1. Lecture 2: Time-Dependent Measurements with Flavor and CP Samples oReconstruction of B meson samples oLifetimes and B 0 oscillation measurements with flavor eigenstate decay

2. Aug 5-7, 2002 D.MacFarlane at SSI 2002 2 B-Flavor Tagging Exclusive B Meson Reconstruction (flavor eigenstates) lifetime, mixing analyses (CP eigenstates) CP analysis Experimental Technique for B Factories  (4S) produces coherent B pair: t   t Time-integrated asymmetries are zero

3. Aug 5-7, 2002 D.MacFarlane at SSI 2002 3 Main Variables for B Reconstruction For exclusive B reconstruction, two nearly uncorrelated * kinematic variables are used: B candidate (energy, 3-momentum) and beam energy in  (4S) frame Signal at  E ~ 0 Signal at m ES ~ m B Resolutions “Energy- substituted mass” * If  E were zero, the variables would be fully correlated; however,  E is typically at least 5 times larger than  beam and so dominates  E

4. Aug 5-7, 2002 D.MacFarlane at SSI 2002 4 Example for Hadronic B Decays m ES EE sidebands signal region B0  J/KSB0  J/KS m ES [GeV/c 2 ]  E [MeV]

5. Aug 5-7, 2002 D.MacFarlane at SSI 2002 5 Continuum Background Suppression  Separate 2-jet continuum from spherical BB events via event shape variables Ratio of second-to-zero th order Fox-Wolfram moments (R 2 ): B decays Continuum R2R2 Angle of thrust axis of “rest of the event” wrt B candidate direction (  T ) cos  T

6. Aug 5-7, 2002 D.MacFarlane at SSI 2002 6  Select intermediate mesons using either mass or mass difference:  After selection, candidates are constrained to nominal masses Inclusive Open Charm States D *+  D 0  + D 0  K -  + D 0  K +  - m(K -  + ) [GeV/c 2 ]  m [GeV/c 2 ]

7. Aug 5-7, 2002 D.MacFarlane at SSI 2002 7 Inclusive Charmonium Signals

8. Aug 5-7, 2002 D.MacFarlane at SSI 2002 8 Flavor Eigenstate Neutral B Sample N tag = 23618 Purity = 84% N tag = 1757 Purity = 96% Charm decay modes B decay modes B A B AR 81.3 fb  B A B AR 81.3 fb  m ES [GeV/c 2 ] Self-Tagging Modes

9. Aug 5-7, 2002 D.MacFarlane at SSI 2002 9 Flavor Eigenstate Charged B Sample N tag = 15915 Purity = 87% N tag = 6245 Purity = 94% Charm decay modes B decay modes B A B AR 81.3 fb  B A B AR 81.3 fb  m ES [GeV/c 2 ] Self-Tagging Modes

10. Aug 5-7, 2002 D.MacFarlane at SSI 2002 10 Golden Sample: (cc)K S CP Eigenstates (2S)K s  c1 K s B A B AR 81.3 fb  B A B AR 81.3 fb  N cand = 974 Purity = 97% Candidates & purity for m ES > 5.27 GeV/c 2 N cand = 150 Purity = 97% N cand = 170 Purity = 89% N cand = 80 Purity = 95%

11. Aug 5-7, 2002 D.MacFarlane at SSI 2002 11 Selecting candidates for B  J/  K L  K L detected by nuclear interactions in EMC or IFR o EMC neutral clusters with energy between 0.2 and 2.0 GeV Veto clusters forming  0 s with any other photon (E  > 30 MeV) Remove clusters (E > 1 GeV) containing two distinct bumps o IFR neutral clusters are 2 or more RPC layers that are unmatched to any projected charged track o Only able to determine angle of K L wrt interaction point, not energy  B candidates formed from mass-constrained J/   l + l - and K L candidates o Since there should be missing momentum along K L direction, cut on difference between observed and expected o Use cuts on J/   l + l - helicity angle (sin 2  h for signal) and B candidate polar angle (sin 2  wrt to z-axis)

