1. 1    hadrons Part I : Lepton Magnetic Moments (cont.) Michel Davier Laboratoire de l’Accélérateur Linéaire, Orsay CERN Academic Training 13-15 June 2005 davier@lal.in2p3.fr

2. 2 Muon Magnetic Anomaly Schwinger 1948 QED Prediction: Computed up to 4 th order [Kinoshita et al.] (5 th order estimated)    QEDQED QEDHadronicWeakSUSY...... or other new physics ?

3. 3 Why Do We Need to Know it so Precisely? BNL (2004) Experimental progress on precision of (g –2)  Outperforms theory pre- cision on hadronic contribution

4. 4 The Muonic (g –2)  Contributions to the Standard Model (SM) Prediction: Source (a)(a) Reference QED ~ 0.3  10 –10 [Schwinger ’48 & others] Hadrons ~ (15  4)  10 –10 [Eidelman-Jegerlehner ’95 & others] Z, W exchange ~ 0.4  10 –10 [Czarnecki et al. ‘95 & others] The Situation 1995 ”Dispersion relation“    hadhad had ... Dominant uncertainty from lowest order hadronic piece. Cannot be calculated from QCD (“first principles”) – but: we can use experiment (!)

5. 5 Hadronic Vacuum Polarization Define: photon vacuum polarization function   (q 2 ) Ward identities: only vacuum polarization modifies electron charge with : Leptonic  lep (s) calculable in QED. However, quark loops are modified by long-distance hadronic physics, cannot (yet) be calculated within QCD Way out: Optical Theorem (unitarity)... Im[ ]  | hadrons | 2... and the subtracted dispersion relation of   (q 2 ) (analyticity) Bouchiat-Michel 1961 Cabibbo-Gatto 1960... and equivalently for a  [had]

6. 6 The R Data Situation (around 1995) Data density and quality unsatisfactory in some crucial energy regions

7. 7 Improved Determination of the Hadronic Contribution to (g –2)  and  (M Z )2 Energy [GeV]Input 1995Input after 1998 2m  - 1.8Data Data (e + e – &  ) + QCD 1.8 – J/  DataQCD J/  -  DataData + QCD  - 40 DataQCD 40 -  QCD Eidelman-Jegerlehner’95, Z.Phys. C67 (1995) 585 Improvement in 4 Steps: Inclusion of precise  data using SU(2) (CVC) Extended use of (dominantly) perturbative QCD Theoretical constraints from QCD sum rules and use of Adler function Alemany-Davier-Höcker’97, Narison’01, Trocóniz-Ynduráin’01, + later works Martin-Zeppenfeld’95, Davier-Höcker’97, Kühn-Steinhauser’98, Erler’98, + others Groote-Körner-Schilcher-Nasrallah’98, Davier-Höcker’98, Martin-Outhwaite- Ryskin’00, Cvetič-Lee-Schmidt’01, Jegerlehner et al’00, Dorokhov’04 + others Since then: Improved determi- nation of the dispersion integral: better data extended use of QCD Better data for the e + e –   +  – cross section CMD-2’02, KLOE’04

8. 8 The Role of  Data through CVC – SU(2) hadrons   W  e+e+ e –e – CVC: I =1 & V W: I =1 & V,A  : I =0,1 & V Hadronic physics factorizes in Spectral Functions : Isospin symmetry connects I=1 e + e – cross section to vector  spectral functions: branching fractions mass spectrum kinematic factor (PS) fundamental ingredient relating long distance (resonances) to short distance description (QCD)

9. 9 QCD Results from  Decays  s (M Z ) = 0.1209 ± 0.0018 (ALEPH’05, theory-dominated error)  s (M Z ) = 0.1183 ± 0.0027 (LEP’00, experiment-dominated error) Evolution of  s (m  ), measured using  decays, to M Z using RGE (4-loop QCD  -function & 3-loop quark flavor matching) shows the excellent compatibility of  result with EW fit: The precise tests with  spectral function show that perturbative QCD can be safely used in an average way above 1.8 GeV

10. 10  –   –  0  : Comparing ALEPH, CLEO, OPAL Good agreement observed between ALEPH and CLEO ALEPH more precise at low s CLEO better at high s Shape comparison only. SFs normalized to WA branching fraction (dominated by ALEPH).

