a ⇒ direct access to a if B is known ● look for small vertical oscillation to put a limit on. — All recent limits have been obtained in this way (CERN, Brookhaven) — Plagued by systematics: g–2 precession interferes strongly! Gift Nr. 2 from Nature

15. Thomas Schietinger PSI, 4 July 2007 Measuring the muon EDM at PSI 15 g–2 Measurement (E821@Brookhaven) A 20-year effort to improve the precision on a from 7 ppm to 0.5 ppm: a = 0.001 165 920 80 (63)

16. Thomas Schietinger PSI, 4 July 2007 Measuring the muon EDM at PSI 16 g–2: the most recent state of affairs a (exp) = 0.001 165 920 80 (63) G.W. Bennett et al.: Final report of the E821 muon anomalous magnetic moment measurement at BNL, Phys. Rev. D 73 (2006) 072003 a (SM) = 0.001 165 918 04 (51) (0.44 ppm) (0.54 ppm) K. Hagiwara, A.D. Martin, D. Nomura, T. Teubner: Improved predictions for g-2 of the muon and QED (M Z 2 ), Phys. Lett. B 649 (2007) 173 a (exp) – a (SM) = (27.6 ± 8.1) × 10 –10 3.4 discrepancy! ● New physics or not? ● The deviation is consistent with LHC-accessible SUSY in the few 100 GeV range... ● A proposed upgrade of E821 to halve the error is currently under review (E969). ● Both experiment and theory are at their limits. For the (beautiful!) history of g–2, see: F.J.M. Farley, Y.K. Semertzidis: The 47 years of muon g–2, Prog. Part. Nucl. Phys. 52 (2004) 1 E969: B.L. Roberts: Muon (g–2): Past, present and future, Nucl. Phys. Proc. Suppl. 155 (2006) 372 J.P. Miller, E. de Rafael, B.L. Roberts: Muon (g–2): experiment and theory Rep. Prog. Phys. 70 (2007) 795

17. Thomas Schietinger PSI, 4 July 2007 Measuring the muon EDM at PSI 17 µEDM at g–2 storage rings ● Search for a vertical oscillation signal in g–2 data (vertical segmentation of some of the electron detectors) ● Seriously limited by two effects: 1) g–2 rotation of spin strongly suppresses the effect of e (spin can be parallel to e vector!) 2) Trajectories of the decay electrons are very different at the two extremes of vertical oscillation, leading to large systematic effects. ● Best current limit from Brookhaven E821: – Only preliminary, but soon to be published (L. Roberts). – Only modest improvement with respect to previous (CERN) experiment. d < 2.4 × 10 –19 e cm R. McNabb et al.: hep-ex/0407008, unpublished

18. Thomas Schietinger PSI, 4 July 2007 Measuring the muon EDM at PSI 18 History of µEDM measurements R. McNabb et al., hep-ex/0407008, unpublished J. Bailey et al., J. Phys. G: Nucl. Phys. 4 (1978) 345 G. Charpak et al., Nuovo Cim. 22 (1961) 1043 D. Berley, G. Gidal, Phys. Rev. 118 (1960) 1086 D. Berley et al., Phys. Rev. Lett. 1 (1960) 144 Stalling progress with conventional storage ring method...

19. Thomas Schietinger PSI, 4 July 2007 Measuring the muon EDM at PSI 19...yet we still have a long way to go!

20. Thomas Schietinger PSI, 4 July 2007 Measuring the muon EDM at PSI 20...yet we still have a long way to go! A new method is needed! W. Bernreuther at the Workshop on the Future of Muon Physics, Heidel- berg, Germany, May 7–10, 1991: W. Bernreuther: The Electric Dipole Moment of the Muon, Z. Phys. C 56 (1992) S97

21. Thomas Schietinger PSI, 4 July 2007 Measuring the muon EDM at PSI 21 Muon spin precession in B and E field ae New strategy for EDM measurement: the “frozen spin” technique! ● Go to lower momentum, install a “magic E field” (radially), such that a vanishes completely: – i.e., return gift Nr. 2 from Nature in exchange for another one! ● The spin remains parallel to the momentum along the orbit (“frozen spin”) ● In the presence of an EDM ( ≠ 0) the spin is slowly rotated out of the orbital plane. ● Much superior sensitivity than with parasitic approach! F. Farley et al.: New Method of Measuring Electric Dipole Moments in Storage Rings, Phys. Rev. Lett. 93 (2004) 052001

