1. Cracking the CKM Triangle or What B A B AR Needs a Billion B’s For Masahiro Morii Harvard University B A B AR Collaboration Cornell, March 2003

2. Masahiro Morii2 Outline Very brief introduction Measurement of angle  B 0      results from B A B AR and Belle Measurement of V ub Upcoming B A B AR result using recoil of fully-reco’ed B Future prospects Where and how B A B AR and Belle will get a billion B’s

3. Cornell, March 2003Masahiro Morii3 CKM Matrix CKM matrix appears in the weak Lagrangian as Unitary matrix translates mass and weak basis 3 real parameters + 1 complex phase CPV in the Standard Model is uniquely predictive Attractive place to look for New Physics The only source of CPV in the Minimal SM Wolfenstein parameters

4. Cornell, March 2003Masahiro Morii4 Unitarity Triangle V is unitary  Consider Dividing by gives the familiar triangle CP violation in B 0 decays gives access to the angles of the Unitarity Triangle

5. Cornell, March 2003Masahiro Morii5 Unitarity Triangle and sin2  sin2  has been measured to ±0.055 You’ve just heard about it from Gabriella Measured sin2  agrees with indirect constraints Angle  known better than any angle/side of the triangle Shrinking  (sin2  ) alone will not reveal new physics

6. Cornell, March 2003Masahiro Morii6 What To Do Next? Must measure the other angles and the sides B Factories good at 3 of them B s mixing at Tevatron V ub from charmless semileptonic B decays Very hard: many long-shot ideas Penguin decays, e.g. B 0   K S CPV in charmless hadronic B decays, e.g. B 0     

7. Cornell, March 2003Masahiro Morii7 Measuring  Time-dependent CP asymmetry in B 0  f CP is CKM phase appears here Easy!

8. Cornell, March 2003Masahiro Morii8 Penguin Pollution Unlike J/  K S, the     mode suffers from significant pollution from the penguin diagrams with a different weak phase To estimate  eff – , we need: P/T ratio – about 0.3 from BR(B  K  )/BR(B   )  = strong phase difference between P and T T = TreeP = Penguin

9. Cornell, March 2003Masahiro Morii9 Mode B A B AR BR  10 6 Belle BR  10 6 Taming Penguins Take advantage of the isospin symmetryisospin symmetry

10. Cornell, March 2003Masahiro Morii10 Bound on  eff –  Full isospin analysis (Gronau & London, 1990) requires and separatelyGronau & London, 1990 Too hard for B A B AR /Belle  Upper limits on average BR Use BR(  0  0 ) to put upper bound on  eff –  Grossman and Quinn, 1998; Charles, 1998 Gronau, London, Sinha, Sinha PLB 514:315-320, 2001 Allowed assumed B A B AR  0  0 limit

11. Cornell, March 2003Masahiro Morii11 B 0   0  0 Branching Ratio CLEO: (PRD65:031103) 9.13 fb -1 BR(  0  0 ) < 5.7×10 –6 (90% CL) B A B AR : (submitted to PRL) 87.9×10 6 BB BR(  0  0 ) < 3.6×10 –6 (90% CL) Belle: (PRD66:092002) 31.7×10 6 BB 2.4  “bump” in the signal Fitted BR = (3.2 ± 1.5 ± 0.7)×10 –6 BR(  0  0 ) < 6.4×10 –6 (90% CL) First observation may come soon Will it be small enough to give us a good  eff –  bound? BELLE

12. Cornell, March 2003Masahiro Morii12 CP Asymmetry in B 0      Same method as the sin2  measurements Difference: the direct CP term cannot be neglected 9 GeV 3.1 GeV  4S B tag B CP Tag using l ±, K ± Moving with  = 0.55 CP final state # of events with

13. Cornell, March 2003Masahiro Morii13 Experimental Challenges Specific to B 0   +   Topology B 0  h  h  simple to reconstruct But no strong kinematical constraints like the J/  mass Significant background from continuum Event-shape variables  Fisher discriminant Particle ID must separate  ± from K ± DIRC (B A B AR ) or Aerogel (Belle) Common with other CP measurements Flavor tagging, vertex reconstruction, etc. And, of course, as much as possible