11. 11 Testing CVC Infer  branching fractions from e + e – data: Difference: BR[  ] – BR[e + e – (CVC) ]: Mode  (  – e + e – ) „Sigma“  –   –  0  + 0.94 ± 0.322.9  –   – 3  0  – 0.08 ± 0.110.7  –  2  –  +  0  + 0.91 ± 0.253.6 leaving out CMD-2 : B  0 = (23.69  0.68) %  (7.4  2.9) % relative discrepancy! preliminary

12. 12 The Problem (revisited) Relative difference between  and e + e – data: zoom No correction for  ± –  0 mass (~ 2.3 ± 0.8 MeV) and width (~ 3 MeV) splitting applied Jegerlehner, hep-ph/0312372 Davier, hep-ex/0312064

13. 13 Evaluating the Dispersion Integral Better agreement between exclusive and inclusive (  2) data than in 1997- 1998 analyses Agreement bet- ween Data (BES) and pQCD (within correlated systematic errors) use QCD use data use QCD

14. 14 Results: the Compilation (including KLOE) Contributions to a  had [in 10 –10 ] from the different energy domains: ModesEnergy [GeV] e+e –e+e –  Low s expansion2m  – 0.558.0 ± 1.7 ± 1.2 rad 56.0 ± 1.6 ± 0.3 SU(2) [  +  – (DEHZ’03) ] 2m  – 1.8[ 450.2 ± 4.9 ± 1.6 rad ]464.0 ± 3.0 ± 2.3 SU(2)  +  – (incl. KLOE) 2m  – 1.8448.3 ± 4.1 ± 1.6 rad –  + – 20 + – 20 2m  – 1.816.8 ± 1.3 ± 0.2 rad 21.4 ± 1.3 ± 0.6 SU(2) 2  + 2  – 2m  – 1.814.2 ± 0.9 ± 0.2 rad 12.3 ± 1.0 ± 0.4 SU(2)  (782) 0.3 – 0.8138.0 ± 1.0 ± 0.3 rad –  (1020) 1.0 – 1.05535.7 ± 0.8 ± 0.2 rad – Other exclusive2m  – 1.824.0 ± 1.5 ± 0.3 rad – J / ,  (2S) 3.08 – 3.117.4 ± 0.4 ± 0.0 rad – R [QCD]1.8 – 3.733.9 ± 0.5 ± 0.0 rad – R [data]3.7 – 5.07.2 ± 0.3 ± 0.0 rad – R [QCD] 5.0 –  9.9 ± 0.2 theo – Sum (incl. KLOE) 2m  –  693.4 ± 5.3 ± 3.5 rad 711.0 ± 5.0 ± 0.8 rad ± 2.8 SU(2)

15. 15 Discussion The problem of the  +  – contribution : Experimental situation: new, precise KLOE results in approximate agreement with latest CMD-2 data  data without m (  ) and  (  ) corr. in strong disagreement with both data sets ALEPH, CLEO and OPAL  spectral functions in good agreement within errors Concerning the remaining line shape discrepancy (0.7- 0.9 GeV 2 ): SU(2) corrections: basic contributions identified and stable since long; overall correction applied to  is (– 2.2 ± 0.5) %, dominated by uncontroversial short distance piece; additional long-distance corrections found to be small  lineshape corrections cannot account for the difference above 0.7 GeV 2 The fair agreement between KLOE and CMD-2 invalidates for the moment the use of  data until a better understanding of the discrepancies is achieved

16. 16 Current Results a  had [ee ]= (693.4 ± 5.3 ± 3.5)  10 –10 a  [ee ]= (11 659 182.8 ± 6.3 had ± 3.5 LBL ± 0.3 QED+EW )  10 –10 Hadronic contribution from higher order : a  had [(  /  ) 3 ] = – (10.0 ± 0.6)  10 –10 Hadronic contribution from LBL scattering: a  had [ LBL ] = + (12.0 ± 3.5)  10 –10 inclu- ding: a  [exp ] – a  [SM ]= (25.2 ± 9.2)  10 –10  2.7 „standard deviations“ Observed Difference with Experiment: BNL E821 (2004): a  exp = (11 659 208.0  5.8) 10  10 Knecht-Nyffeler, Phys.Rev.Lett. 88 (2002) 071802 Melnikov-Vainshtein, hep-ph/0312226.0 Davier-Marciano, Ann. Rev. Nucl. Part. Sc. (2004)