22. Thomas Schietinger PSI, 4 July 2007 Measuring the muon EDM at PSI 22 The “frozen spin” technique ● Turn off the g–2 precession with a radial E field ● Up-down detectors measure decay electrons – Emission of electrons strongly correlated with spin direction, in particular for high- energy electrons ● Look for an up-down asymmetry, building up linearly with time ● Detectors on the inside and outside to measure g –2 precession (cross check) A. Silenko et al.: J-PARC Letter of Intent: Search for the Permanent Muon Electric Dipole Moment at the 10 –24 e cm Level.

23. Thomas Schietinger PSI, 4 July 2007 Measuring the muon EDM at PSI 23 J-PARC letter of intent ● Semertzidis, Farley et al. in 2003 proposed an experiment exploiting the frozen spin technique at J-PARC (PRISM-II FFAG). ● Design: 7-m radius ring, with B = 0.25 T, E = 2 MV/m and p = 500 MeV ( = 11 µs). ● Estimated sensitivity is around 10 –24 e cm ● So far a “virtual project”, realization not likely before 2015. A. Silenko et al.: J-PARC Letter of Intent: Search for the Permanent Muon Electric Dipole Moment at the 10 –24 e cm Level. Klaus Kirch: could we do this at PSI with lower energy muons? What is the motivation to go below 10 –19 e cm?

24. Thomas Schietinger PSI, 4 July 2007 Measuring the muon EDM at PSI 24 Motivations to go below 10 –19 e cm A) Model-independent ● Ambiguity in g–2 measurement ● Generic new physics based on g–2 anomaly B) Model-specific ● Supersymmetry ● Left-right symmetric models ● Any other business model... C) Forget about models altogether: the muon EDM is definitely one of the least tested corners of the SM! ● Side note: this was the principal motivation for the multi-M$ B- factories – not one theory made a specific prediction for sin 2 (other than the SM)

25. Thomas Schietinger PSI, 4 July 2007 Measuring the muon EDM at PSI 25 Ambiguity in g–2 measurement? ● The anomalous muon spin precession measured in Brookhaven is usually attributed to new physics in the muon's magnetic dipole moment: a μ NP = (27.6 ± 8.1) × 10 –10 ● But it could just as well arise from new physics in the muon's electric dipole moment: d μ = (2.4 ± 0.4) × 10 –19 e cm, or a combination of both. ● Current limits are insufficient to resolve the ambiguity. ● Nobody seriously believes that the muon EDM is as large as that... – Lee Roberts: “this would have earth-shaking consequences!” ●...but I could not find anyone who can provide a solid argument as to why it must be smaller! – e.g.: “Water would be unstable!”, “Nucleosynthesis would not have worked!”, “Windows 98 would be stable”, or similar. – How to quantify “earth-shaking”?

26. Thomas Schietinger PSI, 4 July 2007 Measuring the muon EDM at PSI 26 The g–2 anomaly isn't? J. Feng, T.M. Matchev, Y. Shadmi: The Measurement of the Muon's Anomalous Magnetic Moment Isn't, Phys. Lett. B 555 (2003) 89 (updated with latest numbers) !

27. Thomas Schietinger PSI, 4 July 2007 Measuring the muon EDM at PSI 27 Generic new-physics dipole moment If one assumes that both non-SM MDM ( a NP ) and EDM (d µ ) are manifestations of the same new-physics object: and with D a general dipole operator (W. Marciano), then the Brookhaven measurement can be interpreted as i.e. either d µ is of order 10 –22 e cm, or the CP phase is strongly suppressed! J.L. Feng, K.T. Matchev, Y. Shadmi: Theoretical Expectations for the Muon's Electric Dipole Moment, Nucl. Phys. B 613 (2001) 366

