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B0s – B0s Oscillations: A 20-Year Perspective

This presentation provides a comprehensive overview of the observation of B0s – B0s oscillations over the past two decades, focusing on measurements of mixing probabilities and frequencies in the B meson system. It highlights the importance of neutral B meson oscillations in testing fundamental principles of quantum mechanics and the Standard Model. The speaker, Joseph Kroll from the University of Pennsylvania, outlines the historical background, key experiments, and latest findings in this field, emphasizing the significance of precise measurements in understanding particle interactions. The talk delves into the Cabibbo-Kobayashi-Maskawa matrix, oscillation frequencies, and the implications of new particles on the unitary triangle. References are provided for further reading on the topic.

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B0s – B0s Oscillations: A 20-Year Perspective

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  1. The Observation of B0s – B0s Oscillations:a 20 Year Perspective CKM 2006 Nagoya 12-16 Dec 2006 Joseph Kroll University of Pennsylvania 23 Nov 2006, Music Pier, Ocean City, NJ, photo: Tom Welsh

  2. Outline • Reminder of the importance of measuring md,s • Measurements of time integrated mixing probability  • Measurements of md • Measurements of ms I only show published results References highlighted in green If two uncertainties are shown: 1st is statistical, 2nd is systematic J. Kroll (Penn) CKM 2006

  3. From the Abstract: “Combined with the null result from searches for B0$ B0 oscillations at e+e- colliders, our results are consistent with with transitions in the B0s system as favoured theoretically” Our Story Begins 20 Years Ago UA1 1986: Evidence for B0 & B0s mixing C. Albajar et al., Phys. Lett. B 186, 247 (1987) H.-G. Moser, “Dimuon Production at the CERN p-pbar Collider, RWTH Aachen,PITHA 87-22 (1987) B mixing probability: B0s not yet directly observed J. Kroll (Penn) CKM 2006

  4. Common decay modes ! 2-state QM system Eigenstates of 2-state system (neglecting CP violation) “Light” (CP-even) “Heavy” (CP-odd) Start (t=0) with particle Antiparticle exists at time t! Two-State Quantum Mechanical System mass & width J. Kroll (Penn) CKM 2006

  5. “If there is any place where we have a chance to test the main principles of quantum mechanics in the purest way – does the superposition of amplitudes work or doesn’t it – this is it.” comment concerning K0’s R. P. Feynman in Lectures on Physics Vol. III J. Kroll (Penn) CKM 2006

  6. Importance of Neutral B Meson Oscillations fundamental parameters that must be measured Cabibbo-Kobayashi-Maskawa Matrix mass weak Oscillation frequencies (md, ms) determine poorly known Vtd, Vts |Vtd| & |Vtd/Vts| measure one side of Unitary Triangle New particles in loops alter expectations  test Standard EWK Model J. Kroll (Penn) CKM 2006

  7. All factors well known except from Lattice QCD calculations (Okamoto, hep-lat/0510113) Limits precision on Vtd, Vts to ~ 10% Theoretical uncertainties reduced in ratio: ~ 4% PDG 2006 J. Kroll (Penn) CKM 2006

  8. Some History Important prehistory: 1983: long B hadron lifetime 2006 APS Panofsky Prize 1986: 1st evidence of B mixing from UA1 C. Albajar et al., PLB, 186, 247 (1987) 1987: Definitive observation of B0 mixing by ARGUS - indicates UA1 must be Bs, heavy top (>50 GeV) - 1989 confirmed by CLEO H. Albrecht et al., PLB, 192, 245 (1987) M. Artuso et al., PRL, 62, 2233 (1989) 1990’s: LEP, SLC, Tevatron - time-integrated meas. establishes Bs mixes (maximally) - measure time-dependent B0 oscillations - lower limits on Bs oscillation frequency too many references to list individually 2000: B factories improve precision of B0 oscillation frequency Belle: K. Abe et al., PRD 71, 072003 (2005) Babar: B. Aubert et al., PRD 73, 012004 (2006) 2006: Tevatron discovers Bs oscillations - two-sided 90% CL limit by DØ - 1st measurement of oscillation frequency by CDF - definitive observation of oscillation signal by CDF V. M. Abazov et al., PRL, 97, 021802 (2006) A. Abulencia et al., PRL, 97, 021802 (2006) & PRL, 97, 242003 (2006) J. Kroll (Penn) CKM 2006

