Lifetime and Dipole Moments

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1 Precision Measurements with the Muon: Lifetime and Dipole Moments B.L. Roberts Department of Physics Boston University B. Lee Roberts, Workshop on Precision Measurements at Low Energy- PSI - 19 January p. 1/44

2 Outline Introduction to the muon Selected weak interaction parameters Magnetic and electric dipole moments Summary and conclusions. B. Lee Roberts, Workshop on Precision Measurements at Low Energy- PSI - 19 January p. 2/44

3 The Muon: Discovered in 1936 Discovered in cosmic rays by Seth Neddermeyer and Carl Anderson B. Lee Roberts, Workshop on Precision Measurements at Low Energy- PSI - 19 January p. 3/44

4 Confirmed by: Street & Stevenson, Nishina, Tekeuchi & Ichimiya B. Lee Roberts, Workshop on Precision Measurements at Low Energy- PSI - 19 January p. 4/44

5 The Muon Lifetime A precise measurement of τ + leads to a precise determination of the Fermi constantg F B. Lee Roberts, Workshop on Precision Measurements at Low Energy- PSI - 19 January p. 5/44

contribution, plus radiative corrections (including

6 Muon decay gives us unique access to the electroweak scale The V-A theory factorizes into a pure weak contribution, plus radiative corrections (including hadronic). The muon decays only via the weak interaction

7 The Fermi constant is an implicit input to all precision electroweak studies Contains all weak interaction loop corrections. ν µ e.g.mass limits for Higgs Search + W ± t ν e b W ± e +

τ helped predict the mass of the top quark, today, part of the Electroweak working group fits Predicted Input: G F (17 ppm), α (4 ppb at q 2 =0), αm Z (23 ppm), from G F Measured: The Lan experiment

8 τ helped predict the mass of the top quark, today, part of the Electroweak working group fits Predicted Input: G F (17 ppm), α (4 ppb at q 2 =0), αm Z (23 ppm), from G F Measured: The Lan experiment at PSI will accumulate > decays G to ~1 ppm. If LHC provides a Higgs Mass, then the precision of the confrontation with the SM will greatly improve B. Lee Roberts, Workshop on Precision Measurements at Low Energy- PSI - 19 January p. 8/44

9 MuLan has a new ~13 ppm τ measurement Will be officially announced soon MuLan: Dec 2006 Unblinding mulan NEW ~1 ppm result to follow from 2006, and also from the 2007 run B. Lee Roberts, Workshop on Precision Measurements at Low Energy- PSI - 19 January p. 9/44

10 What have we learn from the s death? (Much of it here at PSI) The strength of the weak interaction i.e. the Fermi constant G F (more properly G ) The fundamental nature of the weak interaction i.e. is it scalar, vector, tensor, etc.? Lepton flavor conservation in -decay VEV of the Higgs field: Induced form-factors in nuclear -capture new mucap result! Future Lifetime measurement? The radiative corrections can support another order of magnitude on τ, (beyond mulan) but that would go way beyond the precision of the other electroweak parameters. B. Lee Roberts, Workshop on Precision Measurements at Low Energy- PSI - 19 January p. 10/44

11 Magnetic and Electric Dipole Moments B. Lee Roberts, Workshop on Precision Measurements at Low Energy- PSI - 19 January p. 11/44

12 Magnetic and Electric Dipole Moments B. Lee Roberts, Workshop on Precision Measurements at Low Energy- PSI - 19 January p. 12/44

13 Electric and Magnetic Dipole Moments: ie Γ = ef ψ γψ + F ψσ q ψ 2m ν 1 R R 2 R ν L Muon Magnetic Dipole Momoment a chiral changing Muon EDM B. Lee Roberts, Workshop on Precision Measurements at Low Energy- PSI - 19 January p. 13/44

14 An aside: General Dipole Operator Marciano has introduced the dipole operator with B. Lee Roberts, Workshop on Precision Measurements at Low Energy- PSI - 19 January p. 14/44

15 Muon Magnetic Dipole Moment B. Lee Roberts, Workshop on Precision Measurements at Low Energy- PSI - 19 January p. 15/44

Foley, Schwinger, Kusch-Foley 1947 c 2( α ) 2 + +.. π γ e γ e + γ e vrs.

