1. Measurement of the B 0 s Oscillation Frequency: Matter-Antimatter Transformations at 3 THz Prof. Joseph Kroll University of Pennsylvania UCSD 16 May 2006

2. Joseph Kroll - UCSD Seminar 2 Presenting results on  m s and |V td /V ts | Data are from the CDF Collaboration at Fermilab CDF = 60 Institutions, > 700 Physicists All results are preliminary unless indicated otherwise

3. 16 May 2006Joseph Kroll - UCSD Seminar 3 Tevatron Performance Typical L = 10 32 cm -2 s -1 ∫Ldt = 1.5 fb -1 This analysis uses full data set: 1 fb -1

4. 16 May 2006Joseph Kroll - UCSD Seminar 4 Neutral Meson Flavor Oscillations (Mixing) Due to phase space suppression: K 0 L very long-lived: 5.2 £ 10 -8 s (K 0 S : 0.0090 £ 10 -8 s) 1954: over 50 years ago

5. 16 May 2006Joseph Kroll - UCSD Seminar 5 Long-Lived Neutral Kaon Led to discovery of CP Violation in 1964 (Nobel Prize in 1980) BF(K 0 L !  +  - ) = 0.2% Discovered in 1956 Phys. Rev. 103, 1901 (1956)

6. 16 May 2006Joseph Kroll - UCSD Seminar 6 Neutral Meson Mixing (Continued)

7. 16 May 2006Joseph Kroll - UCSD Seminar 7 Neutral B Meson Flavor Oscillations  = 1/  = 1.6 psec Units: We use ~ =1 and quote  m in ps -1 To convert to eV multiply by 6.582 £ 10 -4

8. 16 May 2006Joseph Kroll - UCSD Seminar 8 Until Two Months Ago… at least 3.5 cycles per lifetime

9. 16 May 2006Joseph Kroll - UCSD Seminar 9 Basic Measurement Principle Measure asymmetry A as a function of proper decay time t “unmixed”: particle decays as particle For a fixed value of  m s, data should yield Amplitude “A” is 1, at the true value of  m s Amplitude “A” is 0, otherwise “mixed”: particle decays as antiparticle

10. 16 May 2006Joseph Kroll - UCSD Seminar 10 Status of Published Results on  m s Results from LEP, SLD, CDF I  m s > 14.4 ps -1 95% CL see http://www.slac.stanford.edu/xorg/hfag/osc/PDG_2006/index.html Amplitude method: H-G. Moser, A. Roussarie, NIM A384 p. 491 (1997)

11. 16 May 2006Joseph Kroll - UCSD Seminar 11 Recent Result from DØ Collaboration 17 <  m s < 21 ps -1 @ 90% CL 1 st reported direct experimental upper bound Probability “Signal” is random fluctuation is 5% V. M. Abazov et al. hep-ex/0603029 submitted to Phys. Rev. Lett.

12. 16 May 2006Joseph Kroll - UCSD Seminar 12 Recent Result from the CDF Collaboration Probability “Signal” is random fluctuation is 0.5%

13. 16 May 2006Joseph Kroll - UCSD Seminar 13 The Flavor Parameters (CKM Matrix) mass eigenstates ≠ weak eigen. weak mass related by Cabibbo-Kobayashi-Maskawa Matrix V is unitary: V y V = 1Measurements + Unitarity assuming 3 generations PDG: S. Eidelman et al. Phys. Lett. B 592, 1 (2004) Ranges are 90% CL These fundamental parameters must be measured

14. 16 May 2006Joseph Kroll - UCSD Seminar 14 Wolfenstein Parametrization Illustrates Hierarchy Original reference: L. Wolfenstein, PRL, 51, p. 1945 (1983) See also: J. Charles et al., Eur. Phys. J. C41, p. 1 (2005); ibid, hep-ph/0406184 from hep-ph/0406184 Expand matrix in small parameter:  = V us = sin  Cabibbo » 0.2 3 £ 3 complex unitary matrix: 3 real & 1 imag. parameters ≡ 3 angles, 1 phase

