1. B.Malaescu ISR e+e- /g-2 HEP 2010 1 ISR cross sections in e + e - and implications on muon g-2 Bogdan MALAESCU ( LAL – Orsay ) ( Representing the BaBar Collaboration )

2. B.Malaescu ISR e+e- /g-2 HEP 2010 2 Outlook The muon magnetic anomaly The BaBar ISR (Initial State Radiation) analysis Test of the method: e + e   +   (  ) Results on e + e    +   (  ) (PRL 103, 231801 (2009)) Combination of all e + e  data Discussion and conclusion

3. B.Malaescu ISR e+e- /g-2 HEP 2010 3 Lepton Magnetic Anomaly: from Dirac to QED Dirac (1928) g e =2 a e =0 anomaly discovered: Kusch-Foley (1948) a e = (1.19  0.05) 10  3 and explained by O(  ) QED contribution: Schwinger (1948) a e =  /2  = 1.16 10  3 first triumph of QED  a e sensitive to quantum fluctuations of fields

4. B.Malaescu ISR e+e- /g-2 HEP 2010 4 More Quantum Fluctuations typical contributions: QED up to O(  4 ),  5 in progress (Kinoshita et al.) Hadrons vacuum polarization light-by-light (models) + ? a new physics ? Electroweak new physics at high mass scale  a  much more sensitive to high scales

5. B.Malaescu ISR e+e- /g-2 HEP 2010 5 Hadronic Vacuum Polarization and Muon (g –2)  Dispersion relation    had  Im[ ]  | hadrons | 2 Dominant uncertainty from lowest-order HVP piece Cannot be calculated from QCD (low mass scale), but one can use experimental data on e + e   hadrons cross section

6. B.Malaescu ISR e+e- /g-2 HEP 2010 6 The E-821 Direct a  Measurement at BNL* Storage ring technique pioneered at CERN (Farley-Picasso…, 1970s), with μ + and μ - data a  obtained from a ratio of frequencies result updated with new value for   /  p (+0.9 10  10 ) (see new review in RPP2009 (Hoecker-Marciano)) a  exp = (11 659 208.9  5.4  3.3) 10  10 (  6.3) (0.54 ppm)  precession  rotation *Bennet et al., 2006, Phys. Rev. D 73, 072003

7. B.Malaescu ISR e+e- /g-2 HEP 2010 7  Measure  [e + e    +   (  FSR )] with high accuracy for vacuum polarization calculations, using the ISR method e + e    +    ISR (  add. )   channel contributes 73% of a  had  Dominant uncertainty also from   Present systematic precision of e  e  experiments CMD-2 0.8% SND 1.5% in agreement KLOE (ISR from 1.02 GeV) 2005 1.3% some deviation in shape 2008 0.9% better agreement  Big advantage of ISR: all mass spectrum covered at once (from threshold to 3 GeV in BABAR), with same detector and analysis  The ISR method needs a very large amount of data at an energy larger than the one at which we measure the cross section  Measure simultaneously  +    ISR (  add. ) and  +    ISR (  add. )  Compare the measured  +    ISR (  add. ) spectrum with QED prediction  Compare to spectral functions from previous e + e  data and  decays  aim for a measurement with <1% accuracy (syst. errors at per mil level) Goals of the BaBar Analysis great interest to clarify the situation as magnitude of possible discrepancy with SM is of the order of SUSY contributions with masses of a few 100 GeV

8. B.Malaescu ISR e+e- /g-2 HEP 2010 8 ISRFSR ISR + add. ISRISR + add. FSR The Relevant Processes e + e    +    ISR (  add. ) and  +    ISR (  add. ) measured simultaneously LO FSR negligible for  at s  (10.6 GeV) 2

9. B.Malaescu ISR e+e- /g-2 HEP 2010 9 BaBar / PEP II  PEP-II is an asymmetric e + e  collider operating at CM energy of  (4S).  Integrated luminosity = 531 fb -1 BaBar DIRC particle ID up to 4-5 GeV/c BaBar IFR: resistive plate chambers BaBar SVT and DCH precision tracking BaBar EMC: 6580 CsI(Tl) crystals, resolution ~1-2 % high E.