14. Cornell, March 2003Masahiro Morii14 B 0 Reconstruction m bc (or m ES ) and  E peak cleanly for the two-body signal K  and KK peaks shifted in  E  Additional discrimination     MC off-resonance data     MC     MC BELLE

15. Cornell, March 2003Masahiro Morii15 Most of the background come from continuum Use event shape variables that represent “jettiness” to suppress them Whole event is jettyThe other B decays spherically Continuum Background Signal udsc background Examples

16. Cornell, March 2003Masahiro Morii16 Fisher Discriminant B A B AR uses the “ CLEO ” Fisher Momentum flow in 9 cones around the candidate axis Output of Fisher goes into the likelihood fit     MC D 0    data Bkg MC m ES sideband data

17. Cornell, March 2003Masahiro Morii17 Bkg MC off-res. data Fisher Discriminant Belle’s Fisher discriminant uses: Modified Fox-Wolfram moments B flight direction Output is turned into a likelihood ratio R Cut at 0.825 removes 95% of continuum background     MC D 0    data reject

18. Cornell, March 2003Masahiro Morii18 Event Sample – B A B AR B A B AR : 87.9×10 6 BB (PRL89:281802)     enhanced for these plots with a cut on Fisher K  continuum

19. Cornell, March 2003Masahiro Morii19 Event Sample – Belle Belle: 85×10 6 BB (hep-ex/0301032) KK Continuum

20. Cornell, March 2003Masahiro Morii20 Maximum Likelihood Fit Start from the physics function: Fold in  t resolution and mis-tag probabilities Multiply by PDFs for m ES,  E B A B AR uses particle ID and Fisher in the fit Belle uses PID in event selection, Fisher to bin the data Add PDFs for background (K , KK, continuum) Feed the candidates and turn the crank…

21. Cornell, March 2003Masahiro Morii21 CP Asymmetries – B A B AR No significant CP asymmetry      enhanced for these plots with a cut on Fisher

22. Cornell, March 2003Masahiro Morii22 CP Asymmetries – Belle Subtract bkg Large CP asymmetry Rate difference (= C  )  t-dependent asymmetry 

23. Cornell, March 2003Masahiro Morii23 CP Fit Results Results made bigger splash than expected B A B AR and Belle disagree by 2.56  Belle result outside physical boundary B A B AR (PRL89:281802) Belle (hep-ex/0301032) S  +0.02 ± 0.34 ± 0.05 C  –0.30 ± 0.25 ± 0.04  0.77 ± 0.27 ± 0.08 B A B AR Belle

24. Cornell, March 2003Masahiro Morii24 Brief History B A B AR 33×10 6 BB B A B AR 60×10 6 BB B A B AR 88×10 6 BB Belle 45×10 6 BB Belle 85×10 6 BB S  stayed apart as the errors shrank C  looks consistent S  stayed apart as the errors shrank C  looks consistent

25. Cornell, March 2003Masahiro Morii25 Crosschecks Both experiments got into extensive crosschecks What is special about  compared to, e.g., J/  K S ? High background, dominated by K  and continuum  Asymmetry in the background?Asymmetry in the background? Two-body decay topology  Different vertexing systematics?Different vertexing systematics? How well did the likelihood fit work? Errors and the likelihood value reasonable? How often should you get an unphysical result? Just how significant are the results?how significant are the results?

26. Cornell, March 2003Masahiro Morii26 Two-Body Vertexing Measure lifetime and mixing in the data BelleB A B AR Mixing in B 0  K  Looking good

27. Cornell, March 2003Masahiro Morii27 Is It Physical? Belle’s 1  ellipse lies outside the physical boundary How likely is this? Suppose truth is on the boundary 60.1% of experiments produce unphysical results 16.6% are more unphysical than the actual Belle result That’s not so bad

28. Cornell, March 2003Masahiro Morii28 Averaging the Rivals B A B AR (PRL89:281802) Belle (hep-ex/0301032) Average S  +0.02 ± 0.34 ± 0.05  0.49 ± 0.27 C   0.30 ± 0.25 ± 0.04  0.77 ± 0.27 ± 0.08  0.51 ± 0.19 Both measurements seem OK Agreement is ~1% level Let’s try averaging Errors largely uncorrelated What can we learn from this? Can we measure  ?