12. Aug 5-7, 2002 D.MacFarlane at SSI 2002 12 Final Candidate Selection  Apply constraint of known m B mass & K L direction to determine momentum p KL  Search for signal in the one remaining variable expressed as: signal bkg EMC Remove measured – expected missing p t [GeV/c]

13. Aug 5-7, 2002 D.MacFarlane at SSI 2002 13 CP Eigenstate Sample: B  J/  K L B A B AR 81.3 fb  B A B AR 81.3 fb  Signal J/  Bkg Fake J/  Bkg N cand = 988 Purity = 55% Estimated with MC Estimated with sidebands Resolution of about 10 MeV for  E after m B constraint

14. Aug 5-7, 2002 D.MacFarlane at SSI 2002 14 Sample B 0  J/  K L Event   KLKL

15. Aug 5-7, 2002 D.MacFarlane at SSI 2002 15 One More Mode for CP Sample N cand = 147 Purity 81% B A B AR 81.3 fb  B A B AR 81.3 fb  BABAR PRL 87, 241801 (2001) BELLE hep-ex/0205021 Conclude: J/  mostly CP even

16. Aug 5-7, 2002 D.MacFarlane at SSI 2002 16 Angular Analysis at BABAR K * modes without  0 K * modes with  0 Projections of fits for amplitudes and rescattering phases:

17. Aug 5-7, 2002 D.MacFarlane at SSI 2002 17 Time-Dependent Analysis Strategies Measurements Higher precision Factorize the analysis into building blocks Increasing complexity a)Reconstruction of B mesons in flavor eigenstates b)B vertex reconstruction c)Flavor Tagging + a + b d)Reconstruction of neutral B mesons in CP eigenstates + a + b + c Analysis Ingredient

18. Aug 5-7, 2002 D.MacFarlane at SSI 2002 18 Measurement of B 0 and B + Lifetime 3. Reconstruct inclusively the vertex of the “other” B meson (B TAG ) 4. Compute the proper time difference  t 5. Fit the  t spectra (4s)  = 0.55 Tag B  z ~ 110 m Reco B  z ~ 65 m ++ zz t  z/c K0K0  D-D- -- -- K+K+ 1.Fully reconstruct one B meson in flavor eigenstate (B REC ) 2.Reconstruct the decay vertex

19. Aug 5-7, 2002 D.MacFarlane at SSI 2002 19  B Decay Time (ps) perfect resolution B-Lifetimes: Time Distributions Production point of B meson is known with good accuracy Proper time difference obtained from distance  z between the two B vertices LEP/CDF B Factories  B Decay Time Difference (ps) perfect resolution Control of the resolution function at negative times  B Decay Time (ps) finite resolution Fit the parameters of the resolution function together with the lifetime finite resolution  B Decay Time Difference (ps)

20. Aug 5-7, 2002 D.MacFarlane at SSI 2002 20 Vertex and  z Reconstruction B rec vertex B rec daughters z 1.Reconstruct B rec vertex from B rec daughters Beam spot Interaction Point B rec direction B tag direction 2.Reconstruct B tag direction from B rec vertex & momentum, beam spot, and  (4S) momentum = pseudotrack B tag Vertex tag tracks, V 0 s 3.Reconstruct B tag vertex from pseudotrack plus consistent set of tag tracks 4.Convert from Δz to Δt, accounting for (small) B momentum in  (4S) frame Result: High efficiency (97%) and σ ( Δz) rms ~ 180μm versus ~ βγcτ = 260μm

21. Aug 5-7, 2002 D.MacFarlane at SSI 2002 21 Conversion from  z to  t Proper time difference: Boost Approximation Improved Boost Approximation 0.2% effect Average  B Approximation Improves resolution by 5% in quadrature

22. Aug 5-7, 2002 D.MacFarlane at SSI 2002 22 Actual Δt Signal Resolution Function (Δ t meas - Δ t true )/ σ(Δ t) Signal MC: Δt resolution function Asymmetric RF: Tracks from long- lived charm in tag vertex ~0.6 ps Event-by-event σ ( Δt) from vertex errors σ(Δ z) [cm] Empirical Models with parameters fit to data: Gaussian convolved with an exponential [lifetime] or Triple Gaussian [mixing, CP]