  9. e, b sample thrust axis c sample 100m background 500m 1983: B Hadron Lifetime Measurement 2006 Panofsky Prize: Bill Ford, John Jaros, Nigel Lockyer Signed impact parameter (no Silicon) PEPII SLC & SLD: xy = 3.5m Z = 17m MAC: E. Fernandez et al., PRL 51 1022 (1983) MarkII: N. Lockyer et al., PRL 51 1316 (1983) J. Kroll (Penn) CKM 2006

  10. Measure probability B decays as B: Measure probability B decays as B as a function of proper decay time t Methods to Measure m Time Integrated (assuming = 0) Mixing first established with time integrated quantities Time Dependent (required for m À ) (LEP, LHC, SLC, Tevatron) m = oscillation frequency J. Kroll (Penn) CKM 2006

  11. First Signature for B Mixing: Like-Charge Leptons Based on semileptonic B decay: Account for: Coherent incoherent J. Kroll (Penn) CKM 2006

  12. UA1: 1st Evidence for B Mixing Measured: for no mixing, but b! c!l etc. Expected: Determined: no mixing disfavored at 2.9 Combination of B0 & B0s mixing 0.1 0.2 C. Albajar et al., Phys. Lett. B 186, 247 (1987) J. Kroll (Penn) CKM 2006

  13. ARGUS: Observation of B0 Oscillations 1 fully reconstructed event with two B0’s (two +) Measured d using r from - dileptons (4.0) - lepton+B0’s (3.0) important uncertainty: B0 to B+ ratio H. Albrecht et al., PLB, 192, 245 (1987) J. Kroll (Penn) CKM 2006

  14. Early 90’s: B0s Mixing Established Example: OPAL Z-pole, hadron colliders R. Akers et al., ZfP, C60, 199 (1993) Extracted: Bs mixing probability Data favor maximal s Bs mixing “discovered” + d from CLEO Fraction of Bs mesons produced J. Kroll (Penn) CKM 2006

  15. Signal Well known background poorly known background (small) 1992: First Direct Evidence of Bs P. Abreu et al. (Delphi) Phys. Lett. B 289, 199 (1992) Sample: 270 K hadronic Z also: D. Buskulic et al. (Aleph) Phys. Lett. B 294, 145 (1992) P. D. Acton et al. (Opal) Phys. Lett. B 295, 357 (1992) J. Kroll (Penn) CKM 2006

  16. Time Dependent Measurement of md • Requires 3 pieces of information per event • Flavor of B at production • Flavor of B at decay • Proper decay time of B • Flavor of B at production – several techniques • “opposite-side” use other B hadron in event: leptons, jet-charge, kaons • “ same-side” use associated particles produced in fragmentation • Flavor of B at decay • requires signal (B0) fraction • inclusive (reconstruct secondary vertex, use “jet-charge”) • partial (lepton, charm) • semi-exclusive or exclusive (lepton+charm, hadronic) • Proper decay time • resolution depends on method used to reconstruct B decay J. Kroll (Penn) CKM 2006

  17. R. Akers et al., ZfP, C60, 199 (1993) ALEPH: 1st Time Dependent Measurement w. lepton tag from “other” B Experimental Effects Measured Asymmetry perfect D proper time effects prod. flavor mistag, backgnd D0 Decay Length (cm) J. Kroll (Penn) CKM 2006

  18. State of the Art: md BaBar: md Belle: B0 lifetime Babar: B. Aubert et al., PRD 73, 012004 (2006) Belle: K. Abe et al., PRD 71, 072003 (2005) J. Kroll (Penn) CKM 2006

  19. md is “easy”: B0 oscillates once every 8 decay times ms is a different story… J. Kroll (Penn) CKM 2006

  20. How Do We Look for “Fast” Oscillation? Measure asymmetry A as a function of proper decay time t “unmixed”:particle decays as particle “mixed”:particle decays as antiparticle For a fixed value of ms, data should yield Amplitude “A” is 1 @ true value of ms Amplitude “A” is 0 otherwise Amplitude method: H-G. Moser, A. Roussarie, NIM A384 p. 491 (1997) Units: [m] = ~ ps-1, ~=1 then m in ps-1. Multiply by 6.582£ 10-4 to convert to eV J. Kroll (Penn) CKM 2006