29. Cornell, March 2003Masahiro Morii29 Significance of CPV Belle rejects non-CPV (S  = C  = 0) at 99.93% CL C  B A B AR + Belle Belle CP is violated in B 0      at 99.9% CL Indication of direct CPV at 99.3% CL Combined result is 3.24  away from CP conservation C  < 0 at 2.68  S  consistent with zero at 1.81 

30. Cornell, March 2003Masahiro Morii30 Bound on  We can’t do isospin analysis without BR(  0  0 ) What else can we do? Start with the following knowledge: S  =  0.49 ± 0.27, C  =  0.51 ± 0.19 sin2  = 0.734 ± 0.055 (P/T)  = 0.28 ± 0.10  (strong phase difference) = no clue Try to put them together Convention by Gronau & Rosner (PRD65:093012) B A B AR + Belle World average BR + theory + salt

31. Cornell, March 2003Masahiro Morii31 How They Fit Together Decay amplitudes can be written as  T = strong phase of T  P = strong phase of P

32. Cornell, March 2003Masahiro Morii32 How They Look Example:  = 23.6° and |P/T| = 0.28 Large negative  C   Large negative   seems to be near 105° Does this allow us to determine  ? 120° 105° 90° 75°60°   = 0° +  The fact that |C   is large for the assumed value of |P/T| helps us to constrain  and 

33. Cornell, March 2003Masahiro Morii33 Fitting  vs.  Fit for ,  and  Inputs: measurements of S , C  and sin2  |P/T| = 0.18–0.38 It works! At 2 , an island gives a poor limit  ln(  ). Contours at each 

34. Cornell, March 2003Masahiro Morii34 Unitarity Triangle Let’s put it on the Unitarity Triangle 84° <  < 124° Agrees with the other constraints! Is this significant? A few caveats …

35. Cornell, March 2003Masahiro Morii35 Caveat 1 – Degeneracy I assumed in the fit that  was in the “right” branch Belle did this in hep-ex/0301032 But we measured only sin2  If we allow all branches A new local minimum appear with just as good likelihood, but not consistent with the SM

36. Cornell, March 2003Masahiro Morii36 Caveat 2 – Accuracy We could fit  because |C  | was measured large That’s why the Belle result, with poorer errors, gives more interesting fit than B A B AR ’s Q: What will happen when we have more data? BelleB A B AR

37. Cornell, March 2003Masahiro Morii37 4 × Data  1/2 × Errors Suppose we shrank the error on S  and C  by 1/2 Does the error on  shrink by half? Short answer: No 1  bound go from 84° – 124° to 91° – 120° i.e. only 1/1.38 Long answer: Depends Where will the central value go?

38. Cornell, March 2003Masahiro Morii38 4 × Data  1/2 × Errors (contd.) Try moving C  by the current 1  error Very different errors on a depending on the central value Is Nature kind enough to give us maximum direct CPV?

39. Cornell, March 2003Masahiro Morii39 Current Status of  Combined measurements of S  and C  can be interpreted as a 1  bound: 84° <  < 124° This relies on |C  | being large Future improvement of the bound unclear Still important to pursue the isospin approach B A B AR (PRL89:281802) Belle (hep-ex/0301032) Average S  +0.02 ± 0.34 ± 0.05  0.49 ± 0.27 C   0.30 ± 0.25 ± 0.04  0.77 ± 0.27 ± 0.08  0.51 ± 0.19

40. Cornell, March 2003Masahiro Morii40 Outline Very brief introduction Measurement of angle  B 0      results from B A B AR and Belle Measurement of V ub Upcoming B A B AR result using recoil of fully-reco’ed B Future prospects Where and how B A B AR and Belle will get a billion B’s

41. Cornell, March 2003Masahiro Morii41 Why V ub Is Interesting Measurement of sin2  is more accurate than the indirect constraint Width of the indirect ellipse determined by |V ub /V cb | Better measurement of |V ub | More stringent test of the Unitarity Triangle

42. Cornell, March 2003Masahiro Morii42 Measuring V ub Measure the rate of charmless semileptonic decays Catch: charm background There are many techniques Exclusive: Inclusive: E l endpoint, M x cut, etc. That’s not a good sign…

