Klaus P. Jungmann via B. Lee Roberts -FNAL Proton Driver Workshop – October 2004 Precision Measurements in Muon Physics A Sampler of Fundmental Measurements with Muonium Prepared by Klaus Jungmann Kernfysisch Versneller Instituut & Rijksuniversiteit Groningen and delivered by B. Lee Roberts Simple Atomic System Atomic Theory Fundamental Constants Fundamental Symmetries Search for New Physics Atomic Physics at Accelerators Precision Measurements … Condensed Matter Physics Chemistry Low energy Muon Beams Muonium (M)

Klaus P. Jungmann via B. Lee Roberts -FNAL Proton Driver Workshop – October 2004 What is it ? What is it good for ? test of electromagnetic bound state theory test of electromagnetic bound state theory fundamental constants fundamental constants tests of fundamental symmetries tests of fundamental symmetries search for New Physics search for New Physics tool for condensed matter research tool for condensed matter research …… …… “Muonium is the bound state of a positive Muon and an Electron” positive Muon and an Electron” “point-like” particles “point-like” particles no (severe) strong interaction effects no (severe) strong interaction effects calculable to required accuracy calculable to required accuracy Muonium (M)

Klaus P. Jungmann via B. Lee Roberts -FNAL Proton Driver Workshop – October 2004 hydrogen-like atom but no strong interaction

Klaus P. Jungmann via B. Lee Roberts -FNAL Proton Driver Workshop – October Theorists are confident that muonium HFS Can be calculated to 10 Hz, if needed (Eides, Pachucki,…)  magnetic moment  , 

Klaus P. Jungmann via B. Lee Roberts -FNAL Proton Driver Workshop – October 2004 Muonium Hyperfine Structure Solenoid   e    in SS Gated Detector MW-Resonator/Kr target Yale - Heidelberg - Los Alamos pulsed beam essential B scan freq. scan old M

Klaus P. Jungmann via B. Lee Roberts -FNAL Proton Driver Workshop – October 2004 Results from LAMPF Muonium HFS Experiment measured: 12 = (35) Hz( 18 ppb) 34 = (43) Hz( 17 ppb) from Breit-Rabi equation: 12    exp = (53) Hz( 12 ppb)  theo = (520)(34)(<100) Hz (<120 ppb)  12      p = (37) (120 ppb) alternatively derived: m   m e = (24)(120 ppb)    ppb)

Klaus P. Jungmann via B. Lee Roberts -FNAL Proton Driver Workshop – October 2004 muonium and hydrogen hfs → proton structure

Klaus P. Jungmann via B. Lee Roberts -FNAL Proton Driver Workshop – October 2004

? 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 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 ! What about Second Generation Leptons?

Klaus P. Jungmann via B. Lee Roberts -FNAL Proton Driver Workshop – October 2004 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)

Klaus P. Jungmann via B. Lee Roberts -FNAL Proton Driver Workshop – October 2004 Present Status of Muonium Ground State Hyperfine Structure No Experimental Activities known at this time Refinement of Theory going on Refinement of Theory going one.g.  Eides, Grotch, “Three-Loop Radiative-Recoil Corrections to Hyerfine Splitting in Muonium”, Phys.Rev.D67, (2003) in Muonium”, Phys.Rev.D67, (2003)  Eidelman, Karshenboim, Shelyuto, “ Hadronic Effects in Leptonic Systems: Muonim Hyperfine Structure and Anomalous Magnetic Moment of Muon”, Muonim Hyperfine Structure and Anomalous Magnetic Moment of Muon”, Can. J. Phys. 80, 1297 (2002) Can. J. Phys. 80, 1297 (2002) …. …. Exploitation of the Atom in Condensed Matter Science Exploitation of the Atom in Condensed Matter Sciencee.g.  Ivanter et al. “On the anomalous muonium hyperfine structure in silicon” J.Phys.: Condens. Matter 15, 7419 (2003) J.Phys.: Condens. Matter 15, 7419 (2003) …. ….

Klaus P. Jungmann via B. Lee Roberts -FNAL Proton Driver Workshop – October 2004 NEVIS CHICAGO-SREL LAMPF LAMPF latest experiment Quoted Uncertainty [kHz] Year History of Muonium Ground State Hyperfine Splitting Measurements

Klaus P. Jungmann via B. Lee Roberts -FNAL Proton Driver Workshop – October 2004 Future Possibilities for Muonium Ground State Hyperfine Structure LAMPF Experiment limited by STATISTICS  more MUONS needed  factor > 100 over LAMPF – pulsed > 5*10 8  + /s  factor > 100 over LAMPF – pulsed > 5*10 8  + /s below 28 MeV/c below 28 MeV/c  new ACCELERATORS  J-PARC ?  Neutrino Factory ?  Eurisol ?  GSI ?  FNAL  ……..