16 It s convenient to write the magnetic moment as a sum of two pieces: Dirac + Pauli moment Radiative corrections contribute to a for leptons γ Dirac Dirac Stern-Gerlach γ g = 2 + α π γ Kusch Schwinger and Foley, Schwinger, Kusch-Foley 1947 c 2( α ) π γ e γ e + γ e vrs. : relative contribution of heavier things B. Lee Roberts, Workshop on Precision Measurements at Low Energy- PSI - 19 January p. 16/44

The SM Value for the muon anomaly (10-10 ) *Hagiwara, et al., hep-ph/0611102, Davier et al., hep-ph/0701163.

17 The SM Value for the muon anomaly (10-10 ) *Hagiwara, et al., hep-ph/ , Davier et al., hep-ph/ see hep-ph/ B. Lee Roberts, Workshop on Precision Measurements at Low Energy- PSI - 19 January p. 17/44

18 Since a represents a sum over all physics, it is sensitive to a wide range of potential new physics B. L. Roberts, Workshop on Precision Measurements at Low Energy- PSI - 19 January p. 18/56

19 Since a represents a sum over all physics, it is sensitive to a wide range of potential new physics muon substructure anomalous couplings γ Triple Gauge Vertex W W g = 2? W ν W boson substructure? B. L. Roberts, Workshop on Precision Measurements at Low Energy- PSI - 19 January p. 19/56

20 Since a represents a sum over all physics, it is sensitive to a wide range of potential new physics muon substructure anomalous couplings SUSY (with large tanβ ) ν χ χ + γ χ 0 γ many other things (extra dimensions, etc.) B. L. Roberts, Workshop on Precision Measurements at Low Energy- PSI - 19 January p. 20/56

Since a represents a sum over all physics, it is sensitive to a wide range of potential new physics muon substructure anomalous couplings SUSY (with

21 Since a represents a sum over all physics, it is sensitive to a wide range of potential new physics muon substructure anomalous couplings SUSY (with large tanβ ) many other things (extra dimensions, etc.) B. L. Roberts, Workshop on Precision Measurements at Low Energy- PSI - 19 January p. 21/56

22 Lowest Order Hadronic from e + e - annihilation B. Lee Roberts, Workshop on Precision Measurements at Low Energy- PSI - 19 January p. 22/44

23 We measure the difference frequency between the spin and momentum precession With an electric quadrupole field for vertical focusing 0 B. Lee Roberts, Workshop on Precision Measurements at Low Energy- PSI - 19 January p. 23/44

24 Experimental Technique (from AGS) Protons Target Pions p=3.1gev/c Muon polarization Muon storage ring injection & kicking focus by Electric Quadrupoles 24 electron calorimeters π ν Inflector B v Injection orbit Central orbit Storage Kicker ring Modules R=711.2cm d=9cm (1.45T) x ~ c = 77 mm β ~ = 10 mrad B dl ~ = 0.1 Tm β R R Electric Quadrupoles B. Lee Roberts, Workshop on Precision Measurements at Low Energy- PSI - 19 January p. 24/44 x c

25 muon (g-2) storage ring Muon lifetime t = 64.4 s (g-2) period t a = 4.37 s Cyclotron period t C = 149 ns B. Lee Roberts, Workshop on Precision Measurements at Low Energy- PSI - 19 January p. 25/44

26 The ± 1 ppm uniformity in the average field is obtained with special shimming tools. inner coilthermal insulation We can shim the dipole, quadrupole sextupole independently wedge dipole correction coil pole piece pole bump beam region programmable current sheet fixed NMR probes outer coils YOKE inner coil g 2 Magnet in Cross Section ρ = 7112 mm B. Lee Roberts, Workshop on Precision Measurements at Low Energy- PSI - 19 January p. 26/44

27 The ± 1 ppm uniformity in the average field is obtained with special shimming tools. 0.5 ppm contours B. Lee Roberts, Workshop on Precision Measurements at Low Energy- PSI - 19 January p. 27/44