43. Cornell, March 2003Masahiro Morii43 B A B AR V ub Measurements B A B AR has released two measurements Electron endpoint (hep-ex/0208081)  ICHEP 2002 (hep-ex/0301001)  submitted to PRL I’m NOT talking about these measurements Instead, I will talk about an upcoming measurement Can’t show the details – Wait for Moriond

44. Cornell, March 2003Masahiro Morii44 Why V ub Is Hard Inclusive Exclusive Poor S/B ratio S/B better Error in extrapolation to full acceptance Model-dependent prediction of BR PDG 2002, p. 706

45. Cornell, March 2003Masahiro Morii45 What Can We Do? Let’s consider an inclusive measurement Smaller theoretical errors Goal: better S/B ratio + larger kinematical acceptance Minimize charm background Reduce extrapolation Best-chance variable: m X = mass of X in B  Xl Used at LEP with moderate success Poor S/B limited their systematic errors We need another trick to improve S/B

46. Cornell, March 2003Masahiro Morii46 Exclusively Reco’ed B Events We have a large sample of  (4S)  BB events with one B fully reconstructed ~1000 decay channels Efficiency ~0.2%/B Look at the other B in these events (“recoil” B) Pure B 0, B ± samples with known momentum Look for leptons with p l > 1 GeV For B ±, take only right-sign leptons Y ± is any combination of  ±, K ±, K S and  0 Our “golden” B  Xl sample

47. Cornell, March 2003Masahiro Morii47 Measuring m X The X in B  Xl is the leftover of the event Charged tracks and unmatched calorimeter clusters Impose 4-momentum conservation, same B masses, zero missing mass  2-C fit Measured vs. generated m X in MC. Resolution ~350 MeV. Almost no bias

48. Cornell, March 2003Masahiro Morii48 Cleaning Up A few more cuts to improve S/B One and only one lepton Charge conservation Small missing mass Special cut using soft pions to reduce B  D  l Kaons come mostly from charm decays Enrich (deplete) b  u decays by vetoing (requiring) them Enriched sample for the measurement Depleted sample for MC vs. data agreement studies

49. Cornell, March 2003Masahiro Morii49 Signal Fit m ES to get the number of B  Xl events Very clean signal  S/B > 1 Comparable to exclusive measurements All eventsm X < 1.55 GeV Normalization from this fit b  ul enriched (~60%)

50. Cornell, March 2003Masahiro Morii50 What’s Coming To get the branching fraction: Cut on m ES and fit m X distribution to get the yield Estimate efficiencies and background Done, but can’t show yet Conference paper in circulation inside B A B AR What to expect: Statistical error ~ best existing measurement (8% on V ub ) Low background  Very small systematics Extrapolation error ~ LEP measurements (10% on V ub )

51. Cornell, March 2003Masahiro Morii51 Current Status of V ub B factories are working hard to improve V ub Exciting results are coming out NOW Use of the recoil B for inclusive BR(b  ul ) has shown great potential Stay tuned for the first result at Moriond Other uses of the recoil B are widely investigated Will not leave any stone unturned Need different approaches with different systematics We pursue all known techniques + new ideas

52. Cornell, March 2003Masahiro Morii52 Closing the Triangle We are attacking the Triangle from all directions But we do need much more data B s mixing at Tevatron V ub from charmless semileptonic B decays Very hard: many long-shot ideas Penguin decays, e.g. B 0   K S CPV in charmless hadronic B decays, e.g. B 0     

53. Cornell, March 2003Masahiro Morii53 Luminosity Projection – PEP-II That’ll give B A B AR a billion B mesons to play with Integrated luminosity [fb -1 ] Peak luminosity [10 33 ] 5 10 15 200 400 600 PEP-II plans to deliver 500 fb -1 by end 2006

54. Cornell, March 2003Masahiro Morii54 Luminosity Projection – KEKB KEKB also shoot for 500 fb -1 by end 2006

55. Cornell, March 2003Masahiro Morii55 Future of B A B AR Accelerators are doing amazing jobs … and will do even better! Can B A B AR take data at  = 16×10 33 ? We designed it for  = 3×10 33 Most of the detector will be OK Will replace a part of the silicon Data rate will flood the DAQ Upgrade CPUs and the network?  A few M$ Improve the trigger system to reduce the event rate