23. Aug 5-7, 2002 D.MacFarlane at SSI 2002 23 Effect of Charm Tracks on  t D flight direction bias  (z tag ) Charm tracks z tag Prompt B tracks  t true  t meas z rec  t meas –  t true < 0  t > 0 z axis D flight direction bias  (z tag ) Charm tracks z tag Prompt B tracks  t true  t meas z rec  t meas –  t true < 0  t < 0 Underlying principle: tag vertex dominates resolution

24. Aug 5-7, 2002 D.MacFarlane at SSI 2002 24 Gaussian-Exponential  t Resolution Model Parameters: f = fraction in core Gaussian component S = scale factor for estimated event-by-event errors  = effective lifetime for charm bias component Core Gaussian Gaussian convolved with exponential Motivated by inclusion of charm decay products in determination of B tag vertex, creating a small bias in the mean residual  t distribution Outlier component (measurement error not applicable) added explicitly to PDF used in likelihood fit with one additional free parameter f outlier Event-by-event uncertainties from vertex fits  (  t)

25. Aug 5-7, 2002 D.MacFarlane at SSI 2002 25 Method for Extracting Lifetime Global unbinned maximum likelihood technique Includes probability-density functions (PDFs) for signal & backgrounds Incorporates model for  t resolution function for signal & background Primary advantages: Incorporates all correlations between parameters describing dataset Extracts maximum statistical precision for desired result Cautions: Need to build reasonable model that incorporates physical correlations Need to thoroughly test the model with Monte Carlo simulation to verify complete understanding

26. Aug 5-7, 2002 D.MacFarlane at SSI 2002 26 Likelihood Function for Lifetime Fits Signal model: Background model: Outlier model: Two single-sided exponentials convolved with signal Gaussian resolution function Prompt and lifetime components convolved with separate background Gaussian resolution function Gaussian with zero mean and fixed 10 ps width Probability Density Function (PDF): Likelihood Function: Assign probabilities for individual events to be signal (p sig,i ) or background (1- p sig,i ), based on observed m ES value and a separate global fit to the m ES distribution for the sample Sum PDFs for charged and neutral samples for a combined fit with a total of 19 free parameters Likelihood Function

27. Aug 5-7, 2002 D.MacFarlane at SSI 2002 27 Likelihood Function for Lifetime Fits Signal model: Background model: Outlier model: Two single-sided exponentials convolved with signal Gaussian resolution function Prompt and lifetime components convolved with separate background Gaussian resolution function Gaussian with zero mean and fixed 10 ps width Probability Density Function (PDF): Likelihood Function: Assign probabilities for individual events to be signal (p sig,i ) or background (1- p sig,i ), based on observed m ES value and a separate global fit to the m ES distribution for the sample Sum PDFs for charged and neutral samples for a combined fit with a total of 19 free parameters

28. Aug 5-7, 2002 D.MacFarlane at SSI 2002 28 Likelihood Function Likelihood Function for Lifetime Fits Signal model: Background model: Outlier model: Probability Density Function (PDF):

29. Aug 5-7, 2002 D.MacFarlane at SSI 2002 29 Signal and Background Probabilities signal: 6967  95 purity  90 % signal: 7266  94 purity  93 % GaussianARGUS function m ES (GeV/c 2 ) wrong-charge contamination m ES (GeV/c 2 ) p sig,i ~ 0p sig,i ~ 0.9 Background properties from sideband events B A B AR 20.6 fb  B A B AR 20.6 fb  Neutral B Mesons Charged B Mesons ARGUS background function:

30. Aug 5-7, 2002 D.MacFarlane at SSI 2002 30 B-Lifetime Measurements  Good agreement with previous lifetime measurements  Excellent control of the time resolution function (parameterization, tails) (error PDG2000 ~ 0.03 ps, stat+syst) BABAR PRL 87, 201803 (2001) Proof of principle for time-dependent analysis at B Factories background B A B AR 20.7 fb  B A B AR 20.7 fb 

31. Aug 5-7, 2002 D.MacFarlane at SSI 2002 31 B-Lifetime Measurements  Good agreement with previous lifetime measurements  Excellent control of the time resolution function (parameterization, tails) (error PDG2000 ~ 0.03 ps, stat+syst) Belle PRL 88, 171801 (2002) Proof of principle for time-dependent analysis at B Factories background Belle 29.1 fb  Belle

