Klaus P. Jungmann, Kernfysisch Versneller Instituut, Groningen, NL

2. A Tutorial on the g-2 Measurement of the Muon Klaus P. Jungmann, Kernfysisch Versneller Instituut, Groningen, NL on behalf of the muon g-2 collaboration 3rd Joint NIPNET ION-CATCHER HITRAP Collaboration Meeting:  2-6 June, 2004, Krakow, Poland Fundamental Laws Quantities Magnetic Moments Standard Model Precision Experiment Fundamental Constants Related Experiments Interpretation

4. Vernon Hughes 1921-2003

5. What means>>fundamental<< ? • Physicists in general: have always a tendency to put their own activities as fundamental  renormalization of meaning • Albert Einstein : >> I would like to know how God has made the world. I am not interested in one or another phenomenon, not in the spectrum of one or another element. I would like to know His Thoughts, everything else are just details.<<  recalls literal meaning, i.e. basic, not deducible law

6. Gravitation Gravitation Electro - Electro - Magnetism Magnetism Magnetism Magnetism Maxwell Electricity Electricity ? ? Physics within the Standard Model Glashow, Salam, t'Hooft, Veltman,Weinberg Weak Weak Electro - Weak Electro - Weak Standard Model Standard Model Strong Strong Grand Grant Unification Unification not yet known? not yet known? Fundamental Interactions – Standard Model Physics outside Standard Model Searches for New Physics

7. TRImP Low Energies & Precision Measurement High Energies & direct observations Possibilities to Test New Models 

9. Magnetic Moment r r e h m s = g L=1h re=a0 2 mc e- ve= ac * Dirac: g = 2 for spin ½ particles * Baryon Octet: ¹ Û g 2 inner structure magnetic momentM = area * current = p a02 * e*ve/(2p a0) = e h / (2 e m c) = “magneton” Bohr Magneton for electrons r e h r ( ) m proton : g 2 = * s > 2 2 . 79 p p 2 m c N r e h r ( ) m ¹ = * - s g 0 neutron: 2 1 . 91 n n 2 m c N * Leptons: ¹ Û g 2 interaction with virtual fields , e.g. QED ... electro n 2 2 - a a a g 2 1 æ ö æ ö muon = = + + + a a a ... ç ÷ ç ÷ 2 3 p p p è ø è ø 2 2 tauon

10. QED - Contributions: am(QED) = 116 584 705.6(2.9) * 10-11(Kinoshita 2000) Weak Interaction Corrections: m m m m m m Dam(weak) = 151(4) * 10-11(Kutho 1992, Degrassi 1998)

11. QED - Contributions: am(QED) = 116 584 705.6(2.9) * 10-11(Kinoshita 2000) Weak Interaction Corrections: m m m m m m Dam(weak) = 151(4) * 10-11(Kutho 1992, Degrassi 1998)

14. The bound state introduces : • the me/Mnucleus mass ratio • the expansion parameter Za Slides taken from T. Beier, GSI

15. The new measurement of the muon magnetic anomaly • at the Brookhaven National Laboratory aims for • 0.35 ppm relative accuracy. • Why? • We have in the listing of fundamental physical constants: • electron magnetic anomaly • 1.159 652 186 9(41) 10 -3 (0.0035 ppm) • muon magnetic anomaly • 1.165 916 02(64) x 10-3(0.55 ppm) Sensitivity to heavier objects larger by (mm/me)2 40 000

18. ! ! Hadronic Corrections for gm-2 Dam(hadr.,1st order) = 6951(75)*10-11 (Davier, 1998) Dam(hadr., higherorder) = -101(6) *10-11 (Krause, 1996) Dam(hadr., light on light) = -79(15) *10-11 (Hayakawa, 1998) Situation Spring 2001

19. Early “Shopping List”

26. The fixed probes 4 ppm Proton NMR

27. Trolley NMR Probes NMR Trolley Fixed NMR Probes Electrostatic Quadrupole Electrodes Trolley Rails Vacuum Vessel

30. 900 000 000 positrons with E > 2GeV in 1999

32. Fourier Spectra for different Run Conditions m- @BNL

34. Systematic Uncertainties, Results Magnetic Field • wp,0 spherical probe 0.05 ppm • wp(R,ti) 17 trolley probes 0.09 ppm • wp(R,t) 150 fixed probes 0.07 ppm • wp(R) trolley measurement 0.05 ppm • < wp> muon distribution 0.03 ppm • wp (RI) others 0.10 ppm total systematic uncertainty dwp=0.17ppm Spin Precession • Pileup 0.08 ppm • Lost muons 0.09 ppm • Coherent Betatron Oscillations 0.07 ppm • Gain Instability 0.12 ppm • others 0.11 ppm total systematic uncertainty dwa,sy = 0.21 ppm total statistical uncertainty dwa,st = 0.6 ppm wp/2p = 61 791 400 (11) Hz wa/2p = 229 073.59(15)(5) Hz