10. B.Malaescu ISR e+e- /g-2 HEP 2010 10   ISR photon at large angle, detected in the EMC  detected tracks of good quality: 1 (for efficiency) or 2 (for physics)  identification of the charged particles (DIRC, DCH)  separate  /KK/  event samples  kinematic fit (not using ISR photon energy) including 1 additional photon (discussed later)  obtain all efficiencies (trigger, filter, tracking, ID, fit) from same data   measure ratio of  to  cross sections to cancel ee luminosity additional ISR vacuum polarization ISR photon efficiency  correct for LO FSR (|FSR| 2 ) contribution in  (QED, <1% below 1 GeV)  additional FSR photons measured otherwise ~2% syst error The Measurement

11. B.Malaescu ISR e+e- /g-2 HEP 2010 11 Used an integrated luminosity of 232 fb -1  4S) on-peak & off peak) Geometrical acceptance (using Monte Carlo simulation) All efficiencies measured on data (data/MC corrections) Triggers (L1 hardware, L3 software), background-filter efficiencies Tracking efficiency Particle ID matrix (ID and mis-ID efficiencies):   K Kinematic fitting reduce non 2-body backgrounds  2 cut efficiency additional radiation (ISR and FSR) secondary interactions Unfolding of mass spectra Consistency checks for  (QED test, ISR luminosity) and  Unblinding R  partial (√s`>0.5 GeV) preliminary results (Tau08, Sept. 2008) Additional studies and checks Final results on  cross section and calculation of dispersion integral (PRL 103, 231801 (2009)) Analysis Steps

12. B.Malaescu ISR e+e- /g-2 HEP 2010 12 Acceptance and efficiencies determined initially from simulation, with data/MC corrections applied Large simulated samples, typically 10  data, using AfkQed generator AfkQed: lowest-order (LO) QED with additional radiation: ISR with structure function method,  assumed collinear to the beams and with limited energy FSR using PHOTOS Phokhara 4.0: (almost) exact second-order QED matrix element, limited to NLO Studies comparing Phokhara and AfkQed at 4-vector level with fast simulation QED test with    (  ) cross section requires reliable NLO generator  (  FSR ) cross section obtained through  (  ) /  (  ) ratio, rather insensitive to detailed description of radiation in MC MC Generators

13. B.Malaescu ISR e+e- /g-2 HEP 2010 13 tag particle (track, ID) candidate (p, , φ) γ ISR   benefit from pair production for tracking and particle ID  kinematically constrained events  efficiency automatically averaged over running periods  measurement in the same environment as for physics, in fact same events!  applied to particle ID with  samples, tracking…  assumes that efficiencies of the 2 particles are uncorrelated  in practice not true  study of 2-particle overlap in the detector (trigger,tracking, EMC, IFR) required a large effort to reach per mil accuracies Particle-related Efficiency Measurements

14. B.Malaescu ISR e+e- /g-2 HEP 2010 14 Kinematic Fitting First analysis to measure cross section with additional photons (NLO)  Two kinematic fits to X X  ISR  add (ISR photon defined as highest energy) Add. ISR fit:  add assumed along beams Add. ‘FSR’ if  add detected  Loose  2 cut (outside BG region in plot) for  and  in central  region  Tight  2 cut (ln(  2 +1) add.ISR <3) for  in  tail region  q q and multi-hadronic ISR background from MC samples + normalization from data using signals from  0  ISR  (qq), and  and  (  0  ) 

15. B.Malaescu ISR e+e- /g-2 HEP 2010 15 QED Test with  sample ISR  efficiency 3.4 syst. trig/track/PID 4.0 BaBar ee luminosity  absolute comparison of  mass spectra in data and in simulation  simulation corrected for data/MC efficiencies  AfkQed corrected for incomplete NLO using Phokhara  strong test (ISR probability drops out for  cross section) (0.2  3 GeV) BaBar

16. B.Malaescu ISR e+e- /g-2 HEP 2010 16 Obtaining the  (  FSR ) cross section Unfolded spectrum Effective ISR luminosity from  (  ) analysis (similar equation + QED) Acceptance from MC + data/MC corrections  mass spectrum unfolded (B. M. arXiv:0907.3791) for detector response Additional ISR almost cancels in the procedure (  (  ) /  (  ) ratio) Correction (2.5  1.0) 10  3   cross section does not rely on accurate description of NLO in the MC generator ISR luminosity from  (  ) in 50-MeV energy intervals (small compared to variation of efficiency corrections)