15. 16 May 2006Joseph Kroll - UCSD Seminar 15 Neutral B Meson Flavor Oscillations Flavor oscillations occur through 2 nd order weak interactions e.g. Same diagrams and formula for  m s for B s except replace “d” with “s” All factors known well except “bag factor” £ “decay constant”  m d = 0.505 § 0.005 ps -1 (1%) (PDG 2005) from Lattice QCD calculations – see Okamoto, hep-lat/0510113 From measurement of  m d derive |V * tb V td | 2

16. 16 May 2006Joseph Kroll - UCSD Seminar 16 B Meson Flavor Oscillations (cont) If we measure  m s then we would know the ratio  m s /  m d Many theoretical quantities cancel in this ratio, we are left with Ratio measures |V td /V ts | This is why  m s is high priority in Run II Using measured  m d & B masses, expected |V ts /V td | Predict  m s » 18 ps -1 We know what to expect M. Okamoto Lattice 2005 hep-lat/0510113 PoS LAT2005 (2005) 013

17. 16 May 2006Joseph Kroll - UCSD Seminar 17 Why is this Interesting? Probe of New Physics Supersymmetric particles4 th Generation Additional virtual particles increase  m s Measured value can be used to restrict parameters in models e.g., Harnik et al. Phys. Rev. D 69 094024 (2004) e.g., W. Huo Eur. Phys. J. C 24 275 (2002)

18. 16 May 2006Joseph Kroll - UCSD Seminar 18 Experimental Steps for Measuring B s Mixing 1. Extract B 0 s signal – decay mode must identify b-flavor at decay (TTT) Examples: 2. Measure decay time (t) in B rest frame (L = distance travelled) (L00) 3. Determine b-flavor at production “flavor tagging” (TOF) “unmixed” means production and decay flavor are the same “mixed” means flavor at production opposite flavor at decay Flavor tag quantified by dilution D = 1 – 2w, w = mistag probability

19. 16 May 2006Joseph Kroll - UCSD Seminar 19 Measuring B s Mixing (cont.) 4. Measure asymmetry these formulas assume perfect resolution for t Asymmetry is conceptual: actually perform likelihood fit to expected “unmixed” and “mixed” distributions

20. 16 May 2006Joseph Kroll - UCSD Seminar 20 1 st Evidence: Time Integrated Mixing:   is the time integrated mixing probability In principle, a measurement of  determines  m - 1 st B d mixing measurements were  measurements -  d = 0.187 § 0.003 (PDG 2005) - this does not work for B s :  s = 0.5 (the limit as x !1 ) Inclusive measurements at hadron colliders, LEP, SLC yield 1987

21. 16 May 2006Joseph Kroll - UCSD Seminar 21 Discovery of Neutral B Flavor Oscillations Implications: m top >50 GeV/c 2 Top quark is heavier than expected Ellis, Hagelin, Rudaz, Phys. Lett. B 192, 201 (1987) UA1 1987: Evidence for B 0 & B 0 s mixing Followed up by observation of B 0 mixing by ARGUS: H. Albrecht et al., (25 June 87) Phys. Lett. B 192, 245 (1987)

22. 16 May 2006Joseph Kroll - UCSD Seminar 22 Measurement … In a Perfect World what about detector effects? “Right Sign” “Wrong Sign”

23. 16 May 2006Joseph Kroll - UCSD Seminar 23 Realistic Effects flavor tagging power, background displacement resolution momentum resolution mis-tag rate 40%  L) ~ 50  m  p)/p = 5%

24. 16 May 2006Joseph Kroll - UCSD Seminar 24 All Effects Together

25. 16 May 2006Joseph Kroll - UCSD Seminar 25 B Physics at Hadron Machines Strong interaction produces bb pairs Example of lowest order (LO)  s 2 Example of next leading order (NLO)  s 3 NLO contribution comparable to LO contribution see P. Nason, S. Dawson, R. K. Ellis Nucl. Phys. B273, p. 49 (1988) called “flavor creation” “gluon splitting” “flavor excitation” b pairs produced close in y