28. Thomas Schietinger PSI, 4 July 2007 Measuring the muon EDM at PSI 28 Model-specific predictions ● Most reasonable models predict lepton EDMs to scale linearly with mass. – Strong bound on d µ from d e < 1.6 × 10 –27 e cm! ● Some models, however, predict quadratic and cubic mass scaling ● Some SUSY variants can give up to 10 –22 e cm, but this involves a lot of tuning – Flavour-violating SUSY a good candidate, but predictions need to be updated in view of new experimental limits on ! – Bartl et al. give d µ ≃ 2.7 × 10 –22 e cm for µ = /2 (SUSY-parameter µ) from stau-smuon mixing, based on BF( ) < 1.1 × 10 –6. – The latest limit from Belle reads BF( ) < 4.5 × 10 –8... K.S. Babu, S.M. Barr, I. Dorsner: Scaling of lepton dipole moments with lepton mass, Phys. Rev. D 64 (2001) 053009 A. Bartl, W. Majerotto, W. Porod, D. Wyler: Effect of supersymmetric phases on lepton dipole moments and rare lepton decays, Phys. Rev. D 68 (2003) 053005 K.S. Babu, B. Dutta, R.N. Mohapatra: Enhanced Electric Dipole Moment of the Muon in the Presence of Large Neutrino Mixing, Phys. Rev. Lett. 85 (2000) 5064

29. Thomas Schietinger PSI, 4 July 2007 Measuring the muon EDM at PSI 29 MSSM with LR, flavor mixing and complex phase ● Input: MSSM at point SPS1a ● Add flavor-violating terms that saturate experimental limits (as of 2003!) on d e, d µ, d, a e, a µ, a, BF(µe), BF(µ), BF(e) ● Smuon-stau mixing can give large d µ : A. Bartl, W. Majerotto, W. Porod, D. Wyler: Effect of supersymmetric phases on lepton dipole moments and rare lepton decays, Phys. Rev. D 68 (2003) 053005 Bartl et al. use BF( ) < 1.1 × 10 –6 (CLEO 2000) Belle 2007: BF < 4.5 × 10 –8 Belle Collab. (K. Hayasaka et al.): New Search for and e Decays at Belle, hep-ex/0705.0650, submitted to Phys. Lett. B BABAR Collab. (B. Aubert et al.): Search for lepton flavor violation in the decay, Phys. Rev. Lett. 95 (2005) 041802 BABAR 2007: BF < 6.8 × 10 –8

30. Thomas Schietinger PSI, 4 July 2007 Measuring the muon EDM at PSI 30 BF( ) [10 –8 ] d µ [10 –23 e cm] 10010 50 30 20 10 CLEO 2000 ● Bartl et al. gave a snapshot of the situation in 2003. ● We need a systematic evaluation as a function of BF( ) in order to assess the situation now and in future. (G. Hiller) Various points in FV MSSM phasespace ● M. Spira (PSI) says he can do that for us. ● Gudrun Hiller (Dortmund) wants to unleash a postdoc on this topic. Bartl et al. 5 E821 limit: 24'000

31. Thomas Schietinger PSI, 4 July 2007 Measuring the muon EDM at PSI 31 BF( ) [10 –8 ] d µ [10 –23 e cm] 10010 50 30 20 10 Belle 2007 Bartl et al. 5 ? ● New Belle limit has dramatic impact (on a linear scale) ● But it is still possible that 5 × 10 –23 e cm will be just barely possible in FV SUSY. ● We shall soon find out! Belle Collab. (K. Hayasaka et al.): New Search for and e Decays at Belle, hep-ex/0705.0650, submitted to Phys. Lett. B

32. Thomas Schietinger PSI, 4 July 2007 Measuring the muon EDM at PSI 32 BF( ) [10 –8 ] d µ [10 –23 e cm] 10010 50 30 20 10 Belle 2007 ● New Belle limit has dramatic impact (on a linear scale) ● But it is still possible that 5 × 10 –23 e cm will be just barely possible in FV SUSY. ● We shall soon find out! Bartl et al. 5 ? ● It is intriguing that a dedicated µEDM experiment would take us roughly to the region probed by at the B factories! ● One could make the point that it is important to have some kind of experimental input on the vertical axis... Belle Collab. (K. Hayasaka et al.): New Search for and e Decays at Belle, hep-ex/0705.0650, submitted to Phys. Lett. B