17. B.Malaescu ISR e+e- /g-2 HEP 2010 17 Systematic uncertainties  s` intervals (GeV) errors in 10  3 Dominated by particle ID (  -ID, correlated  ‘  ’,  -ID in ISR luminosity)

18. B.Malaescu ISR e+e- /g-2 HEP 2010 18 BaBar results (arXiv:0908.3589, PRL 103, 231801 (2009) ) e + e    +   (  FSR ) bare (no VP) cross section diagonal errors (stat+syst)

19. B.Malaescu ISR e+e- /g-2 HEP 2010 19 BaBar results in  region 2-MeV energy intervals

20. B.Malaescu ISR e+e- /g-2 HEP 2010 20 BaBar vs. other experiments at larger mass

21. B.Malaescu ISR e+e- /g-2 HEP 2010 21 VDM fit of the pion form factor add. FSR  Running (VP) BaBar Preliminary Fit

22. B.Malaescu ISR e+e- /g-2 HEP 2010 22 BaBar vs.other ee data (0.5-1.0 GeV) CMD-2 SNDKLOE direct relative comparison of cross sections with BaBar fit (stat + syst errors included) (green band) BaBar BaBar Preliminary Fit

23. B.Malaescu ISR e+e- /g-2 HEP 2010 23 BaBar vs. IB-corrected  data (0.5-1.0 GeV) relative comparison w.r.t. BaBar of  spectral functions corrected for isospin-breaking(IB) IB corrections: radiative corr.,  masses,  -  interference,  masses/widths each  data normalized to its own BR ALEPH CLEOBelle BaBar Preliminary Fit

24. B.Malaescu ISR e+e- /g-2 HEP 2010 24 Computing a   * * arXiv:0906.5443 M. Davier et al. 0.28  1.8 (GeV) BABAR 514.1  3.8 previous e + e  combined 503.5  3.5 *  combined 515.2  3.5 * *

25. B.Malaescu ISR e+e- /g-2 HEP 2010 25 Including BaBar in the e + e  Combination arXiv: 0908.4300 Davier-Hoecker-BM-Yuan-Zhang Improved procedure and software (HVPTools) for combining cross section data with arbitrary point spacing/binning, with full covariance matrices and error propagation

26. B.Malaescu ISR e+e- /g-2 HEP 2010 26 ModesEnergy [GeV] e+e –e+e –   + – 20 + – 20 4m  – 1.816.8 ± 1.3 ± 0.2 rad 21.4 ± 1.3 ± 0.6 SU(2) 2  + 2  – (+BaBar) 4m  – 1.813.1 ± 0.4 ± 0.0 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 excl. (+BaBar)2m  – 1.824.3 ± 1.3 ± 0.2 rad – J / ,  (2S) 3.08 – 3.117.4 ± 0.4 ± 0.0 rad – R [QCD]1.8 – 3.733.9 ± 0.5 theo – R [data]3.7 – 5.07.2 ± 0.3 ± 0.0 rad – R [QCD] 5.0 –  9.9 ± 0.2 theo – Other hadronic contributions from Davier-Eidelman-Hoecker-Zhang (2006)  another large long-standing discrepancy in the  +   2  0 channel !

27. B.Malaescu ISR e+e- /g-2 HEP 2010 27 The Problematic  +  - 2  0 Contribution e + e -   +   2  0 data (CMD2 discarded) preliminary ISR BaBar data: A. Petzold, EPS-HEP (2007) only statistical errors old contribution 16.8  1.3 update 17.6  1.7 probably still underestimated (BaBar)  21.4  1.4 Preliminary

28. B.Malaescu ISR e+e- /g-2 HEP 2010 28 BaBar Multi-hadronic Published Results Still more channels under analysis: K + K , KK  with K 0 Statistical + systematic errors

