Klaus P. Jungmann, Kernfysisch Versneller Instituut, Groningen, NL on behalf of the muon g-2 collaboration 3 rd 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

Vernon Hughes

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

Fundamental Interactions – Standard Model Physics outside Standard Model Searches for New Physics Physics within the Standard Model

TRI  P Possibilities to Test New Models  Low Energies & Precision Measurement High Energies & direct observations

Magnetic Moment * Dirac: g = 2 forspin ½ particles * Baryon Octet: g  2  inner structure proton :g p > 2 neutron: g n  0 * Leptons: g  2  interaction with virtual fields, e.g. QED... electron muon tauon     mc e g 2       cm e. N p       n cm e N                         aa g a r e =a 0 e-e- v e =  c L=1  magnetic moment M = area * current = area * current =  a 0 2 * e*v e /(2  a 0 ) =  a 0 2 * e*v e /(2  a 0 ) = e  / (2 e m c) = e  / (2 e m c) = “magneton” = “magneton” Bohr Magneton for electrons

QED - Contributions: Weak Interaction Corrections: a  (QED) = (2.9) * (Kinoshita 2000)  a  (weak) = 151(4) * (Kutho 1992, Degrassi 1998) 

QED - Contributions: Weak Interaction Corrections: a  (QED) = (2.9) * (Kinoshita 2000)  a  (weak) = 151(4) * (Kutho 1992, Degrassi 1998) 

Slides taken from T. Beier, GSI The bound state introduces : the m e /M nucleus mass ratio the expansion parameter Z 

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 (41) ( ppm) muon magnetic anomaly (64) x (0.55 ppm) Sensitivity to heavier objects larger by (m  /m e ) 2 

Hadronic Corrections for g  -2  a   hadr.,1 st order) = 6951(75)  (Davier, 1998)  a   hadr., higher order) = -101(6)  (Krause, 1996)  a   hadr., light on light) = -79(15)  (Hayakawa, 1998) !! Situation Spring 2001

Early “Shopping List”

The fixed probes 4 ppm Proton NMR

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

positrons with E > 2GeV in 1999

Fourier Spectra for different Run Conditions 

Systematic Uncertainties, Results Magnetic Field  p,0 spherical probe 0.05 ppm  p (R,t i ) 17 trolley probes 0.09 ppm  p (R,t) 150 fixed probes 0.07 ppm  p (R) trolley measurement 0.05 ppm <  p  muon distribution 0.03 ppm   p (R I ) others 0.10 ppm total systematic uncertainty  p =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  a,sy = 0.21 ppm total statistical uncertainty  a,st = 0.6 ppm  p /2  = (11) Hz  a /2  = (15)(5) Hz

a  = a m ca m c e  B = aa pp aa pp  pp - Experiment: Theory: * need  for muon ! * hadronic and weak corrections * various experimental sources of  better 100ppb>  need constants at very moderate *  no concern for (g-2)  accuracy *  a and B (  p ) measured in (g-2)  experiment * c is a defined quantity * m  (   ) is measured in muonium spectroscopy (hfs) NEW 1999 * e  is measured in muonium spectroscopy (1s -2s) NEW 1999 *  p in water known >> probe shape dependence *  3He to  p in water >> gas has no shape effect being improved

QED mm  g-2 hadronic contribution weak contribution New Physics  + e -  HFS, n=1  QED corrections weak contribution  + e -  1S-2S m  QED corrections QED mm  , , g  h

Muonium Hyperfine Structure Solenoid   e    in SS Detector MW-Resonator Yale - Heidelberg - Los Alamos  exp = (53) Hz ( 12 ppb)  theo = (520)(34)(<100) Hz(<120 ppb)    p = (39) (120 ppb) m   m e = (24) (120 ppb)   = (5 2) ( 39 ppb) W. Liu et al. Phys. Rev. Lett. 82, 711 (1999)

Muonium 1S-2S Experiment Laser Diagnostics   Detection -.25 R  1S 2S 244 nm Energy -R  0    e   kin   in  ee Target Mirror Heidelberg - Oxford - Rutherford - Sussex - Siberia - Yale  1s-2s = (9.1)(3.7) MHz  1s-2s = (1.4) MHz m    = (17) m e q     = [ (2.1) ] q e- exp theo V.Meyer et al., Phys.Rev.Lett. 84, 1136 (2000)

Final results from Experiment

Hadronic Corrections for g  -2  a   hadr.,1 st order) = 6951(75)  (Davier, 1998)  a   hadr., higher order) = -101(6)  (Krause, 1996)  a   hadr., light on light) = -79(15)  (Hayakawa, 1998) !!

Final results from Experiment Newest Theory Offer: 2.4 SD from Experiment

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

 e  appears in composite models if  a  as suggested

Muon Magnetic Anomaly in Super Symmetric Models approximate rule :  a  SUSY  1.4    [ (100 GeV/c 2 ) /m g ] 2  tan  goal BNL 821: a  to 0.4   after: U. Chattopadyay and P. Nath, 1995 A t, m 0 vary over parameter space m 0 < 1TeV/c 2 no constraints from dark matter constraint through dark matter     w    w           k ~   k   k ~

? m mm r 0 00 K KK || K     avg a | e a e a| avg g | e g e g| e r             CPTbreakb,a μμ Invariance LorentzbreakH,d,c,b,a μν μμ ? Lepton Magnetic Anomalies in CPT and Lorentz Non-Invariant Models CPT tests Are they comparable- Which one is appropriate  Use common ground, e.g. energies Leptons in External Magnetic Field Bluhm, Kostelecky, Russell, Phys.Rev. D 57,3932 (1998) For g-2 Experiments : Dehmelt, Mittleman,Van Dyck, Schwinberg, hep-ph/ μμ qAiiD 0D μ γ 5 γ μν id ν D μ γ μν ic μν σ H 2 1 μ γ 5 γ μ b μ γ μ am μ D μ (iγ equation DIRAC violating Lorentz and CPT generic    ψ ) 2 c l m a Δω l upspin E | l downspin E l upspin E| l r l 3 4b l a ω l a ω a Δω             avg ll 2 l c l a |aa| cm ω r     μ r e r      :: muonelectron CPT CPT – Violation Lorentz Invariance Violation What is best CPT test ? New Ansatz (Kostelecky) K 0  GeV/c 2 n  GeV/c 2 p  GeV/c 2 e  GeV/c 2   GeV/c 2 Future: Anti hydrogen  GeV/c 2 often quoted: K 0 - K 0 mass difference ( ) e - - e + g- factors (2* ) We need an interaction with a finite strength !

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

Concept works also for (certain) nuclei; Deuteron particularly interesting Exploit huge motional electric fields for relativistic particles in high magnetic fields; observe spin rotation EDM closely related to non standard anomaly in many models!

Klaus P. Jungmann, Kernfysisch Versneller Instituut, Groningen, NL on behalf of the muon g-2 collaboration International Conference on Linear Colliders 04 : April "Le Carré des Sciences", Paris, France Standard Model Precision Experiment Fundamental Constants Related Experiments Interpretation How reliable is Theory ? What mean Speculations built on whishfull definition of Theory Value? What next in Experiment? - Just run again ? - Just run again ? - Is there more to it ? - Is there more to it ? What about Theory ? Are there other Experiments Neede to come further in Physics?

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 Any New Effort to improve significantly on the Muon Magnetic Anomaly will need better constants ! Where should they come from, if not from Muonium Spectroscopy ?

J-PARC is one Possibility There are others as well: as well: Neutrino Factory ? Neutrino Factory ? Muon Collider ? Muon Collider ? GSI ? GSI ? …. ….