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

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

B.Malaescu ISR e+e- /g-2 HEP 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  =  3 first triumph of QED  a e sensitive to quantum fluctuations of fields

B.Malaescu ISR e+e- /g-2 HEP 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

B.Malaescu ISR e+e- /g-2 HEP 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

B.Malaescu ISR e+e- /g-2 HEP 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 (  10 ) (see new review in RPP2009 (Hoecker-Marciano)) a  exp = (  5.4  3.3) 10  10 (  6.3) (0.54 ppm)  precession  rotation *Bennet et al., 2006, Phys. Rev. D 73,

B.Malaescu ISR e+e- /g-2 HEP  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) % some deviation in shape % 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

B.Malaescu ISR e+e- /g-2 HEP 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

B.Malaescu ISR e+e- /g-2 HEP 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.

B.Malaescu ISR e+e- /g-2 HEP   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

B.Malaescu ISR e+e- /g-2 HEP 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, (2009)) Analysis Steps

B.Malaescu ISR e+e- /g-2 HEP 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

B.Malaescu ISR e+e- /g-2 HEP 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

B.Malaescu ISR e+e- /g-2 HEP 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  ) 

B.Malaescu ISR e+e- /g-2 HEP 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

B.Malaescu ISR e+e- /g-2 HEP 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: ) 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)

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

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

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

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

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

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

B.Malaescu ISR e+e- /g-2 HEP BaBar vs. IB-corrected  data ( 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

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

B.Malaescu ISR e+e- /g-2 HEP Including BaBar in the e + e  Combination arXiv: 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

B.Malaescu ISR e+e- /g-2 HEP ModesEnergy [GeV] e+e –e+e –   + – 20 + – 20 4m  – ± 1.3 ± 0.2 rad 21.4 ± 1.3 ± 0.6 SU(2) 2  + 2  – (+BaBar) 4m  – ± 0.4 ± 0.0 rad 12.3 ± 1.0 ± 0.4 SU(2)  (782) 0.3 – ± 1.0 ± 0.3 rad –  (1020) 1.0 – ± 0.8 ± 0.2 rad – Other excl. (+BaBar)2m  – ± 1.3 ± 0.2 rad – J / ,  (2S) 3.08 – ± 0.4 ± 0.0 rad – R [QCD]1.8 – ± 0.5 theo – R [data]3.7 – ± 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 !

B.Malaescu ISR e+e- /g-2 HEP 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

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

B.Malaescu ISR e+e- /g-2 HEP 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  ] = (  4.1  2.6  0.2) 10  10 HVP LBL EW (  4.9) E-821 updated result* (  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

B.Malaescu ISR e+e- /g-2 HEP Conclusions  BaBar analysis of      and      ISR processes completed  Precision goal has been achieved: 0.5% in  region ( 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 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

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

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

B.Malaescu ISR e+e- /g-2 HEP 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)

B.Malaescu ISR e+e- /g-2 HEP 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

B.Malaescu ISR e+e- /g-2 HEP Situation at ICHEP’06 / 08 a  had [ee ]= (690.9 ± 4.4)  10 –10 a  [ee ]= ( ± 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 ( ± 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

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

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

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

B.Malaescu ISR e+e- /g-2 HEP 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

B.Malaescu ISR e+e- /g-2 HEP 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 )

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

B.Malaescu ISR e+e- /g-2 HEP 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

B.Malaescu ISR e+e- /g-2 HEP Backgrounds  background larger with loose  2 cut used in 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 =  BG fractions in at m  values BaBar

B.Malaescu ISR e+e- /g-2 HEP  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  10 -3

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

B.Malaescu ISR e+e- /g-2 HEP 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

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

B.Malaescu ISR e+e- /g-2 HEP Unfolding  Mass Spectrum  measured mass spectrum distorted by resolution effects and FSR (m  vs.  s’)  iterative unfolding method (B. M. arXiv: ) : one step is sufficient  mass-transfer matrix from simulation with corrections from data  2 MeV bins in 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

B.Malaescu ISR e+e- /g-2 HEP 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

B.Malaescu ISR e+e- /g-2 HEP Changes since preliminary results at Tau08  preliminary results Sept. 2008: only GeV (excess/expect. near threshold)  problem explored (Oct 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% GeV  1.0% GeV  1.4% 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

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

B.Malaescu ISR e+e- /g-2 HEP 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

B.Malaescu ISR e+e- /g-2 HEP 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

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

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

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

B.Malaescu ISR e+e- /g-2 HEP 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

B.Malaescu ISR e+e- /g-2 HEP 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