29. B.Malaescu ISR e+e- /g-2 HEP 2010 29 Where are we? including BaBar 2  results in the e+e  combination + estimate of hadronic LBL contribution (Prades-de Rafael-Vainhstein, 2009) yields a  SM [e+e  ] = (11 659 183.4  4.1  2.6  0.2) 10  10 HVP LBL EW (  4.9) E-821 updated result* (11 659 208.9  6.3) 10  10 deviation (ee) (25.5  8.0) 10  10 (3.2  ) updated  analysis +Belle +revisited IB corrections deviation (  ) (15.7  8.2) 10  10 (1.9  ) *new proposal submitted to Fermilab to improve accuracy by a factor 4

30. B.Malaescu ISR e+e- /g-2 HEP 2010 30 Conclusions  BaBar analysis of      and      ISR processes completed  Precision goal has been achieved: 0.5% in  region (0.6-0.9 GeV)  Absolute     cross section agrees with NLO QED within 1.1%  ee      cross section very insensitive to MC generator  full range of interest covered from 0.3 to 3 GeV  Comparison with data from earlier experiments  fair agreement with CMD-2 and SND, poor with KLOE  agreement with  data   Contribution to a  from BaBar is (514.1  2.2  3.1)  10  10 in 0.28-1.8 GeV  BaBar result has an accuracy (0.7%) comparable to combined previous results  Contribution from multi-hadronic channels will continue to be updated with more results forthcoming from BaBar, particularly  +  - 2  0   Deviation between BNL measurement and theory prediction reduced using BaBar     data a  [exp ] – a  [SM ] =(19.8 ± 8.4)  10 –10  +  - from BaBar only 25.5  8.0 combined e + e - including BaBar

31. B.Malaescu ISR e+e- /g-2 HEP 2010 31 Backup Slides

32. B.Malaescu ISR e+e- /g-2 HEP 2010 32 Data on e + e   hadrons CMD-2 (2004) CMD-2 (2006) SND (2006) KLOE (2009)

33. B.Malaescu ISR e+e- /g-2 HEP 2010 33 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 (spectral Functions) branching fractions mass spectrum kinematic factor (PS)

34. B.Malaescu ISR e+e- /g-2 HEP 2010 34 SU(2) Breaking Corrections for SU(2) breaking applied to  data for dominant  –  + contrib.: Electroweak radiative corrections: dominant contribution from short distance correction S EW subleading corrections (small) long distance radiative correction G EM (s) Charged/neutral mass splitting: m  –  m  0 leads to phase space (cross sec.) and width (FF) corrections  -  mixing (EM    –  + decay) corrected using FF model m  –  m  0 *** and   –    0 *** Electromagnetic decays:      ***,    ,    ,   l + l – Quark mass difference m u  m d (negligible) Cirigliano-Ecker-Neufeld’ 02 Lopez Castro et al.’ 06 Marciano-Sirlin’ 88 Braaten-Li’ 90 Alemany-Davier-Höcker’ 97, Czyż-Kühn’ 01 Flores-Baez-Lopez Castro’ 08 Davier et al.’09

35. B.Malaescu ISR e+e- /g-2 HEP 2010 35 Situation at ICHEP’06 / 08 a  had [ee ]= (690.9 ± 4.4)  10 –10 a  [ee ]= (11 659 180.5 ± 4.4 had ± 3.5 LBL ± 0.2 QED+EW )  10 –10 Hadronic HO – ( 9.8 ± 0.1)  10 –10 Hadronic LBL + (12.0 ± 3.5)  10 –10 Electroweak (15.4 ± 0.2)  10 –10 QED (11 658 471.9 ± 0.1)  10 –10 a  [exp ] – a  [SM ]= (27.5 ± 8.4)  10 –10  3.3 „standard deviations“ Observed Difference with BNL using e + e  : Knecht-Nyffeler (2002), Melnikov-Vainhstein (2003).0 Davier-Marciano (2004) Kinoshita-Nio (2006) e + e   BNL Estimate using  data consistent with E-821

36. B.Malaescu ISR e+e- /g-2 HEP 2010 36 Revisited Analysis using  Data: Belle + new IB CMD-2, SND KLOE Relative comparison of  and ee spectral functions (  green band) arXiv:0906.5443 M.Davier et al. Global test of spectral functions: prediction of  BR using ee data  larger disagreement with KLOE slope…