28 We count high-energy electrons as a function of time. B. Lee Roberts, Workshop on Precision Measurements at Low Energy- PSI - 19 January p. 28/44

29 In 1983, just before we started our experiment, theory and experiment were known to about 10 ppm. Theory uncertainty was ~ 9 ppm (10 ppm) (9.4 ppm) CERN ~1983 CERN + Experimental uncertainty was 7.3 ppm Theory a X B. Lee Roberts, Workshop on Precision Measurements at Low Energy- PSI - 19 January p. 29/44

30 E821 achieved 0.5 ppm and the e + e - based theory is also at the 0.6 ppm level. Both can be improved. (9.4 ppm) CERN (10 ppm) CERN (13 ppm) E821 (97) + (5 ppm) E821 (98) + (1.3 ppm) E821 (99) + (0.7 ppm) E821 (00) + (0.7 ppm) E821 (01) World Average + HMNT = Hagiwara, et. al., hep-ph HNMT 2006 e + e a X B. Lee Roberts, Workshop on Precision Measurements at Low Energy- PSI - 19 January p. 30/44

31 Difference with the standard model is 3.4 σ see J. Miller, E. de Rafael and L. Roberts, hep-ph/ B. Lee Roberts, Workshop on Precision Measurements at Low Energy- PSI - 19 January p. 31/44

32 If the electroweak contribution is left out of the standard-model value, we get a 5.1 σ difference. Even if you believe that there is no discrepancy between E821 and the standard model, without the EW contribution there is a significant difference. Now if you will permit me a flight of fancy... B. Lee Roberts, Workshop on Precision Measurements at Low Energy- PSI - 19 January p. 32/44

33 It s amusing to note that if we assume that SUSY is the source of the (g-2) difference, it forms a consistent picture with other constraints on the SUSY LSP (lightest supersymmetric partner) being the dark matter candidate. 800 tan β = 10, > 0 m 0 (GeV) scalar mass m χ ± = 104 GeV g-2 ± 1σ ± 2σ m h = 114 GeV gaugino mass WMAP restrictions m 1/2 (GeV) Historically muon (g-2) has played an important role in restricting models of new physics. CMSSM calculation Following Ellis, Olive, Santoso, Spanos, Phys. Rev. D 71, (2005) (provided by K. Olive 3/07) B. Lee Roberts, Workshop on Precision Measurements at Low Energy- PSI - 19 January p. 33/44

34 To continue this flight of fancy for a moment If SUSY exists, the sleptons will mix, and there is a connection between a, D, e ~ e ~ e ~ e B B ~ ~ MDM, EDM ~ ~ B. Lee Roberts, Workshop on Precision Measurements at Low Energy- PSI - 19 January p. 34/44

Electric Dipole Moments E.M. Purcell and N.F.

35 Electric Dipole Moments E.M. Purcell and N.F. Ramsey, Phys. Rev. 78 (1950) The argument against electric dipole moments, in another form, raises directly the question of parity. B. Lee Roberts, Workshop on Precision Measurements at Low Energy- PSI - 19 January p. 35/44

36 Transformation Properties of Electric and Magnetic Dipole Moments An EDM implies both P and T are violated. Assuming CPT symmetry, an EDM at a measureable level would imply non-standard model CP. B. Lee Roberts, Workshop on Precision Measurements at Low Energy- PSI - 19 January p. 36/44

37 B. Lee Roberts, Workshop on Precision Measurements at Low Energy- PSI - 19 January p. 37/44

38 e EDM (e.cm) Hg n Multi Higgs Left - Right MSSM φ ~ 1 MSSM φ ~ α/π Excluded region (Tl atomic beam) Commins (2002) d e < 1.6 x e.cm E. Hinds e-edm experiment at Imperial College with YbF molecules is starting to explore this region Standard Model with thanks to Ed Hinds B. Lee Roberts, Workshop on Precision Measurements at Low Energy- PSI - 19 January p. 38/44

39 Muon EDM: Naïve scaling would imply that but in some models the dependence is greater. B. Lee Roberts, Workshop on Precision Measurements at Low Energy- PSI - 19 January p. 39/44

40 Muon EDM Limits: CERN3 and BNL B. Lee Roberts, Workshop on Precision Measurements at Low Energy- PSI - 19 January p. 40/44

a implications for the muon EDM Feng et al. Old E821 bounds 3(1) X 10 9 + + 2 σ 1 σ B.

