Hadronic and e e spectra, contribution to (g-2) and QCD studies

Transcription

1 Hadronic and e e spectra, contribution to (g-2) and QCD studies Bogdan MALAESCU LPNHE Paris In collaboration with M. Davier, S. Descotes-Genon, A. Hoecker, Z. Zhang 19/03/2013 1

2 Outlook Introduction: the muon magnetic anomaly & QCD fits Updates of the ALEPH spectral functions Data on e + e hadrons Combination of all e + e data (HVPTools) Results on a Discussion and conclusions B.Malaescu, e+e- /g-2 & QCD 2

3 Hadronic Vacuum Polarization and Muon (g 2) Dominant uncertainty for the theoretical prediction: 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 Im[ ] hadrons 2 had Dispersion relation Bouchiat and Michel, 1961 B.Malaescu, e+e- /g-2 & QCD 3

4 Theoretical Prediction of R 2 s 0 ds s s (1) (0) R, U ( s0) 12 SEW Im U ( s i ) Im U ( s i ) s0 s0 s 0 0 (1,0) 1 Optical Theorem: Im ud ( s), V / A v1 a1,0 ( s) 2 Problem: Im (J) V/A (s) contains hadronic physics that cannot be predicted by QCD in this region of the real axis However, owing to the analyticity of (s), one can use Cauchy s theorem: 0 R( s ) ds w( s) Im ( s i ) 0 s 0 Im(s) 1 ds w( s) ( s) 2i s s 0 spectral function Potential problems for OPE s = Re(s) s = s 0 4

5 and QCD: The Operator Product Expansion Full theoretical ansatz, including nonperturbative operators via the OPE: (in the following: a s = s / ) Perturbative quark-mass terms: EW correction: (neglected) C m ( s ) m ( s ) ( s ) i 0 j 0 U, ij 0 i, j u, d, s s0 ( 0) mq R, ( s0 ) VCKM SEW 1 EW 2 (2, ) ( D) U U U D 4,6,... Perturbative contribution 3 4 ds s s s 2 i D( s) s s 0 0 s0 s S s 0 1 n where: D( s) K ( ) ( ) 2 n as s 4 n 0 Adler function to avoid unphysical subtractions: d ( s) D( s) s ds C Nonperturbative contribution ( s ; ) O( ) ( D) U U U 0 D /2 dimo D s0 5

6 Spectral Moments Exploit shape of spectral functions to obtain additional experimental information: s 0 k s s dr, U ( s0) R, U ( s0) ds 1 s s ds k Le Diberder-Pich, PL B289, 165 (1992) The region where OPE fails and we have small statistics is suppressed. Theory prediction very similar to R : 2 (2, mq, k ) R, U ( s0 ) VCKM SEW P EW U U D 4,6,... k ( k ) (0, k ) ( k ) ( D, k ) with corresponding perturbative and nonperturbative OPE terms Because of the strong correlations, only four moments are used. 2 We fit simultaneously ( m s ) and the leading D=4,6,8 nonperturbative contributions 6

7 Updated ALEPH Spectral Functions Problem identified for the publicly available ALEPH covariance matrix: treatment of the statistical correlations from the unfolding Thanks to D. Boito for bringing this issue to our attention! Redone unfolding of the, 2, 3, 3 and 3 spectral functions, using the IDS method: iterative unfolding (MC truth reweighting) with regularization provides a result with small systematic uncertainties (tested through a data-driven method) and full information on uncertainties and correlations allows for an improved treatment of structures (reduced effects of the regularization) comparing to the SVD method used before Updated spectral functions to be released soon B.Malaescu, e+e- /g-2 & QCD 7

8 Update of the Spectral Function B.Malaescu, e+e- /g-2 & QCD 8

9 2 3 Spectral Functions B.Malaescu, e+e- /g-2 & QCD 9

10 3 3 Spectral Functions B.Malaescu, e+e- /g-2 & QCD 10

11 V & A Spectral Functions B.Malaescu, e+e- /g-2 & QCD 11

12 V+A & V-A Spectral Functions B.Malaescu, e+e- /g-2 & QCD 12

13 Comparison of moment integrals Previous: New: B.Malaescu, e+e- /g-2 & QCD 13

14 Comparison of QCD results B.Malaescu, e+e- /g-2 & QCD 14

15 Comparison of g-2 results Previous: New: Small changes in physics results (QCD & g-2) to the updates in the unfolding B.Malaescu, e+e- /g-2 & QCD 15

16 HVP: Data on e + e hadrons CMD-2 (2004) CMD-2 (2006) SND (2006) KLOE (08&10) (ISR) B.Malaescu tau, e+e- /g-2 FF workshop

17 BaBar results ( PRL 103, (2009); PRD 86(2012) ) BaBar Absolute + - cross section agrees with NLO QED within 1.1% diagonal errors (stat+syst) e + e + ( FSR ) bare (no VP) cross section FF workshop

18 BaBar results in region 2-MeV energy intervals B.Malaescu, e+e- /g-2 & QCD 18

19 BaBar fit vs. e + e - data (stat + syst errors included) B.Malaescu tau, e+e- /g-2 FF workshop

20 To be added soon: KLOE 2012 data Recently published KLOE data ( ), using the normalization with respect to the muon spectrum Need to take into account correlations with respect to previous measurements B.Malaescu, e+e- /g-2 & QCD 20

21 BaBar vs. IB-corrected data ( GeV) PRD 86(2012) 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 B.Malaescu tau, e+e- /g-2 FF workshop

22 e e Combination for the Channel arxiv: (EPJ C) Davier-Hoecker-BM-Zhang Improved procedure and software (HVPTools) for combining cross section data with arbitrary point spacing/binning B.Malaescu tau, e+e- /g-2 FF workshop

23 Obtaining the average cross section quadratic interpolation of the data points/bins for each experiment local weighted average performed (account for different point spacing/binning) possible bias tested using a GS model: negligible for quadratic interpolation full covariance matrices: correlations between the data points/bins of an experiment (corrections & systematic errors) and between experiments (ex: VP) error propagation using toy simulations average dominated by BaBar and KLOE, BaBar covering full range B.Malaescu, e+e- /g-2 & QCD 23

24 Obtaining the average cross section local 2 used for error rescaling Error scale factor error integrand (dispersion integral) B.Malaescu, e+e- /g-2 & QCD 24

25 a Contributions for Various Experiments e e ± 2.8 (1.00) * ± 3.5 (1.00) New average ± 3.5 (1.00) Still difference in shape (KLOE) Provided fraction of the full integral *arxiv: (EPJ C) Davier-Hoecker-Lopez Castro-BM-Mo-Toledo Sanchez-Wang-Yuan-Zhang 25

26 The Problematic Contribution old contribution (Davier-Eidelman-Hoecker-Zhang, 2006) update including preliminary ISR BaBar data: A. Petzold, EPS-HEP (2007) e + e data (CMD2 discarded) Essentially normalization difference: cross-checks very desirable B.Malaescu, e+e- /g-2 & QCD 26

27 Updated Channels Latest BABAR Results a : 13.35± ±0.35 *arxiv:1201:5677 * a : 0.35± ±0.02 ** ** a : 0.064± ±0.007 **arxiv:1103:3001 * B.Malaescu tau, e+e- /g-2 FF workshop

28 R e e Hadrons B.Malaescu, e+e- /g-2 & QCD 28

29 R e e Hadrons Sum of exclusive channels PRELIMINARY Statistical uncertainty Total uncertainty 29

30 R e e Hadrons Sum of exclusive channels PRELIMINARY Statistical uncertainty Total uncertainty B.Malaescu, e+e- /g-2 & QCD 30

31 Correlation matrix R e e Hadrons Statistical uncertainty Total uncertainty Total covariance matrix: takes into account correlations -for statistical and systematic uncertainties of a given measurements -between the measurements of a given channel -between various different channels -conservative uncertainties on isospin relations (missing channels) Short range correlations for statistical uncertainties Longer range correlations for systematic uncertainties Cross-check performed with sum of individual contributions to a had Ongoing efforts to exploit Ree for QCD studies B.Malaescu tau, e+e- /g-2 31

32 Status of a including latest BaBar 4 ; 2K2 and 2K2 0 results in the e+e combination + latest QED calculation (Kinoshita et al.) yields a SM [e+e ] = ( ) E-821 updated result* deviation (ee) ( ) (3.6 ) latest update of the analysis +Belle +revisited IB corrections Deviation ( ) ( ) (2.5 ) HVP LBL EW ( 4.9) ( ) *new project at Fermilab to improve accuracy by a factor 4 B.Malaescu, e+e- /g-2 & QCD 32

33 Discussion and Conclusions Updated ALEPH spectral functions: small impact on physics results Comparison of 2 data sets BABAR in fair agreement with CMD-2 and SND, poor with KLOE BABAR in good agreement with data Previous /ee disagreement strongly reduced 2.9 (2006) 2.4 ( update) 1.5 (including BaBar-2 ); 1.8 (including the 2010 KLOE 2 results) 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, depending on the data used for HVP), but not sufficient to establish a contribution from new physics Determined Ree and its full covariance matrix, from the sum of individual channels B.Malaescu, e+e- /g-2 & QCD 33

34 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 & 2010 & 2012 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 contribution from multi-hadronic channels will continue to be updated with more results forthcoming from BaBar, particularly more ee data expected from VEPP-2000 in Novosibirsk experimental error of E-821 direct a measurement is a limitation, already now new project at Fermilab to improve accuracy by a factor 4 project at JPARC B.Malaescu, e+e- /g-2 & QCD 34

35 Backup Slides B.Malaescu, e+e- /g-2 & QCD 35

36 Lepton Magnetic Anomaly: from Dirac to QED Dirac (1928) g e =2 a e =0 anomaly discovered: Kusch-Foley (1948) a e = ( ) 10 3 and explained by O( ) QED contribution: Schwinger (1948) a e = /2 = first triumph of QED a e sensitive to quantum fluctuations of fields B.Malaescu, e+e- /g-2 & QCD 36

37 More Quantum Fluctuations +? a new physics? typical contributions: QED up to O( 5 ) (Kinoshita et al.) Hadrons vacuum polarization light-by-light (models) Electroweak new physics at high mass scale δa l m l 2 M 2 B.Malaescu a much more sensitive to high scales, e+e- /g-2 & QCD 37

38 The Perturbative Prediction Perturbative prediction of Adler function given to N 3 LO Perturbative coefficients of Adler function series, known to n=4 (K 4 49) P. Baikov, et al., arxiv: [hep-ph] da s dlns n s s n s n 0 ( a ) a 2 a a ( s) a ( s ) a 2 ( s )... s dependence of a s driven by running: In practice, use Taylor development in s s 0 0 s 0 n K ( ) A ( a ) (0) ( ) n n RGE -function, known to n=3 ln ss 0 s 1 i i 3 i 4 n i d 1 2e 2 e e as ( s0e ) 2 φ Im(s) s =ζ s 0 s = s 0 Re(s) How to compute the integral in the complex plane? How to perform a scale transformation? 38

39 Numerical Methods CIPT: at each step use Taylor series to compute as () s from the value found at the previous step FOPT: fixed order Taylor expansion around the physical value as ( s0) and the integration result is cut at the same order in a s (s 0 ) Im(s) CIPT Re(s) FOPT s = s 0 Remarks: - Potential problem for FOPT due to the use of Taylor series for large η - Avoided by CIPT (use small steps) - Analytically, the FOPT result can also be obtained by making small steps, with a fixed order cut of the result at each step, BUT the RGE is modified at each step! 39

40 Situation at ICHEP 06 / 08 a had [ee ] = (690.9 ± 4.4) a [ee ] = ( ± 4.4 had ± 3.5 LBL ± 0.2 QED+EW ) Hadronic HO ( 9.8 ± 0.1) e + e BNL Hadronic LBL + (12.0 ± 3.5) Electroweak (15.4 ± 0.2) QED ( ± 0.1) Knecht-Nyffeler (2002), Melnikov-Vainhstein (2003) Davier-Marciano (2004) Kinoshita-Nio (2006) B.Malaescu, e+e- /g-2 & QCD Observed Difference with BNL using e + e : a [exp] a [SM] = (27.5 ± 8.4) standard deviations Estimate using data consistent with E

41 Computing a (GeV) BABAR previous e + e combined * combined * 2.4 * * *arxiv: (EPJ C) Davier-Hoecker-Lopez Castro-BM-Mo-Toledo Sanchez-Wang-Yuan-Zhang 41

42 Situation in arxiv: (EPJC) FF workshop

43 The E-821 Direct a Measurement at BNL* Storage ring technique pioneered at CERN (Farley-Picasso, 1970s), with μ + and μ - data precession rotation a obtained from a ratio of frequencies result updated with new value for / p ( ) (see review in RPP2009 (Hoecker-Marciano)) a exp = ( ) ( 6.3) (0.54 ppm) *Bennet et al., 2006, Phys. Rev. D 73,

44 Revisited Analysis using Data: Belle + new IB Relative comparison of and ee spectral functions ( green band) arxiv: (epjc) M.Davier et al. slope CMD-2, SND KLOE Global test of spectral functions: prediction of BR using ee data larger disagreement with KLOE B.Malaescu, e+e- /g-2 & QCD 44

45 HVP: Data through CVC SU(2) W: I =1 & V,A CVC: I =1 & V : I =0,1 & V W hadrons e + e hadrons Hadronic physics factorizes (spectral Functions) B.Malaescu, e+e- /g-2 & QCD 45

46 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) Marciano-Sirlin 88 Braaten-Li 90 Cirigliano-Ecker-Neufeld 02 Lopez Castro et al. 06 Alemany-Davier-Höcker 97, Czyż-Kühn 01 Flores-Baez-Lopez Castro 08 Davier et al. 09 B.Malaescu, e+e- /g-2 & QCD 46

47 Revisited Analysis Data: new IB corrections B.Malaescu, e+e- /g-2 & QCD 47

48 Revisited Analysis using Data: including Belle B.Malaescu, e+e- /g-2 & QCD 48

49 BABAR QED Test with sample 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) BaBar (0.2 3 GeV) B.Malaescu ISR efficiency 3.4 syst. trig/track/pid 4.0, e+e- /g-2 & QCD BaBar ee luminosity 49

50 BaBar vs.other ee data interference region) mass calibration of BaBar checked with ISR-produced J/ expect ( ) MeV at peak mass determined through VDM mass fit m ω fit m ω PDG = ( ) MeV Novosibirsk data precisely calibrated using resonant depolarization comparison BaBar/CMD-2/SND in - interference region shows no evidence for a mass shift B.Malaescu, e+e- /g-2 & QCD 50

51 BaBar vs. other experiments at larger mass B.Malaescu, e+e- /g-2 & QCD 51

52 Consistency of Experiments with Average B.Malaescu tau, e+e- /g-2 52

53 Combined Spectral Functions Comparison B.Malaescu, e+e- /g-2 & QCD 53

54 BaBar Multi-hadronic Published Results Statistical + systematic errors Still more channels under analysis: K + K, KK with K 0 B.Malaescu, e+e- /g-2 & QCD 54