  21. Start 2006: Published Results on ms >3.4 cycles per lifetime source: http://www.slac.stanford.edu/xorg/hfag/osc/PDG_2006/index.html Results from LEP, SLD, CDF I ms > 14.4 ps-1 95% CL Amplitude 1 0 Average 0.48 § 0.43 Amplitude @ ms = 15 ps-1 15 Frequency ms (ps-1) J. Kroll (Penn) CKM 2006

  22. Ingredients in Measuring Bs Oscillations Decay mode tags b flavor at decay opposite-side K– jet charge 2nd B tags production flavor Proper decay time from displacement (L) and momentum (p) Dilution D = 1 – 2w w = mistag probability = efficiency D2 = effective tagging power J. Kroll (Penn) CKM 2006

  23. D. Buskulic et al., PLB 311 425 (1993) Aleph: Golden Event Bonus: Same-side K+ Opp.-side e- Produced as J. Kroll (Penn) CKM 2006 This paper reported the 1st precise measurement of m(Bs)

  24. Key Experimental Issues Uncertainty on Amplitude Signal size Signal to Background Full reconstruction critical a large ms Production flavor Tag performance Proper time Resolution For limit on ms must know S/B, D, t J. Kroll (Penn) CKM 2006

  25. Inclusive vertexing method exploiting unique CCD detector Example of e+e- Analysis: SLD Electron beam polarization Provided unique flavor tag Limits K. Abe et al., PRD 67, 012006 (2003) J. Kroll (Penn) CKM 2006

  26. Highlights of Tevatron Analyses Details see F. Bedeschi (CDF) & G. Weber (DØ) in WG3 J. Kroll (Penn) CKM 2006

  27. The Challenge CDF: Run 197716 Event 1859 J. Kroll (Penn) CKM 2006

  28. DØ Semi-muonic Signals & Lifetime Oscillation analysis Lifetime Measurement Signal: 5,176 Signal: 26,700 most precise single measurement V. M. Abazov et al., PRL97 241801 (2006) J. Kroll (Penn) CKM 2006

  29. CDF: Semileptonic Signals Total signal: 61500 J. Kroll (Penn) CKM 2006

  30. Correction Factor (MC) Decay Time Reconstructed quantity Semileptonics: Correction for Missing Momentum resolution (fs) T = 2/ms proper decay time (ps) Reconstructed momentum fraction J. Kroll (Penn) CKM 2006

  31. CDF Fully Reconstructed Signal Cleanest decay sequence Also partially reconstructed decays: Also use 6 body modes: Total hadronic signal 8700 J. Kroll (Penn) CKM 2006

  32. Oscillation period for ms = 18 ps-1 Decay Time Resolution: Hadronic Decays Maximize sensitivity: use candidate specific decay time resolution <t> = 86 £ 10-15 s ¼ period for ms = 18 ps-1 Superior decay time resolution gives CDF sensitivity at much larger values of ms than previous experiments J. Kroll (Penn) CKM 2006

  33. Same Side Flavor Tags A. Ali, F. Barreiro ZfP C30 635 (1986); M. Gronau, A. Nippe, J.L. Rosner, PRD 47 1988 (1993); M. Gronau, J.L. Rosner PRD 49 254 (1994) Charge of K tags flavor of Bs at production Particle id very important CDF TOF critical (dE/dx too) So far only used by CDF Most powerful flavor tag: D2 = 4-5% Opposite-side tags: CDF: D2 = 1.8% DØ: D2 = 2.5% J. Kroll (Penn) CKM 2006

  34. March 2006: Result DØ Collaboration V. M. Abazov et al., Phys. Rev. Lett. Vol. 97, 021802 (2006) J. Kroll (Penn) CKM 2006

  35. DØ Result (Continued) 1st reported direct experimental upper bound Probability “Signal” is random fluctuation is 5% 17 < ms < 21 ps-1 @ 90% CL V. M. Abazov et al., PRL97 021802 (2006) J. Kroll (Penn) CKM 2006

  36. April 2006: Result from the CDF Collaboration A. Abulencia et al., PRL97 062003 (2006) Probability that random fluctuations mimic this signal is 0.2% (3) Assuming signal hypothesis: measure ms likelihood ratio Next goal was to observe signal with > 5 significance J. Kroll (Penn) CKM 2006