Klaus P. Jungmann via B. Lee Roberts -FNAL Proton Driver Workshop – October 2004 What other experiments besides the Ground State Hyperfine Structure are possible ? 1s → 2s transition

Klaus P. Jungmann via B. Lee Roberts -FNAL Proton Driver Workshop – October 2004

Muonium 1S-2S Experiment -.25 R  1S 2S 244 nm Energy -R  0    e   kin Laser Diagnostics   Detection   in  ee Target Mirror Heidelberg - Oxford - Rutherford - Sussex - Siberia - Yale

Klaus P. Jungmann via B. Lee Roberts -FNAL Proton Driver Workshop – October 2004

Muonium1s-2s At RAL

Klaus P. Jungmann via B. Lee Roberts -FNAL Proton Driver Workshop – October 2004

Results:  1s-2s = (9.1)(3.7) MHz  1s-2s = (1.4) MHz m    = (17) m e (0.8ppm) q     = [ (2.1) ] q e-  (2.2 ppb) exp theo

Klaus P. Jungmann via B. Lee Roberts -FNAL Proton Driver Workshop – October 2004 Future Possibilities for Muonium 1s-2s Interval RAL Experiment limited by STATISTICS RAL Experiment limited by STATISTICS  more MUONS needed  factor > 1000 over RAL – pulsed > 5*10 8  + /s below 28 MeV/c below 28 MeV/c  would enable cw laser spectroscopy ! (precision !)  new ACCELERATORS  J-PARC ?  Neutrino Factory ?  Eurisol ?  GSI ? .....

Klaus P. Jungmann via B. Lee Roberts -FNAL Proton Driver Workshop – October 2004 QED mm mm  , , g   g-2 hadronic contribution weak contribution New Physics  + e -  HFS, n=1   QED corrections weak contribution  + e -  1S-2S m  QED corrections

Klaus P. Jungmann via B. Lee Roberts -FNAL Proton Driver Workshop – October 2004 QED mm mm  , , g   + e -  HFS, n=1  QED corrections weak contribution  + e -  1S-2S m  QED corrections  g-2 hadronic contribution weak contribution New Physics

Klaus P. Jungmann via B. Lee Roberts -FNAL Proton Driver Workshop – October 2004 a  = a m ca m c e  B = aa pp aa pp  pp - Experiment: Fundamental Constants of Interest to g-2 Theory: * need  for muon ! * hadronic and weak corrections * various experimental sources of  better 100ppb>  need constants at very moderate *  no concern for (g-2)  even with recent corrections accuracy *  a and B (  p ) measured in (g-2)  experiment * c is a defined quantity * m  (   ) is measured in muonium spectroscopy (hfs) NEW 2000 * 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

Klaus P. Jungmann via B. Lee Roberts -FNAL Proton Driver Workshop – October 2004  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 ?

Klaus P. Jungmann via B. Lee Roberts -FNAL Proton Driver Workshop – October 2004 Muonium – Antimuonium Conversion up to Now Did first Search for Conversion Amato et al. Phys.Rev.Lett. 21, 1709 (1968) Predicted M-M Conversion Named System “Muonium” ?

Klaus P. Jungmann via B. Lee Roberts -FNAL Proton Driver Workshop – October 2004

Present Activities concerning Muonium – Antimuonium Conversion No Experimental Activities known at this time No Experimental Activities known at this time Theory is proposing lots of models Theory is proposing lots of modelse.g.  Clark, Love “Muonium-Antimuonium Oscillations and Massive Majorana Neutrinos”, hep-ph/ hep-ph/  Gusso, Pires, Pires, Rodrigues da Silva “Minimal Model, lepton Mixing and Muonium- Antimuonium Conversion”, hep-ph/ Muonium- Antimuonium Conversion”, hep-ph/  ….

Klaus P. Jungmann via B. Lee Roberts -FNAL Proton Driver Workshop – October 2004 Future Possibilities for Muonium – Antimuonium Searches PSI Experiment limited by STATISTICS  more MUONS needed  factor > 1000 over PSI – pulsed > 1*10 9  + /s  factor > 1000 over PSI – pulsed > 1*10 9  + /s below 28 MeV/c below 28 MeV/c  new ACCELERATORS  J-PARC ?  Neutrino Factory ?  Eurisol ?  GSI ?  FNAL .....

Klaus P. Jungmann via B. Lee Roberts -FNAL Proton Driver Workshop – October 2004 Old Muonium for Muonium-Antimuonium Conversion ? P(M)  sin 2 [const * (G MM /G F )*t]*exp[-  *t] Background  exp(- n  *t) ; n-fold coincidence detection For G MM << G F M gains over Background P(M) / Background  t 2 * exp[+(n-1)*  *t]  Pulsed ACCELERATOR

Klaus P. Jungmann via B. Lee Roberts -FNAL Proton Driver Workshop – October 2004

Summary Muonium has provided information on –QED –lepton flavor conservation –fundamental constants fine-structure constant  m  /m e   /  p – proton structure At a high-flux muon facility all of these could be improved.