37. B.Malaescu ISR e+e- /g-2 HEP 2010 37 Revisited Analysis using  Data: including Belle

38. B.Malaescu ISR e+e- /g-2 HEP 2010 38 Revisited Analysis  Data: new IB corrections

39. B.Malaescu ISR e+e- /g-2 HEP 2010 39 m  m  and similarly for   single track efficiency  correlated loss probability f 0  probability to produce more than 2 tracks f 3 Data/MC Tracking Correction to  cross sections

40. B.Malaescu ISR e+e- /g-2 HEP 2010 40 Particle identification required to separate XX  final processes Define 5 ID classes using cuts and PID selectors (complete and orthogonal set) Electrons rejected at track definition level (E cal, dE/dx) All ID efficiencies measured  x  I  a tighter  ID (  h ) is used for tagging in efficiency measurements and to further reject background in low cross section regions. Particle Identification Barrel Backward EndcapForward Endcap Z IFR  IFR X IFR Y IFR * isolated muons M  > 2.5 GeV  efficiency maps (p,v 1,v 2 ) impurity (1.1  0.1) 10  3 * correlated efficiencies/close tracks  maps (dv 1,dv 2 )

41. B.Malaescu ISR e+e- /g-2 HEP 2010 41 Data/MC PID corrections to  and  cross sections Two running periods with different IFR performance  

42. B.Malaescu ISR e+e- /g-2 HEP 2010 42 PID separation and Global Test All ‘xx’  solve for all xx (0) and compare with no-ID spectrum and estimated syst. error hist: predicted from PID dots: measured (no ID) m   (GeV)  N (o) ii BaBar

43. B.Malaescu ISR e+e- /g-2 HEP 2010 43 Backgrounds  background larger with loose  2 cut used in 0.5-1.0 GeV mass range  q q and multi-hadronic ISR background from MC samples + normalization from data using signals from  0  ISR  (qq), and  and  (  0  )  global test in background-rich region near cut boundary m  (GeV) multi-hadrons  Fitted BG/predicted = 0.968  0.037 BG fractions in 10 -2 at m  values BaBar

44. B.Malaescu ISR e+e- /g-2 HEP 2010 44  2 cut Efficiency Correction  depends on simulation of ISR (FSR), resolution effects (mostly ISR  direction) for  and    2 cut efficiency can be well measured in  data because of low background  main correction from lack of angular distribution for additional ISR in AfkQed  common correction: 1% for loose  2, 7% for tight     additional loss for  because of interactions studied with sample of interacting events much better study now, 2 independent methods loose    secondary interactions data/MC 1.51  0.03 syst error 0.3 - 0.9  10 -3

45. B.Malaescu ISR e+e- /g-2 HEP 2010 45 Additional ISR   Angular distribution of add. ISR /beams! Energy cut-off for add. ISR in AfkQed

46. B.Malaescu ISR e+e- /g-2 HEP 2010 46 Additional FSR   Angle between add  and closest track Large-angle add.ISR in data  AfkQed Evidence for FSR data  AfkQed FSR ISR data/MC  0.96  0.06  1.21  0.05

47. B.Malaescu ISR e+e- /g-2 HEP 2010 47 Checking Known Distributions Cos  * in XX CM /   flat at threshold 1+cos 2  *     sin 2  *    P>1 GeV track requirement  loss at cos  *  1

48. B.Malaescu ISR e+e- /g-2 HEP 2010 48 Unfolding  Mass Spectrum  measured mass spectrum distorted by resolution effects and FSR (m  vs.  s’)  iterative unfolding method (B. M. arXiv:0907-3791) : one step is sufficient  mass-transfer matrix from simulation with corrections from data  2 MeV bins in 0.5-1.0 GeV mass range, 10 MeV bins outside  most salient effect in  -  interference region (little effect on a   ) Mass (GeV) Absolute difference unfolded(1)  raw data unfolded(2)  unfolded(1) Statistical errors (band) Relative difference BaBar