26. 16 May 2006Joseph Kroll - UCSD Seminar 26 B Physics at Hadron Machines (cont.) b quarks then fragment to B hadrons B factories running on Y(4S) only produce lightest B mesons Hadron colliders (and e + e - colliders running above Y(4S)) produce other B’s fragmentation is hard: B hadron gets large fraction of b quark E Many unique B measurements at hadron colliders e.g.,  m s, B s rare decays, observation B c,  b lifetime

27. 16 May 2006Joseph Kroll - UCSD Seminar 27 B Production at Tevatron The inclusive b cross-section is enormous: on the order of 100  b For L = 10 31 cm -2 s -1 (10 32 )   £ L = 1kHz (10kHz) Much of this not useful (trigger, acceptance, analysis selection criteria) The useful cross-section is order 10  b This is still well above production cross-section at B Factories, Z pole The CDF Collaboration, D. Acosta et al., Phys. Rev. D65, 052005 (2002) B factory rate: L = 10 34 cm -2 s -1   £ L = 10 Hz  £ L » 100 Hz

28. 16 May 2006Joseph Kroll - UCSD Seminar 28 Trigger Strategy for B Physics Exploit the characteristics of B production and decay 1. B mass relatively large  decay products have relatively high p T require p T > 1.5 – 2.0 GeV/c or larger 2. B decay produces high p T leptons (electron and muon) B !  X, e X & B ! J/  X, J/  !  +  - 3. B’s have long decay distance trigger on displaced tracks B0sB0s D-sD-s ++ -- K-K- K+K+ d0d0 4. Combine lepton & displaced track  b large, but  inelastic » 10 3 larger

29. 16 May 2006Joseph Kroll - UCSD Seminar 29 Silicon tracking Drift chamber Lumi monitor Hadronic Calorimetry Muon systems Iron shielding Solenoid and TOF Electromagnetic Calorimetry CDF II Front-end elec. & DAQ: 7.6 MHz clock (132 ns)

30. 16 May 2006Joseph Kroll - UCSD Seminar 30 Key Features of CDF for B Physics “Deadtime-less” trigger system –3 level system with great flexibility –First two levels have pipelines to reduce deadtime –Silicon Vertex Tracker: trigger on displaced tracks at 2 nd level Charged particle reconstruction – Drift Chamber and Silicon –excellent momentum resolution: R = 1.4m, B = 1.4T –lots of redundancy for pattern recognition in busy environment –excellent impact parameter resolution Particle identification –specific ionization in central drift chamber (dE/dx) –Time of Flight measurement at R = 1.4 m –electron & muon identification

31. 16 May 2006Joseph Kroll - UCSD Seminar 31 Silicon Vertex Tracker (SVT) d0d0 Luciano Ristori, INFN-Pisa

32. 16 May 2006Joseph Kroll - UCSD Seminar 32 Example of Specific Trigger for B Physics Hadronic Path – designed for B 0 s ! D - s  + Level 1 - 2 XFT tracks with p T > 1.5 GeV - opposite charge -  < 135 o - |p T1 | + |p T2 | > 5.5 GeV Level 2 - confirm L1 requirements - both XFT tracks - SVT  2 <15 - 120  m< |d 0 | <1mm - 2 o <  < 90 o - Decay length L xy > 200  m Level 3 - confirm L2 with COT & SVX “offline” quality track reco. At Level 3 using trigger criteria

33. 16 May 2006Joseph Kroll - UCSD Seminar 33 Semileptonic B 0 s Decay Modes Fully reconstructed better decay time resolution Lower statistics Signal 3,700 Not fully reconstructed poorer decay time resolution Higher statistics Signal 36,000 Hadronic } { }{ Majority of signal collected with displaced track trigger

34. 16 May 2006Joseph Kroll - UCSD Seminar 34 Example: Fully Reconstructed Signal Cleanest decay sequence Four charged particles in final state: K + K -  +  - Also use 6 body modes: Used for  m s analysis Signal: 1600 This mode only