32. Aug 5-7, 2002 D.MacFarlane at SSI 2002 32 Measurement of B 0 B 0 Mixing 3. Reconstruct Inclusively the vertex of the “other” B meson (B tag ) 5. compute the proper time difference  t (4s)  = 0.55 Tag B  z ~ 110 m Reco B  z ~ 65 m ++ zz t  z/c K0K0  D-D- -- -- K+K+ 1. Fully reconstruct one B meson in flavor eigenstate (B rec ) 2. Reconstruct the decay vertex 3. Reconstruct Inclusively the vertex of the “other” B meson (B tag ) 4. Determine the flavor of B tag to separate Mixed and Unmixed events Tag B  z ~ 110 m 5. compute the proper time difference  t 6. Fit the  t spectra of mixed and unmixed events

33. Aug 5-7, 2002 D.MacFarlane at SSI 2002 33 Methods for B Flavor Tagging Many different physics processes can be used Secondary lepton Kaon(s) Soft pions from D * decays Fast charged tracks Primary lepton

34. Aug 5-7, 2002 D.MacFarlane at SSI 2002 34  Use charge correlations with decay products to define two physics categories o “Lepton” o “Kaon”  Multivariable techniques used to combine PID, kinematic variables, correlations, event information o e.g., primary lepton without PID, soft pions from D* decays o Multivariable analysis with neural network techniques: “NT1”, “NT2” categories Flavor Tagging for Mixing Study

35. Aug 5-7, 2002 D.MacFarlane at SSI 2002 35 Electron ID at BABAR o Match track to EMC cluster o 0.89 < E EMC /p < 1.2 o EM shower shape requirements o DCH dE/dx and DIRC Cherenkov angle consistent with electron hypothesis eff e=91%,  misid=0.13%

36. Aug 5-7, 2002 D.MacFarlane at SSI 2002 36 Electron ID at Belle o Match track to ECL cluster o E ECL /p ratio requirement o EM shower shape requirements, track- cluster matching o DCH dE/dx, TOF, ACC consistent with electron hypothesis eff e=94%,  misid=0.5%

37. Aug 5-7, 2002 D.MacFarlane at SSI 2002 37 Muon ID at BABAR o # int. lengths in IFR >2.2 o Difference in measured and expected int. length <1 o Match bet’n extrapolated track and IFR hits o Requirements on average and spread of # of IFR hits per layer eff  =75%,  misid=2.5%

38. Aug 5-7, 2002 D.MacFarlane at SSI 2002 38 Muon ID at Belle o Difference in measured and expected range o Match bet’n extrapolated track and KLM hits o Likelihood based selection eff  =90%,  misid=1% Open = Loose; Closed = Tight Efficiency Pion fake rate

39. Aug 5-7, 2002 D.MacFarlane at SSI 2002 39 Some Inputs to NN Tagger Opening angle between input track and thrust axis of recoil B Sum of energy within 90 o of estimated W direction Opening angle between input track and missing momentum vector CMS momentum of input track

40. Aug 5-7, 2002 D.MacFarlane at SSI 2002 40 Flavor Tagging Performance in Data Tagging category Fraction of tagged events  (%) Wrong tag fraction w (%) Mistag fraction difference  w (%) Q =  (1-2w) 2 (%) Lepton 10.9  0.39.0  1.4 0.9  2.2 7.4  0.5 Kaon35.8  1.017.6  1.0-1.9  1.515.0  0.9 NT1 7.7  0.222.0  2.1 5.6  3.2 2.5  0.4 NT2 13.8  0.335.1  1.9-5.9  2.7 1.2  0.3 ALL68.4  0.726.1  1.2 The large sample of fully reconstructed events provides the precise determination of the tagging parameters required in the CP fit Highest “efficiency” Smallest mistag fraction B A B AR 29.7 fb  B A B AR 29.7 fb  Error on sin2  and  m d depend on the “quality factor” Q approx. as:

41. Aug 5-7, 2002 D.MacFarlane at SSI 2002 41 B-Mixing Analysis:Time Distributions perfect flavor tagging, time resolution realistic mistag probability, finite time resolution

42. Aug 5-7, 2002 D.MacFarlane at SSI 2002 42 Triple-Gaussian  t Resolution Model Core Gaussian Tail Gaussian Outlier Gaussian Parameters: f = fractions in tail and outlier S = scale factor for estimated event- by-event errors b = bias factor due to inclusion of charm products in tag vertex Event-by-event uncertainties from vertex fits  (  t)

43. Aug 5-7, 2002 D.MacFarlane at SSI 2002 43 Monte Carlo Correlation:  (  t) and residual  t bias z axis z tag Prompt B tracks Charm tracks D flight direction  (  t) smallest,  t bias zero  (z tag ) D flight direction bias  (z tag ) Charm tracks z tag Prompt B tracks  (  t) largest,  t bias largest

44. Aug 5-7, 2002 D.MacFarlane at SSI 2002 44 Mistag fraction versus vertex error for kaon tags Yet another correlation! Tests of likelihood fit with full Monte Carlo shows bias of +0.007  0.003 for  m d (about 40% of statistical error!) Mystery: Resolved! p t spectrum of wrong-sign kaons softer than those in correct-tag processes Systematic difference in p t leads to correlation

45. Aug 5-7, 2002 D.MacFarlane at SSI 2002 45 Fit Results for Signal Resolution Parameters Run 1Run 2 S core 1.37  0.091.18  0.11 b core lepton0.06  0.13-0.04  0.16 b core kaon-0.22  0.08-0.25  0.09 b core NT1-0.07  0.15-0.45  0.21 b core NT2-0.46  0.12-0.20  0.16 b tail -5.0  4.2-7.5  2.4 f tail 0.014  0.0200.015  0.010 f outlier 0.008  0.0040.000  0.014 Non-zero bias for kaons

46. Aug 5-7, 2002 D.MacFarlane at SSI 2002 46 Additions to the Likelihood Function 1. Allow for difference in B 0 vs B 0 mistag rates PDFs now depend on tag state as well 2. Allow for prompt and non-prompt background components Adds fractions for each tagging category, effective lifetime for non-prompt component, and “effective dilutions” for both 8 parameters 4+1+8 parameters

47. Aug 5-7, 2002 D.MacFarlane at SSI 2002 47 Blind Analyses  Analyses were done “blind” to eliminate possible experimenters’ bias o In general, measurements of a quantity “X” are done with likelihood fits – blinding achieved by replacing “X” with “X+R” in likelihood fits R is drawn from a Gaussian with a width a few times the expected error Random number sequence is “seeded” with a “blinding string” The reported statistical error is unaffected Allows all systematic studies to be done while still blind

48. Aug 5-7, 2002 D.MacFarlane at SSI 2002 48  m d Likelihood Fit Combined unbinned maximum likelihood fit to  t spectra of mixed and unmixed events in the B flavor sample All  t parameters extracted from data Correct estimate of the error and correlations Fit Parameters#Main Sample mdmd 1Signal Mistag fractions for B 0 and B 0 tags8Signal Signal resolution function 2x8 *Signal Description of background  t5+8Sidebands Background  t resolution2x3 *Sidebands B lifetime from PDG 20020  B = 1.548 ps Total parameters44 * 2 running periods

49. Aug 5-7, 2002 D.MacFarlane at SSI 2002 49 Likelihood Function for Mixing Fits Signal model: Background model: Outlier model: PDF with  m d [1] for mixed and unmixed events convolved with triple Gaussian signal resolution function [8] for 2 periods of alignment. Dilutions and dilution differences [8] are also incorporated. Prompt and lifetime components [5] for mixed and unmixed samples convolved with a common background double Gaussian resolution function [3] for 2 periods of alignment. Separate dilutions and dilution differences incorporated [8]. Incorporated into resolution functions as Gaussian, with zero mean and fixed 8 ps width Probability Density Function (PDF): Likelihood Function: Assign probabilities for individual events to be signal (p sig,i ) or background (1- p sig,i ), based on observed m ES value and a separate global fit to the m ES distribution for the sample Sum PDFs for mixed and unmixed samples for a combined fit with a total of 44 free parameters 1+2x8+8 parameters 5+2x3+8 parameters