56. Cornell, March 2003Masahiro Morii56 B A B AR Trigger Upgrade Bottleneck: data transport to the Event Builder Will saturate at 3.5 kHz Must keep L-1 rate low Idea: teach L-1 what L-3 is doing = 3-D tracking PEP-II collisions Level-1 trigger Level-3 trigger 238 MHz Event store ~150 Hz 2 kHz B A B AR Detector Event builder z 0 of all tracks in L-1 events Physics Background

57. Cornell, March 2003Masahiro Morii57 ZPD Module Need some brain power to do 3-D tracking in the Level-1 trigger 24 Gbit/s incoming data Fixed latency < 2  s Z 0 -P T Discriminators 8 modules carrying 6 big (4 Mgates) FPGAs Designed and built at Harvard

58. Cornell, March 2003Masahiro Morii58 Summary B A B AR and Belle are working hard to crack the Unitarity Triangle CPV in B 0      gives 84° <  < 124° at 1  Future improvement depends on more data + some luck … and a whole lot more data for isospin analysis Better measurements on V ub are coming Recoil B analysis shows great promise With 10 9 B’s/experiment by 2006, we will learn a lot more about the Unitarity Triangle Is it really closed, or will we see a sign of New Physics?

59. Cornell, March 2003Masahiro Morii59 >

60. Cornell, March 2003Masahiro Morii60 Wolfenstein Parameters It is convenient to parameterize the CKM matrix as:  and  are arbitrary and  (1) CPV tucked into the smallest elements V ub and V td Obvious place to look for New Physics contributions NP should appear as inconsistent values of  and  across different measurements Enter the Unitarity Triangle…

61. Cornell, March 2003Masahiro Morii61 Parameterizing the CKM Matrix Without the 3 rd generation, life is much simpler Assume small mixing between 2 nd and 3 rd generations This is not unitary at  ( 3 )  Need V ub and V td sine of the mixing angle

62. Cornell, March 2003Masahiro Morii62 Wolfenstein Parameters Given, Unitarity

63. Cornell, March 2003Masahiro Morii63 Isospin Analysis (Gronau-London) CG coeff. No I = 1 term because of Bose statistics CP I gluon = 0  No penguin in A I=2  No CPV in A +0

64. Cornell, March 2003Masahiro Morii64 B Flight Direction Angle  B of the B candidate momentum relative to the beam axis Signal Background ~flat BELLE

65. Cornell, March 2003Masahiro Morii65 Sphericity Angle Angle  S between the sphericity axes of the B candidate and the rest of the event Cut at 0.8 removes 83% of the continuum background B A B AR     MC background reject

66. Cornell, March 2003Masahiro Morii66 Systematic Errors on S , C  B A B AR : Dominated by the shape of the particle ID variable Belle: Uncertainties of the background fractions Vertexing resolution uncertainty Fit bias near the physical boundary for S  All measurements are statistically limited

67. Cornell, March 2003Masahiro Morii67 Background Asymmetry Measure asymmetry in background-enriched samples qq continuum in mass sideband K  by flipping PID Also try Tighter  event selection Fit/tagging bias in non-CP sample Nothing strange Belle

68. Cornell, March 2003Masahiro Morii68 Monte Carlo Fit Test Generate ~10000 pseudo experiments to study: Reproducibility of the central values Likelihood values Pull distributions Measured errors  2 ln(  /  max ) = 1 Parabolic errors  (C   Everything looks reasonable Belle  (S  

69. Cornell, March 2003Masahiro Morii69 Branching Fractions ModeB A B AR (10  6 ) Belle (10  6 ) KK 17.8 ± 1.1 ± 0.821.8 ± 1.8 ± 1.5 KK 12.5 ± 2.4 ± 1.2 KK 18.8 ± 3.0 ± 1.5 KK 7.7 ± 3.2 ± 1.6  5.4 ± 0.7 ± 0.45.1 ± 1.1 ± 0.4  7.0 ± 2.2 ± 0.8  < 3.3< 5.6 K+KK+K < 1.1< 0.5 K+KK+K < 1.4< 3.8 K0KK0K < 10.6< 13 All Preliminary