35. 16 May 2006Joseph Kroll - UCSD Seminar 35 1992: First Direct Evidence of B s Signal Well known background poorly known background (small) Signal: 16.0 § 4.3 (  ) 17.0 § 4.5 (K *0 K) D. Buskulic et al. (Aleph) Phys. Lett. B 294, 145 (1992) also: P. Abreu et al. (Delphi) Phys. Lett. B 289, 199 (1992) P. D. Acton et al. (Opal) Phys. Lett. B 295, 357 (1992) Sample: 450K hadronic Z

36. 16 May 2006Joseph Kroll - UCSD Seminar 36 The Same Signal at CDF Today 48,000 s Purity: 75% from direct semileptonic B 0 s decay

37. 16 May 2006Joseph Kroll - UCSD Seminar 37 Lifetime Measurement production vertex 25  m £ 25  m Decay position Decay time in B rest frame  B 0 s ) = 1.538 § 0.040 ps (statistical error only) PDG 2006: 1.466 § 0.059 ps

38. 16 May 2006Joseph Kroll - UCSD Seminar 38 Aside: Recent  b Lifetime from CDF Uses fully reconstructed  b ! J/   instead of semileptonic:  c + l - l Analysis led by UCSD post-docs M. Neubauer, E. Lipedes Signal 542 § 38

39. 16 May 2006Joseph Kroll - UCSD Seminar 39 Unexpected result: Lifetime much larger than previously measured Precision of this measurement comparable to World average Problem with semileptonics? - sample composition - boost correction Measured lifetimes with control modes (B 0, B + ) agree well with other exps. Next step for CDF: use  b !  c 

40. 16 May 2006Joseph Kroll - UCSD Seminar 40 Decay Time Resolution: Hadronic Decays = 86 £ 10 -15 s ¼ period for  m s = 18 ps -1 Oscillation period for  m s = 18 ps -1 Maximize sensitivity: use candidate specific decay time resolution Superior decay time resolution gives CDF sensitivity at much larger values of  m s than previous experiments

41. 16 May 2006Joseph Kroll - UCSD Seminar 41 Measuring Resolution in Data Use large prompt D meson sample CDF II, D. Acosta et al., PRL 91, 241804 (2003) Real prompt D + from interaction point pair with random track from interaction point Compare reconstructed decay point to interaction point

42. 16 May 2006Joseph Kroll - UCSD Seminar 42 Semileptonics: Correction for Missing Momentum Reconstructed quantity Correction Factor (MC)Decay Time

43. 16 May 2006Joseph Kroll - UCSD Seminar 43 B Flavor Tagging We quantify performance with efficiency  and dilution D  = fraction of signal with flavor tag D = 1-2w, w = probability that tag is incorrect (mistag) Statistical error  A on asymmetry A (N is number of signal) statistical error scales with  D 2

44. 16 May 2006Joseph Kroll - UCSD Seminar 44 Two Types of Flavor Tags Opposite side Same sideBased on fragmentation tracks or B ** + Applicable to both B 0 and B 0 s − other b not always in the acceptance − Results for B + and B 0 not applicable to B 0 s + better acceptance for frag. tracks than opp. side b Reminder: for limit on  m s must know D Produce bb pairs: find 2 nd b, determine flavor, infer flavor of 1 st b Calibrate on B +, B 0 data Must rely on MC for D Requires Extensive comparison data and MC

45. 16 May 2006Joseph Kroll - UCSD Seminar 45 Types of Opposite Side Flavor Tags Lepton tags Jet charge tag Kaon tag mistags from jet from b (b) has negative (positive) charge on average low  high D high  low D Largest  D 2 @ B factories Not used in present analysis TOF

46. 16 May 2006Joseph Kroll - UCSD Seminar 46 Calibrate with Large Statistics Samples of B + & B 0 Example: semileptonic signals Results:  D 2 = 1.54 § 0.05 [  m d = 0.509 § 0.010 (stat) § 0.016 (syst)] Hadronic signals: B + (D 0  + ) = 26,000 B 0 (D -  + ) = 22,000