50. Aug 5-7, 2002 D.MacFarlane at SSI 2002 50 Final Tagged Mixing Sample Gaussian ARGUS function p sig,i ~ 0p sig,i ~ 0.96 Background properties from sideband events Lepton Kaon Lepton NT2NT1

51. Aug 5-7, 2002 D.MacFarlane at SSI 2002 51 BABAR PRL 88, 221802 (2002) Mixing with Hadronic Sample B A B AR 29.7 fb  B A B AR 29.7 fb  Precision measurement consistent with world average Signal: m ES >5.27 Bgnd: m ES <5.27

52. Aug 5-7, 2002 D.MacFarlane at SSI 2002 52 Mixing Asymmetry with Hadronic Sample Unfolded raw asymmetry  t [ps] Folded raw asymmetry |  t| [ps] B A B AR 29.7 fb  B A B AR 29.7 fb 

53. Aug 5-7, 2002 D.MacFarlane at SSI 2002 53 Systematic Errors on  m d [md][md] Description of background events0.004 Background fractions, sideband extrapolation Background  t structure and resolution Peaking B+ background  t resolution and detector effects0.005 Silicon detector residual misalignment  t resolution model  (  t) requirement Fit bias correction and MC statistics0.003 Fixed lifetime from PDG2000 *0.006 Total0.010 * Now improved with PDG2002

54. Aug 5-7, 2002 D.MacFarlane at SSI 2002 54 Mixing in Hadronic Modes at Belle BELLE 29.1 fb  BELLE

55. Aug 5-7, 2002 D.MacFarlane at SSI 2002 55 1. Fully reconstruct one B meson in CP eigenstate (B rec ) 2. Reconstruct the decay vertex 1. Fully reconstruct one B meson in CP eigenstate (B rec ) 2. Reconstruct the decay vertex 5. compute the proper time difference  t 6. Fit the  t spectra of B 0 and B 0 tagged events 5. compute the proper time difference  t 6. Fit the  t spectra of B 0 and B 0 tagged events Measurement of sin2  3. Reconstruct Inclusively the vertex of the “other” B meson (B tag ) 4. Determine the flavor of B tag to separate B 0 and B 0 (4s)  = 0.56 Tag B  z ~ 110 m Reco B  z ~ 65 m -- zz t  z/c K0K0  KS0KS0 -- ++ ++

56. Aug 5-7, 2002 D.MacFarlane at SSI 2002 56 Time-Dependent CP Asymmetries Use the large statistics B flav data sample to determine the mistag probabilities and the parameters of the time-resolution function Time-dependence of CP-violating asymmetry in Time-dependence of (Assuming no confusion of B rec state)

57. Aug 5-7, 2002 D.MacFarlane at SSI 2002 57 Summary  Precision measurements of lifetimes and B0 oscillations have been performed at the B Factories o Require the development of all techniques for B reconstruction, determination of vertex separation, tagging of the recoil B state at decay, unbinned maximum likelihood fitting and validation procedures o Results are in excellent agreement with previous results and represent some of the single most-precise measurements available  m d = 0.516 ± 0.016 (stat) ± 0.010 (syst) ps -1 BELLE preprint-02/020, hep-ex/0207022, to appear in PLB BABAR PRL 88, 221802 (2002)  m d = 0.528 ± 0.017 (stat) ± 0.011 (syst) ps -1  Tomorrow o Apply tools to measurement of CP violation in neutral B decays

58. Aug 5-7, 2002 D.MacFarlane at SSI 2002 58 Bibliography: Lecture 2 1.[lifetime] BABAR Collab., B.Aubert et al., PRL 87, 201803 (2001) 2.[lifetime] Belle Collab., K.Abe et al., PRL 88, 171801 (2002) 3.[mixing] BABAR Collab., B.Aubert et al., PRL 88, 221802 (2002) 4.[mixing] Belle Collab, T.Tomura et al., hep-ex/0207022, to appear in PLB 5.[mixing] BABAR Collab., B.Aubert et al., hep-ex/0201020, to appear in PRD