49. B.Malaescu ISR e+e- /g-2 HEP 2010 49 Obtaining the  (  ) cross section  ratio  ISR lumi  LO formula should behave smoothly (HVP effects on resonances cancel) Use measured lumi in 50-MeV bins averaged in sliding 250-MeV bins for smoothing Unfolded spectrum Effective ISR luminosity from  (  ) analysis (similar equation + QED) Acceptance from MC + data/MC corrections Additional ISR almost cancels in the procedure (  (  ) /  (  ) ratio) Correction (2.5  1.0) 10  3   cross section does not rely on accurate description of NLO in the MC generator

50. B.Malaescu ISR e+e- /g-2 HEP 2010 50 Changes since preliminary results at Tau08  preliminary results Sept. 2008: only 0.5-3 GeV (excess/expect. near threshold)  problem explored (Oct. 2008- Feb. 2009): trigger/BGFilter, ee background   `  ’ re-investigated  direct measurement achieved using ID probabilities before: model for correlated loss, no precise direct check  significant changes  efficiency for ISR lumi  +0.9%  contamination in `  ’ sample    cross section   1.8% 0.525 GeV  1.0% 0.775 GeV  1.4% 0.975 GeV  other changes: - MC unfolding mass matrix corrected for data/MC differences (small) - ISR lumi now used in 50-MeV sliding bins, instead of global fit - cancellation of add ISR in  /  ratio studied/corrected  extensive review

51. B.Malaescu ISR e+e- /g-2 HEP 2010 51 f 2 Story

52. B.Malaescu ISR e+e- /g-2 HEP 2010 52 BaBar vs.other ee data  interference region) CMD-2 SND  mass calibration of BaBar checked with ISR-produced J/    expect  (0.16  0.16) MeV at  peak   mass determined through VDM mass fit m ω fit  m ω PDG =  (0.12  0.29) MeV  Novosibirsk data precisely calibrated using resonant depolarization  comparison BaBar/CMD-2/SND in  -  interference region shows no evidence for a mass shift BaBar Preliminary Fit

53. B.Malaescu ISR e+e- /g-2 HEP 2010 53 Obtaining the average cross section local weighted average performed full covariance matrices and error propagation local  2 used for error rescaling average dominated by BaBar and KLOE, BaBar covering full range relative weights integrand (dispersion integral) error error scale factor

54. B.Malaescu ISR e+e- /g-2 HEP 2010 54 Consistency of Experiments with Average

55. B.Malaescu ISR e+e- /g-2 HEP 2010 55 g-2 Values for Various Mass Intervals (  10  10 )

56. B.Malaescu ISR e+e- /g-2 HEP 2010 56 Combined Spectral Functions Comparison

57. B.Malaescu ISR e+e- /g-2 HEP 2010 57 Discussion BaBar 2  data complete and the most accurate, but expected precision improvement on the average not reached because of discrepancy with KLOE however, previous  /ee disagreement strongly reduced 2.9  (2006)  2.4  (  update)  1.5  (including BaBar) a range of values for the deviation from the SM can be obtained, depending on the 2  data used: BaBar 2.4  all ee 3.2  all ee  BaBar 3.7  all ee  KLOE 2.9   1.9  all approaches yield a deviation, but SM test limited by systematic effects not accounted for in the experimental analyses (ee) and/or the corrections to  data at the moment some evidence for a deviation (2  4  ), but not sufficient to establish a contribution from new physics

58. B.Malaescu ISR e+e- /g-2 HEP 2010 58 Perspectives first priority is a clarification of the BaBar/KLOE discrepancy: - origin of the ‘slope’ (was very pronounced with the 2004 KLOE results, reduced now with the 2008 results) - normalization difference on  peak (most direct effect on a  ) - Novosibirsk results in-between, closer to BaBar - slope also seen in KLOE/  comparison; BaBar agrees with  further checks of the KLOE results are possible: as method is based on MC simulation for ISR and additional ISR/FSR probabilities  test with  analysis contribution from multi-hadronic channels will continue to be updated with more results forthcoming from BaBar, particularly 2  2  0 more ee data expected from VEPP-2000 in Novosibirsk experimental error of E-821 direct a  measurement is a limitation, already now  new proposal submitted to Fermilab to improve accuracy by a factor 4  project at JPARC