41 a implications for the muon EDM Feng et al. Old E821 bounds 3(1) X σ 1 σ B. Lee Roberts, Workshop on Precision Measurements at Low Energy- PSI - 19 January p. 41/44

42 Spin Frequencies: in B field with MDM & EDM 0 spin difference frequency = ω s - ω c B. Lee Roberts, Workshop on Precision Measurements at Low Energy- PSI - 19 January p. 42/44

43 Spin Frequencies: in B field with MDM & EDM 0 spin difference frequency = ω s - ω c B. Lee Roberts, Workshop on Precision Measurements at Low Energy- PSI - 19 January p. 43/44

44 Spin Frequencies: in B field with MDM & EDM 0 The motional E - field, β X B, is much stronger than laboratory electric fields (~GV/m). (not ω a B ω η B. Lee Roberts, Workshop on Precision Measurements at Low Energy- PSI - 19 January p. 44/44 ω β x B

45 Dedicated EDM Experiment 0 Use a radial E-field to turn off the ω a precession With ω a = 0, the EDM causes the spin to steadily precess out of the plane. ω η B. Lee Roberts, Workshop on Precision Measurements at Low Energy- PSI - 19 January p. 45/44

46 since ω 2 = ω a2 + ω η2, the Δ SM could be an EDM what value EDM would this correspond to? obviously this would be exciting. See: Feng, et al., Nucl. Phys. B 613 (2001) 366 The present limits are: SM value < *preliminary B. Lee Roberts, Workshop on Precision Measurements at Low Energy- PSI - 19 January p. 46/44

47 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 To prove the spin is frozen E v E + + θ + 2θ B B 0 (a) 1 Time [arb.] 2 B. Lee Roberts, Workshop on Precision Measurements at Low Energy- PSI - 19 January p. 47/44

See the Poster: Search for a -EDM A. Adelmann 1, K. Kirch 1, C.J.G. Onderwater 2, T. Schietinger 1, A. Streun 1 hep-ex/0606034 B = 1 T p = 125 MeV/c β = 0.

48 See the Poster: Search for a -EDM A. Adelmann 1, K. Kirch 1, C.J.G. Onderwater 2, T. Schietinger 1, A. Streun 1 hep-ex/ B = 1 T p = 125 MeV/c β = 0.77, γ = 1.57 P 0.9 In 1 year of PSI E = 0.64 MV/m R = 0.35 m B. Lee Roberts, Workshop on Precision Measurements at Low Energy- PSI - 19 January p. 48/44

49 The storage ring is modest in size Injection studies look promising. B. Lee Roberts, Workshop on Precision Measurements at Low Energy- PSI - 19 January p. 49/44

50 Summary and Outlook A dedicated m-edm experiment could be developed here at PSI that could reach interesting sensitivity. This would provide a unique opportunity for PSI to contribute to the worldwide effort in precision physics. The muon has provided us with much knowledge on how nature works, and there is plenty of room for future surprises. Muon (g-2), with a precision of 0.5 ppm, has a 3.4 σ discrepancy with the standard model using e + e - data for the hadronic contribution. This new physics would show up in an EDM and perhaps LFV as well. B. Lee Roberts, Workshop on Precision Measurements at Low Energy- PSI - 19 January p. 50/44

51 THE END B. Lee Roberts, Workshop on Precision Measurements at Low Energy- PSI - 19 January p. 51/44

52 Present EDM Limits Particle Present EDM limit (e-cm) SM value (e-cm) n 3 x (90%CL) to e x (90%CL) < < Hg 2.1 x (95%CL) *not yet final B. Lee Roberts, Workshop on Precision Measurements at Low Energy- PSI - 19 January p. 53/44

(Lifetime and) Dipole Moments

Precision Measurements with the Muon: (Lifetime and) Dipole Moments B.L. Roberts Department of Physics Boston University roberts @bu.edu http://physics.bu.edu/roberts.html B. Lee Roberts, APPEAL07, CAST,