35. Theory: * need a for muon ! * hadronic and weak corrections *various experimental sources of a<better 100ppb>need constants at very moderate *a no concern for (g-2)maccuracy wa wammc Experiment: wp = am = mm wa emB - wp mp * wa and B (wp) measured in (g-2)m experiment <better 0.35 and 0.1 ppm> * c is a defined quantity <“infinite” accuracy> *mm (mm) is measured in muonium spectroscopy (hfs) <better 120 ppb> NEW 1999 *em is measured in muonium spectroscopy (1s -2s) <better 1.2 ppb> NEW 1999 *mp in water known >> probe shape dependence<< <better 26 ppb> *m3He to mp in water >> gas has no shape effect << <better 4.5 ppb> being improved

36. m g-2 hadronic contribution weak contribution New Physics QED QED h mm, a, gm mm m+e- DnHFS, n=1 m+e- Dn1S-2S QED mm mm a QED corrections weak contribution mm QED corrections

37. Muonium Hyperfine Structure Yale - Heidelberg - Los Alamos Solenoid Dnexp = 4 463 302 765(53) Hz ( 12 ppb) Dntheo = 4 463 302 649(520)(34)(<100) Hz(<120 ppb) mm /mp = 3.183 345 13(39) (120 ppb) mm/me = 206.768 273(24) (120 ppb) a-1= 137.036 010 8(5 2)( 39 ppb) Sm m+ e- Detector m+in MW-Resonator W. Liu et al. Phys. Rev. Lett. 82, 711 (1999)

38. Muonium 1S-2S Experiment Heidelberg - Oxford - Rutherford - Sussex - Siberia - Yale m++ e-+ Ekin 0 -.25 Rm 2S 244 nm Energy exp Dn 1s-2s = 2455 528 941.0(9.1)(3.7) MHz Dn 1s-2s = 2455 528 935.4(1.4) MHz mm+= 206.768 38 (17) me qm+= [ -1 -1.1 (2.1) 10-9 ] qe- 244 nm theo -Rm 1S m+ Detection m+ Laser Mirror m+e- Target Diagnostics m+in V.Meyer et al., Phys.Rev.Lett. 84, 1136 (2000)

39. Final results from Experiment E821 @BNL

40. ! ! Hadronic Corrections for gm-2 Dam(hadr.,1st order) = 6951(75)*10-11 (Davier, 1998) Dam(hadr., higherorder) = -101(6) *10-11 (Krause, 1996) Dam(hadr., light on light) = -79(15) *10-11 (Hayakawa, 1998)

43. Final results from Experiment E821 @BNL Newest Theory Offer: 2.4 SD from Experiment

45. Note:Even if there will be a difference between muon g-2 and theory established and unquestioned, it does not carry a tag about the nature of the difference! We will need further experiments then to learn more! Such as: - searches for rare muon decays - search for a muon edm - ..............................

46. m eg appears in composite models if Dam as suggested

47. ~ Muon Magnetic Anomaly in Super Symmetric Models Z k ~ ~ m m m m k k g g • no constraints from dark matter • constraint through dark matter ~ ~ w w + + - - m m ~ n • At, m0 vary over • parameter space • m0 < 1TeV/c2 approximate rule : DamSUSY» 1.4 * 10-9 * [ (100 GeV/c2) /mg ]2* tan b ~ goal BNL 821: am to 0.4 * 10-9 after: U. Chattopadyay and P. Nath, 1995

48. Lepton Magnetic Anomalies in CPT and Lorentz Non - Invariant Models | | - m m - 0 0 18 CPT tests K K = £ r 10 K m 0 K - - | g g | | a a | - + - + - - 3 12 e e e e = = × × £ × r 1.2 10 2 10 e g a avg avg ? ? Are they comparable - Which one is appropriate • often quoted: • K0- K0 mass difference (10-18) • e- - e+ g- factors (2* 10-12) • We need an interaction • with a finite strength! Use common ground, e.g. energies Þ generic CPT and Lorentz violating DIRAC equation 1 n μ μ μ μν μ μ ν ψ - - - - + + = (i γ D m a γ b γ γ H σ ic γ D id γ γ D ) 0 μ μ μ 5 μν μν μν 5 2 º ¶ - iD i qA m μ μ a , b break CPT a , b , c , d , H break Lorentz Invariance μ μ μ μ μν μν μν Leptons in External Magnetic Field - + l l l = - » - Δω ω ω 4b a a a 3 - + l l - | E E | Δω h spin up spin down a = » r l - 2 l m c E l spin up 57 Bluhm , Kostelecky, Russell, Phys. Rev. D ,3932 (1998) For g - 2 Experiments : - | a a | ω h = × c - + l l r l 2 a m c avg l Dehmelt, Mittleman,Van Dyck, Schwinberg, hep - ph/9906262 Þ - - 21 24 £ × £ × r 1.2 10 r 3.5 10 electron muon μ e : : CPT– Violation Lorentz Invariance Violation • What is best CPT test ? • New Ansatz (Kostelecky) • K0  10-18 GeV/c2 • n  10-30 GeV/c2 • p  10-24 GeV/c2 • e 10-27 GeV/c2 • m 10-23GeV/c2 • Future: • Anti hydrogen 10-18 GeV/c2

50. CPT and Lorentz Invariance from Muon Experiments Muonium: new interaction below 2* 10-23 GeV Muon g-2: new interaction below 4* 10-22 GeV (CERN) 15 times better expected from BNL V.W. Hughes et al., Phys.Rev. Lett. 87, 111804 (2001)