  37. Sensitivity 31.3 ps-1 A/A = 6.1 Hadronic & semileptonic decays combined Resulting Improved Analysis published on-line on 12 Dec 2006 A. Abulencia et al., PRL97 242003 (2006) J. Kroll (Penn) CKM 2006

  38. Measured Value of ms Hypothesis of A=1 compared to A=0 - log(Likelihood) J. Kroll (Penn) CKM 2006

  39. Significance: Probability of Fluctuation Probability of random fluctuation determined from data 28 of 350 million random trials have L < -17.26 Probability = 8 £ 10-8(5.4) Have exceeded standard threshold to claim observation -17.26 J. Kroll (Penn) CKM 2006

  40. Asymmetry (Oscillations) in Time Domain Period 0.35 ps Aside: for B0 Period = 12.6 ps J. Kroll (Penn) CKM 2006

  41. Summary of CDF Results on B0s Mixing A. Abulencia et al., PRL97 242003 (2006) Observation of Bs Oscillations and precise measurement of ms Precision: 0.7% Probability random fluctuation mimics signal: 8£10-8 ( 2.83 THz, 0.012 eV) Most precise measurement of |Vtd/Vts| J. Kroll (Penn) CKM 2006

  42. Why CDF? • Tevatron delivered required luminosity • “Deadtime-less” 3-level trigger system with great flexibility • First two levels have pipelines to reduce deadtime • Silicon Vertex Tracker: trigger on displaced tracks at 2nd 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 (25m £ 25m beam) Silicon layer on beampipe (Layer00) at 1.5cm • Particle identification • specific ionization in central drift chamber (dE/dx) • Time of Flight measurement at R = 1.4 m • electron & muon identification J. Kroll (Penn) CKM 2006

  43. Conclusions • 20 year quest has come to a conclusion • Bs oscillations observed • ms precisely measured • fundamental parameters measured • rapid oscillations made it very challenging to observe • Long B lifetime and significant B mixing prerequisite to observe CP violation at the B factories • Next step is to look for CP violation in Bs decays • expect sin2s to be very small (few % asymmetry) • large value  unambiguous signal of new physics • More exciting times ahead for flavor physics J. Kroll (Penn) CKM 2006

  44. Backup Slides J. Kroll (Penn) CKM 2006

  45. Time of Flight Detector (TOF) Kaon ID for B physics • 216 Scintillator bars, 2.8 m long, 4 £ 4 cm2 • located @ R=140 cm • read out both ends with fine mesh PMT • (operates in 1.4 T B field – gain down ~ 400) • anticipated resolution TOF=100 ps • (limited by photostatistics) Measured quantities: s = distance travelled t = time of flight p = momentum Derived quantities: v = s/t m = p/v J. Kroll (Penn) CKM 2006

  46. Produce bb pairs: find 2nd b, determine flavor, infer flavor of 1st b Two Types of Flavor Tags Opposite side + Applicable to both B0 and B0s −other b not always in the acceptance Same side Based on fragmentation tracks or B** + better acceptance for frag. tracks than opp. side b −Results for B+ and B0not applicable to B0s Reminder: for limit on ms must know D J. Kroll (Penn) CKM 2006

  47. jet from b (b) has negative (positive) charge on average Types of Opposite Side Flavor Tags Lepton tags low  high D mistags from Jet charge tag high  low D Kaon tag Not used in present analysis Largest D2 @ B factories TOF J. Kroll (Penn) CKM 2006

  48. Calibrate with Large Statistics Samples of B+ & B0 Example: semileptonic signals Results: D2 = 1.54 § 0.05 [ md = 0.509 § 0.010 (stat) § 0.016 (syst)] Hadronic signals: B+ (D0+) = 26,000 B0 (D-+) = 22,000 J. Kroll (Penn) CKM 2006

  49. Compare PerformanceData and Simulation Check prediction for kaon tag on B+, B0  K Good agreement between data & MC Systematic based on comparisons  K J. Kroll (Penn) CKM 2006

  50. Based on correlation between charge of fragmentation particle and flavor of b in B meson Same Side Flavor Tags TOF Critical (dE/dx too) J. Kroll (Penn) CKM 2006

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