47. 16 May 2006Joseph Kroll - UCSD Seminar 47 Increase Tagging Power with “Binning” Example: lepton tags  p t rel

48. 16 May 2006Joseph Kroll - UCSD Seminar 48 Performance of OST’s is Poor – Why? Part of the problem is acceptance of opposite side b Generator Level study from K. Lannon, Ph. D. Dissertation, Illinois, 2003 Also opposite-side B hadron can mix: D = 1 – 2  = 0.76

49. 16 May 2006Joseph Kroll - UCSD Seminar 49 Same Side Flavor Tags Based on correlation between charge of fragmentation particle and flavor of b in B meson TOF Critical (dE/dx too) Decay of P-wave mesons B ** also contributes to B 0, B + (not B 0 s ) Expected correlations different for B +, B 0, B 0 s Ali & Barriero, Z. Phys. C 30, 365 (1986) Gronau, Nippe, Rosner PRD 47, 1988 (1993) Gronau & Rosner, PRD 49, 254 (1994)

50. 16 May 2006Joseph Kroll - UCSD Seminar 50 Time of Flight Detector (TOF) 216 Scintillator bars, 2.8 m long, 4 £ 4 cm 2 located @ R=140 cm read out both ends with fine mesh PMT (operates in 1.4 T B field – gain down ~ 400) measured resolution  TOF =100 - 130 ps (limited by photostatistics) Kaon ID for B physics Measured quantities: s = distance travelled t = time of flight p = momentum Derived quantities: v = s/t m = p/  v

51. 16 May 2006Joseph Kroll - UCSD Seminar 51 Kaons Produced in Vicinity of B’s Larger fraction of Kaons near B 0 s compared to B 0, B +, as expected Ph. D. Thesis, Denys Usynin

52. 16 May 2006Joseph Kroll - UCSD Seminar 52 Compare Performance Data and Simulation Check prediction for kaon tag on B +, B 0 Good agreement between data & MC Systematic based on comparisons K K  

53. 16 May 2006Joseph Kroll - UCSD Seminar 53 Flavor Tagging Summary Same-side kaon tag increases effective statistics £ 3 – 4  D 2 Hadronic (%)  D 2 Semileptonic (%) Muon 0.48 § 0.06 (stat)0.62 § 0.03 (stat) Electron 0.09 § 0.03 (stat)0.10 § 0.01 (stat) JQ/Vertex 0.30 § 0.04 (stat)0.27 § 0.02 (stat) JQ/Prob. 0.46 § 0.05 (stat)0.34 § 0.02 (stat) JQ/High p T 0.14 § 0.03 (stat)0.11 § 0.01 (stat) Total OST 1.47 § 0.10 (stat)1.44 § 0.04 (stat) SSKT 3.42 § 0.98 (syst)4.00 § 1.02 (syst)

54. 16 May 2006Joseph Kroll - UCSD Seminar 54 Combining it all unbinned maximum likelihood fit = Before fitting for  m s : test whole procedure by on B d mixing fix  m s integrate over true decay length ct and true k-factor get A(  m s ) k k kkk k=sig,bg sig for each event: pdg

55. 16 May 2006Joseph Kroll - UCSD Seminar 55 Amplitude Scan: Hadronic Decays

56. 16 May 2006Joseph Kroll - UCSD Seminar 56 Amplitude Scan: Semileptonic Decays

57. 16 May 2006Joseph Kroll - UCSD Seminar 57 Combined Amplitude Scan

58. 16 May 2006Joseph Kroll - UCSD Seminar 58 Results: Amplitude Scan A/  A = 3.5 Sensitivity 25.3 ps -1

59. 16 May 2006Joseph Kroll - UCSD Seminar 59 Measured Value of  m s - log(Likelihood) Hypothesis of A=1 compared to A= 0

60. 16 May 2006Joseph Kroll - UCSD Seminar 60 Significance: Probability of Fluctuation Probability of random fluctuation determined from data Probability = 0.5% (2.8  ) Below threshold to claim “observation” Continue improving analysis to increase potential significance