33. Thomas Schietinger PSI, 4 July 2007 Measuring the muon EDM at PSI 33 A µEDM experiment at PSI?

34. Thomas Schietinger PSI, 4 July 2007 Measuring the muon EDM at PSI 34 Muons at PSI

35. Thomas Schietinger PSI, 4 July 2007 Measuring the muon EDM at PSI 35 Muons at PSI µE1 area

36. Thomas Schietinger PSI, 4 July 2007 Measuring the muon EDM at PSI 36 µE1 beamline and area Existing infrastructure For comparison: my car p = 220 MeV 50.63 MHz (19.75 ns) p µ = 125 MeV pion decay channel (8 m, 4–5 T) Muon “beam”: ● ~400 mm mrad emittance ● ~10 8 µ + / s ● Bunch width 3.9 ns FWHM µ sµsµ µ I.C. Barnett et al. : Nucl. Instr. and Meth. A 455 (2000) 329; also: http://ltp.web.psi.ch

37. Thomas Schietinger PSI, 4 July 2007 Measuring the muon EDM at PSI 37 Concept for an experiment at PSI Apply frozen spin technique at lower energy than J-PARC proposal: ● PSI µE1: p μ =125 MeV ( = 0.76,  = 1.55), P μ = 92% ● Choose B = 1 T (conventional magnet, straightforward change of polarity) ⇒ 42 cm orbit radius, radial E-field 0.64 MV/m (64 kV across 10 cm gap). Trade off high intensity of muon beam for beam quality, selecting the muons to be injected into the ring: ● Reduce from 100 MHz to ~200 kHz ● One muon at a time! Measurement time ≈ µ = 3.4 µs. ● Assume run-time of 2 × 10 7 s, times 200 kHz gives 4 × 10 12 electron decays (per year) ● Clockwise and counter-clockwise operation (systematics)

38. Thomas Schietinger PSI, 4 July 2007 Measuring the muon EDM at PSI 38 µE1 beamline and area For comparison: my car A ~1-m-diameter storage ring with support fits in comfortably

39. Thomas Schietinger PSI, 4 July 2007 Measuring the muon EDM at PSI 39 Artist's impression (A. Streun)

40. Thomas Schietinger PSI, 4 July 2007 Measuring the muon EDM at PSI 40 Recycle CHAOS spectrometer? ● Magnetic spectrometer with full 360˚ acceptance in horizontal plane, ± 7˚ vertically ● Used to study scattering off hydrogen targets ● 12-cm diameter inner bore for target insertion ● Equipped with wire chambers for tracking 95 cm diameter 20 cm gap up to 1.6 T field bionic woman (S. Ritt) Magnet still in storage at TRIUMF! G.R. Smith et al.: The CHAOS spectrometer for pion physics at TRIUMF, Nucl. Instr. and Meth. A 362 (1995) 349

41. Thomas Schietinger PSI, 4 July 2007 Measuring the muon EDM at PSI 41 Sensitivity estimate Uncertainty on from a simple asymmetry counting experiment with N decays: F. Farley et al.: New Method of Measuring Electric Dipole Moments in Storage Rings, Phys. Rev. Lett. 93 (2004) 052001 A : electron asymmetry, assume A = 0.3 P : polarization of muons J-PARC proposal: = 11 µs, = 0.978, P = 50%, B = 0.25 T ⇒ = 4 × 10 –3 /√N ; N = 4 × 10 16 ⇒ = 2 × 10 –11 d µ < 10 –24 e cm PSI proposal: = 3.4 µs, = 0.76, P = 90%, B = 1.0 T ⇒ = 2.4 × 10 –3 /√N ; N = 4 × 10 12 ⇒ = 10 –9 d µ < 5 × 10 –23 e cm Muon statistics is the dominant factor!

42. Thomas Schietinger PSI, 4 July 2007 Measuring the muon EDM at PSI 42 Electron asymmetry A ● Theoretically best possible A is given by A = √(127/1260) = 0.31748... ● It drops below 0.3 only for > 0.815 ● A = 0.3 (as in Farley et al.) is an excellent assumption!!

43. Thomas Schietinger PSI, 4 July 2007 Measuring the muon EDM at PSI 43 Main challenges ● Injection – Cannot use conventional kicker due to very short turn-around time (11.6 ns) – Possible solution: resonance injection at half-integer tune using a non-linear field perturbator (inflector) ● Injection trigger – Minimal latency between detection of “good muon” and ramp-up of inflector ● Detector – B-field, limited space, systematics issues ● Data processing / storage – O(10 12 ) muon decays, almost all of them carry interesting information!