17. 17 What if the deviation in a  is real ? effect of SUSY loops considered since a long time (Fayet 1981) chargino (2 states) and neutralino (4 states) loops broad range of predictions depending on masses and couplings for illustration: assume degenerate masses M SUSY in all loops and large tan  =  a  SUSY  sign(  ) 13 10 -10 (100 GeV  M SUSY ) 2 tan  favouring sign(  ) =+1 for 3< tan  <40  100< M SUSY <600 GeV other generic possibility: radiative muon mass scenarios, chiral symmetry breaking loop effect originating from a high mass scale M (dynamics, extra- dimensions, …) a  M  C (m   M) 2 with C of order 1  M  2 TeV

18. 18 Perspectives New proposal approved by BNL (E969) : use of same storage ring increase muon rate (reduce pion background by using backward decays) expect to reach 0.2 ppm (x5 better) Proposal for a new experiment at JPARC (0.05 ppm ?) Future experimental input for hadronic vacuum polarization expected from: New CMD-2 results forthcoming, especially at low and large  +  – masses More data from KLOE (real R measurement) BABAR ISR:  +  – SF over full mass range, multihadron channels (2  + 2  – and  +  –  0 already available) difficult with foreseen data to reduce uncertainty of HVP below 0.3 ppm additional work on LBL hadronic contribution is needed (0.3 ppm  ?)

19. 19    hadrons Part II : Atomic physics at the high-energy frontier Michel Davier Laboratoire de l’Accélérateur Linéaire, Orsay CERN Academic Training 13-15 June 2005 davier@lal.in2p3.fr

20. 20 Motivation atomic physics experiments have made important contributions to particle physics, such as the study of electroweak interference genuine table-top experiments competing with frontier high-energy accelerators for the study of fundamental interactions such experiments cannot replace high-energy experimentation which remains the only way to unambiguously observe new phenomena and disentangle the relevant pieces but they are complementary and provide an alternative for exploring deviations from SM expectations and in some cases unique, as for the search for symmetry-violating observables, such as electric dipole moments

21. 21 Electroweak interference in atomic transitions shortly after the discovery of Neutral Currents (Gargamelle), it was proposed (C. Bouchiat- M.A. Bouchiat 1974) to look for their effect in atomic transitions through P violation (APV) can Z 0 affect atomic radiative transitions ? interference between photon and Z exchange between an electron and a nucleus can be investigated taking advantage of the R-L asymmetry originating from the P-violating weak amplitude (A Z odd odd under P) A LR = 2 Re (A Z odd  A  ) A Z odd  g 2  M Z 2 A   e 2  q 2 g  e A LR  q 2  M Z 2 two possibilities polarized electron scattering (SLAC 1978) q 2  1 GeV 2 A LR  10 -4 atoms expect q 2  (m e  c) 2 = (1  Bohr orbit) 2 A LR  10 -15 wrong !

22. 22 Toward reasonable asymmetries in atoms important enhancement mechanisms have been found Z 3 law (Bouchiat-Bouchiat 1974) 1. electron orbital deformed in the vicinity of nucleus where short-range interaction occurs  equivalent to charge Z with radius a 0  Z  q 2  Z 2 2. different nucleons act coherently  effect  A  Z nuclear weak charge Q W = 2 [ (2Z+N) v u + (2N+Z) v d ] coupled to a e =  N  Z (4 sin 2  W  1)   N choose highly forbidden EM transitions ex. 6S 1/2  7S 1/2 in Cs E 1 transition strictly forbidden, Z exchange possible through PV  E 1 PV E 1 PV  10 -11 atomic units (e a 0 ), in quadrature wrt E 1 (T invariance) M 1 transition allowed, but suppressed  A LR = Im E 1 PV  M 1  0.5 10 -4 acceptable Z3Z3

23. 23 Different approaches Two lines of attack: work with allowed M 1 transitions with large Z Tl, Pb, Bi SNR reasonable  easier experiments complicated atomic structure  limited by precision of calculations Oxford, Seattle, Novosibirsk, Moscow use highly forbidden M 1 transitions 6S 1/2  7S 1/2 in Cs SNR much smaller, more difficult experiments large asymmetry single valence e with tight atomic core  possibility of precise theory ENS-Paris, Boulder (Cs), Berkeley (Tl) to enhance SNR a static E field is applied  induced amplitude E 1 ind interfering with E 1 PV compromise between asymmetry (still  10 -6 ) and SNR