61. 16 May 2006Joseph Kroll - UCSD Seminar 61 Determination of |V td /V ts | Previous best result: D. Mohapatra et al. (Belle Collaboration) hep-ex/0506079 CDF

62. 16 May 2006Joseph Kroll - UCSD Seminar 62 Summary of CDF Results on B 0 s Mixing First direct measurement of  m s Precision: 2.4% Probability of random fluctuation: 0.5% Most precise measurement of |V td /V ts | All results are preliminary ( 2.76 THz, 0.011 eV)

63. 16 May 2006Joseph Kroll - UCSD Seminar 63 Perspective and Outlook Mixing in Neutral Kaons –led to discovery of CP violation –necessary condition for matter antimatter asymmetry in Universe. Mixing in B 0 mesons –led to possibility of observing CP Violation in another system –validated that SM mechanism for CP Violation is dominant mechanism. Discovery of B 0 mixing pointed to a much heavier top quark: –Results on B 0 s mixing could point to heavier new particles or exclude them Establishing B 0 s mixing sets the stage for the next step: –measuring CP asymmetries in B 0 s decays –could produce unambiguous signals of new physics. We are coming to the end of a long story: –a 20 year quest to measure  m s –a tremendous technical achievement –allows precise measurement of fundamental parameters

64. 16 May 2006Joseph Kroll - UCSD Seminar 64 Additional Slides for Reference

65. 16 May 2006Joseph Kroll - UCSD Seminar 65 Systematic Uncertainties related to absolute value of amplitude, relevant only when setting limits –cancel in A/  A, folded in in confidence calculation for observation –systematic uncertainties are very small compared to statistical Hadronic Semileptonic

66. 16 May 2006Joseph Kroll - UCSD Seminar 66 Systematic Uncertainties on  m s systematic uncertainties from fit model evaluated on toy Monte Carlo have negligible impact relevant systematic unc. from lifetime scale Syst. Unc SVX Alignment0.04 ps -1 Track Fit Bias0.05 ps -1 PV bias from tagging0.02 ps -1 All Other Sys< 0.01ps -1 Total0.07 ps -1 All relevant systematic uncertainties are common between hadronic and semileptonic samples

67. 16 May 2006Joseph Kroll - UCSD Seminar 67 Amplitude Scan: Hadronic Period 1 B s ! D s  / D s 

68. 16 May 2006Joseph Kroll - UCSD Seminar 68 Amplitude Scan: Hadronic Period 2 B s ! D s  / D s 

69. 16 May 2006Joseph Kroll - UCSD Seminar 69 Amplitude Scan: Hadronic Period 3 B s ! D s  / D s 

70. 16 May 2006Joseph Kroll - UCSD Seminar 70 Semileptonic Scan: Period 1

71. 16 May 2006Joseph Kroll - UCSD Seminar 71 Semileptonic Scan: Period 2

72. 16 May 2006Joseph Kroll - UCSD Seminar 72 Semileptonic Scan: Period 3

73. 16 May 2006Joseph Kroll - UCSD Seminar 73 The Unitarity Triangles V is unitarity  geometric representation: triangle in complex plane Im Re V i1 V * k1 V i2 V * k2 V i3 V * k3 There are 6 triangles Kaon UT Beauty UT flat n.b. these triangles are rescaled by one of the sides i = 1 is previous page

74. 16 May 2006Joseph Kroll - UCSD Seminar 74 The Beauty Unitary Triangle  of Chau & Keung parametrization is 

75. 16 May 2006Joseph Kroll - UCSD Seminar 75 http://www.slac.stanford.edu/xorg/ckmfitter/ckm_intro.html J. Charles et al., Eur. Phys. J. C41, p. 1 (2005); ibid, hep-ph/0406184 Results from CKM Fitter with recent CDF  m s result

76. 16 May 2006Joseph Kroll - UCSD Seminar 76 http://www.slac.stanford.edu/xorg/ckmfitter/ckm_intro.html J. Charles et al., Eur. Phys. J. C41, p. 1 (2005); ibid, hep-ph/0406184