44. Thomas Schietinger PSI, 4 July 2007 Measuring the muon EDM at PSI 44 Resonance injection method ● Developed for injection into commercial tabletop synchrotron light-sources – AURORA series (50 cm orbit radius), MIRRORCLE (15.6 cm!) by photon production laboratories, Ltd. ● Perturbator excites half-integer betatron resonance (e.g. 3/2), decay to stable orbit over several turns H. Yamada et al.: Development of the hard X-ray source based on a tabletop electron storage ring, Nucl. Instr. and Meth. A 467/468 (2001) 122 T. Takayama et al.: Resonance injection method for the compact superconducting SR-ring, Nucl. Instr. and Meth. B 24/25 (1987) 420 H. Yamada: Commissioning of aurora: The smallest synchrotron light source, J. Vac. Sci. Technol. B 8 (1990) 1628 H. Yamada: Novel X-ray source based on a tabletop synchrotron and its unique features, Nucl. Instr. and Meth. B 199 (2003) 509 http://www.photon-production.co.jp/

45. Thomas Schietinger PSI, 4 July 2007 Measuring the muon EDM at PSI 45 Injection study for µEDM project ● Andreas Adelmann, using TRACY program ● 20 turns ramp of non-linear perturbator ● Acceptance ±7 mm / ±11 mrad, average latency for acceptable μ: ~1.2 μs ● Average measurement time = 3.4 μs ● ~200 kHz repetition rate for perturbator – Challenging, in particular for “random” ramp-up – Can we trigger the perturbator in time to catch the “good” muon? Injection phase space diagram (TRACY) http://slsbd.psi.ch/pub/slsnotes/tmeta9902/ stable orbits Injection turns Acceptance

46. Thomas Schietinger PSI, 4 July 2007 Measuring the muon EDM at PSI 46 Beam schematic p (2 mA, 590 MeV) (220 MeV) µ (125 MeV) B E B µE1 beam line inflector design orbit (r = 42 cm) ~20 turns injection radial capacitor (1 T) (6.4 kV/cm) trigger ● Pions produced in thick target ● Capture muons from backward decay of pions ⇒ polarized muons (P μ = 92%) ● Upon “good muon”-trigger, inflector ramps down non-linear perturbation field over a period of 20 turns ● Resonance injection at half-integer Target E

47. Thomas Schietinger PSI, 4 July 2007 Measuring the muon EDM at PSI 47 Detector ● Identifies direction of decay e ± (at least up- or downwards) ● Energy resolution helps (at least low energy cutoff) ● Full reconstruction nice but probably not necessary (some segmentation in,, z) ● Timing below 1 ns desirable (at least 10 ns) ● Limited space and B-field will be challenging! ● RooFit toy Monte Carlo study in progress to study requirements in detail. ● Full GEANT4 simulation of a possible detector setup in preparation Technology so far completely open! K. Kirch

48. Thomas Schietinger PSI, 4 July 2007 Measuring the muon EDM at PSI 48 RooFit toy Monte Carlo ● Toy Monte Carlo producing events by drawing event variables from probability density functions (pdfs) ● Variables in our case: – reduced energy [0,∞]; – positron polar angle cos() [–1,1]; – positron azimuthal angle [–/2,/2]; – decay time t. ● Construct 4-dimensional pdf W(cos(),,,t ;, P µ, ) to generate events, then fit for to study statistical error as a function of event number and cuts. ● In practice, generation in 4D much too inefficient ⇒ generate uncorrelated variables separately ● Also, fit has trouble converging in 4D ⇒ produce time-dependent asymmetry, simple linear fit. ● Useful to study effect of experimental constraints (energy threshold, time- out, fiducial volume etc.) on statistical error (first order detector optimization)

49. Thomas Schietinger PSI, 4 July 2007 Measuring the muon EDM at PSI 49 RooFit toy Monte Carlo Variable distributions for = 0 cos() t pdf blue: pdf

50. Thomas Schietinger PSI, 4 July 2007 Measuring the muon EDM at PSI 50 RooFit toy Monte Carlo Variable distributions for = 2 × 10 – 4 cos() t blue: pdf cos() pdf

51. Thomas Schietinger PSI, 4 July 2007 Measuring the muon EDM at PSI 51 RooFit toy Monte Carlo Final asymmetry for: ● 10 7 events ( = 50 sec. data taking at PSI) ● with = 5 × 10 –6 (current limit) ● and > 0.7 (no energy bins) Error roughly consistent with expectation from formula given in Farley et al.