24. 24 The 1982 Cs experiment in ENS-Paris 7S 1/2 6S 1/2 6P 3/2 excitation 540 nm fluorescence 1470 nm strongly-forbidden transition Cs M.A. Bouchiat et al 6S-7S excitation of Cs (vapour cell) with circularly polarized light transverse E field applied detected signal: circularly polarized fluorescence 7S-6P first evidence for APV: measured asymmetry 8  away from 0 12% experimental and 8% theoretical precision (atomic physics) agreement with SM Q w =  70  8 (exp)  6 (th) Q w SM =  73   N =  77

25. 25 Progress in Cs theory (Ginges-Flambaum 04) 10% 4% 0.5%

26. 26 The Boulder Cs experiment 85-88 Q W =  71.5  1.8 1.7 exp  0.7 th 97 Q W =  72.06  0.46 0.29 exp  0.36 th  Q W = Q W  Q W SM = 1.06  0.48 99 revised theory  Q W = 0.45  0.48 experiment stopped : “BEC easier and more rewarding” (Wieman) C. Wieman et al. same transitions as in Paris expt applied E field major difference: Cs atomic jet investigation of systematic effects : time-consuming (runs 20:1) great progress toward precision experiment

27. 27 The second Cs experiment in ENS-Paris (1) pulsed pump-probe detection through stimulated emission  amplification of asymmetry longitudinal E field to assist transition (Stark) 7S 1/2 6S 1/2 6P 3/2 pump 540 nm probe 1470 nm strongly-forbidden transition very complex device: 7 lasers, Cs vapour cell, fast switches, precision polarimetry, frequency stabilisation on atomic transitions, frequent reversals of field and polarisation Cs

28. 28 The second Cs experiment in ENS-Paris (2) many difficulties with the Cs vapour cell in longitudinal E field great progress achieved in recent years result with a precision of 2.4% obtained agreement with Boulder result (0.4%) experiment stopped

29. 29 Current projects in APV Berkeley (D. Budker) Yb (  isotopes) Seattle (N. Fortson) single Ba  (Paul trap) Saint-Petersbourg K 41 Stony Brook (L. Orozko) Fr (trapping/spectroscopy) Pisa, Legnaro,… Fr KVI Fr, Ra not on a short timescale…

30. 30 Level of sensitivity required for Higgs Q W = Q W SM  0.800 S  0.007 T = 0.45  0.48  sensitivity to S (  0.6) sensitive LEP observables to S (  0.15) and T (  0.15) T 3  sensitive to ln(M H ) than S S= 1/6  ln (M H /100 GeV) APV competitive for M H if precision exp  th reaches 0.05 %, competitive for S with 0.15 % similar conclusion for MSSM LEPEWWG 04

31. 31 APV and SM radiative corrections E158 SLAC diffusion Møller e  Anthony 04  APV, Møller and NuTeV have comparable sensitivities to rad. corr.

32. 32 APV and new physics if the new physics beyond SM is not specified, then it is prudent to test the electroweak couplings independently of a model from this point of view, Q W measures a combination of v u et v d which is orthogonal to what is deduced from e N  e X scattering with e  a e Q W = 2 a e [ (2Z+N) v u + (2N+Z) v d ] coherent on the nucleus (  for v e (a u, a d ) terms) LEP did not measure v u and v d NC neutrinos  v u, v d, a u, a d  AVP complementary e d

33. 33 APV and new physics : an example extra-dimensions of physical space 3 + d  compact dimensions (radius R  = 1/M c ) : fermions and bosons d  extra-dimensions (radius R  ) : gravitation Kaluza-Klein excitations of bosons : Z 0  Z 0 n M 2 n = M 2 Z + n 2 M 2 c many degrees of freedom possibles : where are the fields propagating (bulk, brane?), universality not garanteed simpler models : M c > 6 TeV (LEP-2)  10 TeV (LHC) M c > 2 TeV (present Q W, C. Bouchiat) however, some models can be built  insensitive with LEP and visible with APV (Delgado-Pomarol-Quiros 99, Cheung-Landsberg 03) a 0.1 % determination of Q W would have a reach  5 TeV in a ‘direction’ which could be blind to high-energy experiments

34. 34 Conclusion on APV real achievement of APV expts: to be sensitive to EW unification scale through atomic transitions table-top expt with 2-eV laser can tell us about 2-5 TeV physics! some difficulty to continue these experiments atomic physics community busy with many interesting developments using cold atoms and BE condensates “not worth doing because LHC will do it better” however hard to imagine more different techniques complementarity