70. Cornell, March 2003Masahiro Morii70 Direct CP Violation A CP ModeB A B AR Belle KK  0.05 ± 0.06 ± 0.01  0.06 ± 0.08 ± 0.01 KK 0.00 ± 0.11 ± 0.02  0.04 ± 0.19 ± 0.03 KK –0.17 ± 0.10 ± 0.020.45 ± 0.15 ± 0.02  All Preliminary

71. Cornell, March 2003Masahiro Morii71 CPV in B  charmless ModeBaBar CPV with B   Sin2  -eff ] S: C: 0.02+/-0.34+/-0.05 -0.35+/-0.25+/-0.04 CPV with B  ”  ” A(  C(  S(   C(   S(  A(  -0.22 +/- 0.08 +/- 0.07 0.45 +0.18/-0.19 +/0.09 0.16 +/- 0.25 +/- 0.07 0.38 +/- 0.19/-0.20 +/- 0.11 0.15+/- 0.25 +/- 0.05 0.19 +/- 0.14 +/- 0.11 Direct CP: K -     0    ’K+ (run 1 for Acp)  run 1 for Acp)  (run 1 for Acp)  (run 1 for Acp)  (run 1 for Acp)  (run 1) J/  (run 1) J/  (run 1) DcpK+ (run 1 & run 2) -0.102+/-0.050+/-0.016 0.09+/-0.09+/-0.01 -0.17+/-0.10+/-0.02 -0.03+/-0.18+/-0.02 -0.11+/-0.11+/-0.02 -0.01+/-029(0.31)+/-0.03 -0.05+/-0.20+/-0.03 -0.43+/-0.36(0.30)+/-0.06 0.00+/-0.27+/-0.03 -0.044+/-0.076+/-0.012 0.002+/-0.030+/-0.004 0.04+/-0.22+/-0.004 0.17+/-0.23+/-0.09(0.07) Some 2 sigma effects but no real asymmetry observed

72. Cornell, March 2003Masahiro Morii72 B   analysis: the idea (1) b u u d d   B0B0 V ub V ud I=1 I=0,1,2  I=1/2,3/2 I=1/2 I 3 =1/2 W Diff. EW Phase:  V ub b d u d u   B0B0 V tb I=1 I=0,1  I=1/2 I=1/2 I 3 =1/2 g I=0,1 I 3 =0 because I g =0 V td

73. Cornell, March 2003Masahiro Morii73 B   analysis: the idea (2) B0 Mix    e -i  T +- P +- e +i  T -+ P -+ e +i  T +- P +- e +i  T 00 P 00 e -i  T -+ P -+ e -i  T 00 P 00   I=1/2  P 00 =1/2(P +- +P -+ )  5 amplitudes (complex) + 1 weak phase – 1 irrelevant strong phase = 10 parameters to fit in the Dalitz plot.

74. Cornell, March 2003Masahiro Morii74 B   analysis: the idea (3) Dalitz Plot for B 0      A fit to the Dalitz plot will allow to extract the 10 parameters (including  ) if statistics is enough

75. Cornell, March 2003Masahiro Morii75 Why V ub Is So Hard V ub is related to the total rate This cannot be measured because of charm background Inclusive measurements must make kinematical cuts (e.g. on p lepton ) to remove charm Must extrapolate to full range  9  15% errors Large background subtraction  7  22% errors Exclusive measurements have less background Rate prediction depends on models  15  20% errors

76. Cornell, March 2003Masahiro Morii76 A new way of measuring  R. Alexan et al. hep-ph/0209194 Final states obtained by popping a qq pair  both interfering amplitude are of order 3 CP Direct CPV is generated through the CP-eigenstate of D 0 meson (-)(-)

77. Cornell, March 2003Masahiro Morii77 How PEP-II Will Increase  According to J. Seeman: Lower  y * in HER/LER  × 1.56 Raise currents and number of bunches  × 1.4 Move tunes to half integer for lower tune shifts  × 1.25 Continuous LER injection  × 1.2 Total × 3.3  16 × 10 33 /cm 2 /s Hope to get 7.5 ×10 33 /cm 2 /s by July 2003 with more later