52. Thomas Schietinger PSI, 4 July 2007 Measuring the muon EDM at PSI 52 Various systematics issues... ● Vertical E field component: E ⊥ < 10 –4 E rad. – Most dangerous: local vertical E field components ● Rotational misalignments and residual g–2 precession ● Instabilities of E, B fields, detector,......but many ways to control them: ● Injection of μ + and μ – – Factor 3 less statistics for μ – ● Clockwise and counter-clockwise orbit ● g–2 precession for calibration ● Spin rotation? F. Farley et al.: New Method of Measuring Electric Dipole Moments in Storage Rings, Phys. Rev. Lett. 93 (2004) 052001

53. Thomas Schietinger PSI, 4 July 2007 Measuring the muon EDM at PSI 53 Impact of a PSI measurement ● Rule out EDM explanation for Brookhaven MDM anomaly ● Rule out (or confirm) naïve relation between new physics MDM and EDM for the case CP ≈ 1. ● Explore the region down to 5 × 10 –23 e cm ●... long before J-PARC (or anyone else) can get there.

54. Thomas Schietinger PSI, 4 July 2007 Measuring the muon EDM at PSI 54 * Astro-particle physics * Ultracold neutrons * Lepton flavor * Nuclear physics * Workshop on Precision Measurements at Low Energy Future Particle Physics Research at PSI 18.–19.01.2007 at the Paul Scherrer Institut, Villigen, Switzerland Review speakers D. Dubbers, Heidelberg W. Henning, Darmstadt G. Hermann, Heidelberg K. Jungmann, Groningen Y. Kuno, Osaka H. Rauch, Wien S. Paul, München L. Roberts, Boston S. Schönert, Heidelberg N. Severijns, Leuven C. Weinheimer, Münster Organizing committee H. Gäggeler, Bern & PSI R. Eichler, PSI & ETHZ A. Rubbia, ETHZ K. Kirch, PSI A. van Loon, PSI Information: ltp.web.psi.ch Registration: anita.vanloon@psi.ch Poster presentation Poster contributions are highly welcome and will be a central part of the meeting. We call for presentation of new ideas and projects in astro-particle, ultracold neutron, lepton flavor and nuclear physics as well as concerning new accelerators and high power target stations. Deadline for submissions is December 20th, 2006.

55. Thomas Schietinger PSI, 4 July 2007 Measuring the muon EDM at PSI 55 Current status of the project ● Poster presentation at PSI workshop was met with enthusiasm: – C. Petitjean: “the highlight of the workshop” – K. Jungmann: “for just 0.25% of its annual budget, PSI could have a profound impact on muon physics” ● Strong interest to participate from Boston University (Lee Roberts) and Groningen (Gerco Onderwater) “once the project gets going”. ● Paper on compact storage ring design is in preparation. ● Next steps: – Look for interested parties, with emphasis on Swiss Universities! ● Zurich interested in designing a detector (U. Straumann) – The lead must come from outside institutes (PSI alone does not have the resources to drive this project!) – With a larger proto-collaboration, can envisage writing a letter of intent for the next PSI user meeting (early 2008).

56. ...about µEDM at PSI!... #1: It allows you to push a fundamental parameter by four orders of magnitude!...wow! #17: It will establish a completely new method, which ultimately has the potential to probe down to 10 –26 e cm. #25: It makes optimal use of existing facilities at PSI. #38: It ensures that PSI remains a key player in fundamental muon physics. #53: It attracts a large fraction of the g–2 com-munity to PSI (Brookhaven, Groningen, etc.). #69: It gives you the chance to build a muon storage ring (not many labs have one!). #80: It offers attractive opportunities to utilize the latest detector technologies. #94: It lets you gain expertise in reson- ance injection into small storage rings. (ask us about the other 92 reasons!)

57. Thomas Schietinger PSI, 4 July 2007 Measuring the muon EDM at PSI 57 #43: It is the natural continuation of the hugely successful muon g–2 experiments #60: Experience in storing muons is relevant for future big muon projects (neutrino factory, muon collider) #85: It continues the great tradition of muon experiments at PSI. #3: It will be so much fun. #27: It represents in interesting challenge for power supply systems. OK, here are five more: