1. RHUL Group Meeting 18. Dec. 03Henning Flächer 1 Hadronic Mass Moments from Semileptonic B Meson Decays at BABAR Henning Flächer OUTLINE Mass Moment Measurement Interpretation in context of HQET Conclusions Motivation Fully reconstructed B mesons Event selection

2. RHUL Group Meeting 18. Dec. 03Henning Flächer 2 Motivation CKM matrix describes quark mixing by relating the weak- to the mass- eigenstates and accommodates CP violation. Semileptonic B decays give direct access to |V ub | and |V cb | Allow for factorization of leptonic and hadronic currents. Advantages of inclusive B decays: large rates OPE provide expansions for inclusive observables like: semileptonic decay width mean values of hadronic mass distributions mean values of lepton momentum spectra Precise theoretical calculations if OPE provides consistent framework Γ SL  |V cb | 2 (1+corrections)

3. RHUL Group Meeting 18. Dec. 03Henning Flächer 3 |V cb | and |V ub | from semileptonic B decays B  Xl with l=e,  b  c l b c W No interaction between W → lν and c-quark When measuring |V cb | we look for b → c transitions Due to the strong interaction it is only possible to measure B→X c lν In semileptonic B decays final state interaction is reduced to a minimum Only then it is possible to relate b→c to B→X c X c can be D, D*, D** & D (*) (n)π Invariant mass of X c is our observable!

4. RHUL Group Meeting 18. Dec. 03Henning Flächer 4 Non-perturbative parameters appear in the expansion which need to be measured by experiment Theory: The way towards |V cb | Operator Product Expansions within the context of Heavy Quark Effective Theory provide a powerful tool to predict decay rates with very high precision (2%) Important assumption:Quark-Hadron Duality Similar expansions in other variables: Inclusive B decays: invariant mass of X-system In b→ s γ gamma decays: photon energy Consistency needs to be tested and verified!!!

5. RHUL Group Meeting 18. Dec. 03Henning Flächer 5 Analysis Method

6. RHUL Group Meeting 18. Dec. 03Henning Flächer 6 Fully Reconstructed B-Mesons Reconstruct one B candidate in the event: A big step forward! Reconstruction efficiency rather low, only ~ 0.4 %  only possible at a B-Factory like BaBar! With a data set of 89 M BB pairs (Run1+2 only) we obtain ~ 350 000 fully reconstructed B mesons Considering the semileptonic branching fraction we finally obtain 350000 x 2 x 10.8% ~ 70 000 semileptonic decays.

7. RHUL Group Meeting 18. Dec. 03Henning Flächer 7 Semiexclusive B reconstruction Consider the following decays: Add π+, π0, K+, K0s iteratively until: Advantages: Breco momentum Breco Flavour Background reduction (combinatorics) m ES sideband Lepton required on recoil side Disadvantage: limited statistics

8. RHUL Group Meeting 18. Dec. 03Henning Flächer 8 What is X c ? Decays B  X c l v: Four resonances above D* Four non-resonant decays Broad mass spectrum above the two narrow resonances (D,D*) D* D Mass spectrum on detector level: M X det (GeV) with Moment: (weighted sum)

9. RHUL Group Meeting 18. Dec. 03Henning Flächer 9 Event Topology BB -> Breco (X,l,Pmiss) Apply Energy and Momentum conservation E Breco + E X + E l + E - E PEPII = 0 P Breco + P X + P l + P - P PEPII = 0  4 Constraints + Mass Constraints M(Breco)=M(X,l, )  + 1 ConstraintsX-System (4 measured parameters) Lepton (3 measured parameters) Missing Neutrino (3 unmeasured parameters) B reco candidate (4 measured parameters) Observable: Invariant mass of X-System := Mx Kinematically closed environment – reconstruction of all kinematic quantities (energies, momenta, masses) in the B meson rest frame can be achieved!

10. RHUL Group Meeting 18. Dec. 03Henning Flächer 10 Selection Identification of exactly one lepton with P* > 0.9 GeV Event quality cuts: |E miss -p miss | < 0.5 GeV Breco Quality: P > 40% Event Selection: Furthermore: E miss > 0.5 GeV & p miss > 0.5 GeV Total charge |ΔQ| ≤ 1 7100 signal and 2100 background events Lepton charge consistent with prompt B decay

11. RHUL Group Meeting 18. Dec. 03Henning Flächer 11 Analysis Strategy Subtract Background from misreconstructed B mesons Calibrate measured masses event-by-event Subtract remaining B Background Apply efficiency and acceptance corrections To obtain the true mean value of the hadronic mass distribution we need to: Extract as a function of the minimal lepton momentum P*=0.9GeV P*=1.5GeV

12. RHUL Group Meeting 18. Dec. 03Henning Flächer 12 Effect of kinematic Fit: Resolution Functions Kinematic Fit improves resolution of the invariant mass M X Almost unbiased measurement irrespective of final state Reduction of branching fraction dependence

13. RHUL Group Meeting 18. Dec. 03Henning Flächer 13 Calibration Curve True modes: D D* D** (two narrow +two broad) X H (4 spin dependent D (*) PI)  Large variety of different models and different final states M x true binning (example) Define calibration curve independent of underlying model!  binning in bins of M x true

14. RHUL Group Meeting 18. Dec. 03Henning Flächer 14 Calibration Curves Relate measured hadronic mass to true mass of X-system: linear relation as function of true mass irrespective of decay and underlying model 4 X H reso 4 X H nreso D* D Application of calibration results in true mass irrespective of decay mode and model

15. RHUL Group Meeting 18. Dec. 03Henning Flächer 15 If correction factor  1 and RMS small for PDF variations (i.e. dropping contributions to X H reso and X H nreso ) only a small systematic error for model and branching fraction dependence is achieved! Extraction Method – Full Formula The full formula has not only to take into account the mass bias but it must also account for lepton acceptance and efficiency differences R i. correction factor  Since we measure M x we of course also can get M x n Calibrate the measured mass event-by-event: Subtract remaining background

16. RHUL Group Meeting 18. Dec. 03Henning Flächer 16 Distribution of Bias Factors P*>1.1 GeV P*>0.9GeV RMS(P*>0.9) = 0.01 GeV 2 RMS(P*>1.1) = 0.01 GeV 2 Vary assumptions for X model: Change X composition: disregard single decay modes and combinations, i.e. drop them in pairs, triplets etc. and observe how MC correction changes Small model dependence! (GeV 2 ) Spread is small compared to other error sources: stat. error: 0.05 GeV 2 det. sys. error: 0.03 GeV 2 background: 0.04 GeV 2

17. RHUL Group Meeting 18. Dec. 03Henning Flächer 17 Result: First and Second Moment of M X Distribution Clear P* min dependence, reflecting increasing contribution from high mass final states. Points are highly correlated

18. RHUL Group Meeting 18. Dec. 03Henning Flächer 18 Crosscheck on MC Derive calibration and background subtraction from MC and apply to independent “MC data” sample. Works both, for lower P* min cut and differentially in bins of P* Moment Difference to true value

19. RHUL Group Meeting 18. Dec. 03Henning Flächer 19 Apply the complete extraction procedure to this data sample and measure as a function of the lepton momentum. Crosscheck on Data – Partial Reconstruction of D* + Select a data control sample where the true underlying mass is know Use the decay B0  D* + lν: Partially reconstruct D* decays by identifying a slow charged pion M D* 2

20. RHUL Group Meeting 18. Dec. 03Henning Flächer 20 Consistency of Results We split the data into statistically independent subsamples and repeated the measurement. Statistical Errors only!

21. RHUL Group Meeting 18. Dec. 03Henning Flächer 21 Interpretation in Context of HQET

22. RHUL Group Meeting 18. Dec. 03Henning Flächer 22 Reminder of Expansion perturbative expansion in α s non-perturbative expansion to first, second and third order in 1/m B Determine parameters Λ and λ 1 λ 2 known from B*-B and D*-D mass splitting Λ – mass difference between B meson and b quark λ 1 – negative of kinetic energy squared of b quark λ 2 - chromo-magnetic coupling of b quark spin to “brown muck” α s (2) 1/m B 1/m B 2 1/m B 3 One expansion for every P* cut

23. RHUL Group Meeting 18. Dec. 03Henning Flächer 23 Interpretation in context of HQET Fit for Λ and λ 1 by minimizing χ 2 taking correlations between data points into account The extracted parameters describe all hadronic mass moment measurements Prediction of P* dependence for using Λ from b  s γ and at P*min =1.5 GeV results in less consistent description. OPE prediction using CLEO data only and from b  s  OPE fit to the BABAR data  Calculations from Falk and Luke (Phys.Rev.D57:424-430,1998)

24. RHUL Group Meeting 18. Dec. 03Henning Flächer 24 Results in λ 1 -Λ plane Hadronic Mass Moments from all three Experiments overlap in same region. Band in λ 1 -Λ plane from b  sγ slightly offset Experimental Errors only! Δχ 2 =1 ellipse This fit is performed in the MS scheme for comparison with other experiments We extract λ 1 = -0.36 ± 0.09 GeV 2 and Λ = 0.53 ± 0.09 GeV CLEO: λ 1 = -0.24 ± 0.07 GeV 2 and Λ = 0.35 ± 0.07 GeV (experimental errors only)

25. RHUL Group Meeting 18. Dec. 03Henning Flächer 25 A more comprehensive Approach “External Input” Based on improved OPE calculations in the  (1S) mass scheme (Phys. Rev. D67. 05012, 2003) we can now include moment measurements in the fit as well as  SL  Simultaneous extraction of  HQE parameters and |V cb | ! (development of fit code in close collaboration with theorists) Calculate  SL from BABAR data only!  life time measurements and BR(B  Xl ) have by now reached a precession that makes  SL (BABAR) very competitive! Two possibilities: 1.Check consistency of the HQE calculations by comparing hadron moments from BABAR with other moment measurements (“external input”) 2.Use the BABAR hadron moments together with  SL (BABAR) to obtained an improved determination of |V cb | “BABAR Input” MeV

26. RHUL Group Meeting 18. Dec. 03Henning Flächer 26 Consistency of the HQE: Hadron Moments vs. Lepton Moments BABAR only Simultaneous extraction of |V cb |, m b 1S, and 1 1S from a fit to the HQE in the 1S mass scheme (O(1/m B 3 ) parameters are fixed in the fit) |V cb | - m b 1S plane 1 1S - m b 1S plane Note:  2 =1 contour include already part of the theory errors. Only O(1/m B 3 ) uncertainties are not included! Good agreement between BABAR moments and other hadron moment measurements Good agreement between BABAR moments and other hadron moment measurements  2 =1 contour of hadron moments and lepton moments do not overlap  indication for large O(1/m B 3 ) corrections or maybe even more …? (bear in mind that  SL is common in both fits!)

27. RHUL Group Meeting 18. Dec. 03Henning Flächer 27 |V cb | extracted using BABAR data only Caveat: We still have to establish the consistency of the OPE to at least the same level of accuracy we would like to achieve for |V cb | (<1%)! Precise measurement of |V cb | with input from BaBar data alone (life time, branching fractions, moments) and very competitive (3% total error)! [previous inclusive Vcb measurement from BABAR: |V cb | = 42.3  0.7(exp)  2.0(theo) ~5% (Phys. Rev. D67, 2002) ] BABAR only MeV * * Contributed to EPS03 in Aachen

28. RHUL Group Meeting 18. Dec. 03Henning Flächer 28 Summary and Conclusion We have measured the first and second moment of the M X distribution for different P* cuts (0.9 to 1.6 GeV). With a completely new and unique extraction approach we were able to overcome model uncertainty which leads to a significant improvement of the hadronic mass moment measurement. Using a simultaneous extraction of |V cb |, m b 1S, and 1 1S from a fit to the HQE calculations we obtain an improved measurement of Vcb which is based on BABAR data only! A comparison with other hadron moment measurements from CLEO and DELPHI demonstrates good agreement. A consistency test of hadron and lepton moments in the framework of the OPE leads to inconclusive results and demonstrates again the importance of the determination of all the O(1/m B 3 ) parameters from data. More moment measurements from different  More moment measurements from different physics processes will be needed to test HQET+OPE to the level of <1%. physics processes will be needed to test HQET+OPE to the level of <1%.

29. RHUL Group Meeting 18. Dec. 03Henning Flächer 29 Backup Slides

30. RHUL Group Meeting 18. Dec. 03Henning Flächer 30 The PEP-II B-Factory E [GeV] e + / e - 9.0 / 3.1 I [mA] e + / e - 1550 / 1175 Bunches 1034 L [cm -2 s -1 ] 6.582 x 10 33 L int [pb -1 /day] 395.1 Energy asymmetric e+-e- collider (peak performance)

31. RHUL Group Meeting 18. Dec. 03Henning Flächer 31 PEP-II and BaBar Performance This analysis is based on Run1+2 only (82 fb -1 ) Continuous improvement in delivered and recorded luminosity!

32. RHUL Group Meeting 18. Dec. 03Henning Flächer 32 The BABAR - Detector Cerenkov Detector (DIRC) 144 quartz bars 11000 PMTs 1.5 T Solenoid Electromagnetic Calorimeter 6580 CsI(Tl) crystals (electrons/photons) Drift Chamber 40 layers Instrumented Flux Return iron / RPCs (muon / neutral hadrons) Silicon Vertex Tracker 5 layers, double sided strips e + (3.1 GeV) e - (9 GeV) SVT: 97% efficiency, 15  m z hit resolution (inner layers, perp. tracks) SVT+DCH:  (p T )/p T = 0.13 %  p T + 0.45 % DIRC: K-  separation 4.2  @ 3.0 GeV/c  3.0  @ 4.0 GeV/c EMC:  E /E = 2.3 %  E -1/4  1.9 %

33. RHUL Group Meeting 18. Dec. 03Henning Flächer 33 Checks on Background Subtraction Select events where lepton charge is inconsistent with prompt B decay Fit MC shapes to data to obtain normalization Charged B’s Neutral B’s Contribution from B 0 -B 0 mixing _ MC scaling factor compatible with 1 0.8<P*<1.0 1.0<P*<1.4 P*>1.4 1.0<P*<1.4P*>1.4