1. Aart Heijboer 1 July 7, nikhef colloquium mixing at CDF Aart Heijboer University of Pennsylvania/CDF Outline for today Introduction and motivation The measurement Collecting the signal Measuring the decay time Flavour tagging Results Eat a herring Bram's Defense Down hill from there Measurement of the Bs-Bsbar Oscillation Frequency hep-ex/0606027 submitted to PRL

2. Aart Heijboer 2 July 7, nikhef colloquium Flavor Oscillations B s and B s mesons can transform into each other. They form a single QM system: M11=M22 (cpt) in the simplest case (CP), M and gamma are real. Then ML= M11-M12, MH=M22+M12 M H = M +  M/2 M L = M -  M/2  M = 2M 12 b s t W s b _ t W _ _ BsBs BsBs H not diagonal  B and B are not mass eigenstates the mass eigenstates are: _ V ts The Schrodinger equation: :

3. Aart Heijboer 3 July 7, nikhef colloquium    Pmt e BBP P e BBP mix t umix t     cos1 2 1 2 / /     Oscillation probability as function of time life time oscillation frequency =  M [ 1 ps -1 ~ 7 x 10 -4 eV (~1.5x10 -13 m b ) ] Solving the time dependent SE b s t W s b _ t W _ _ BsBs BsBs Because of a coupling between the two states, we get: two separate mass eigenstates oscillation between B s and B s We have seen that before

4. Aart Heijboer 4 July 7, nikhef colloquium test Energy eigenstates (normal modes) time Classical analogon By measuring the frequency, we are measuring the strength of the coupling

5. Aart Heijboer 5 July 7, nikhef colloquium Motivation New physics is constrained by testing prediction of SM... in particular: test unitarity of the CKM matrix pretty well known not wel known and interesting To get at V td : measure  m d (B d oscillations) hard to calculate (lattice QCD). uncertainty: 10% 1.21  0.05 q=s or d If we measure  m s, we can form the ratio which allows for much more accurate measurement of V ts /V td (hep-lat/0510113) b s t s b t BsBs BsBs V ts

6. Aart Heijboer 6 July 7, nikhef colloquium Motivation 2005 Limit on  m s was already helping to measure CKM matrix... Plot Combines many different measurements to constrain  and . Check that all measurements are consistent: i.e. that CKM matrix is unitary. V td =A 3 (1-  -i  ) Turn the argument around: standard model prediction: Go measure if SM is right. If the answer is no.....

7. Aart Heijboer 7 July 7, nikhef colloquium Motivation: new physics New particles can enhance the B s B s transition harnik et al. hep-ph/0212180 supersymmetry with large mixing between squarks  m s is sensitive to new physics Phys.Lett.B596:229-239,2004 Z'

8. Aart Heijboer 8 July 7, nikhef colloquium  =1.54 ps  m d =0.5 ps -1 B s vs B d BdBd  =1.41 ps  m s =~20 ps -1 BsBs  d =0.18 can measur e  m d by measuring  == 1 1+ (  m) -2 1 2 fraction of mixed events  s =1/2  O(10 -3 ) no information on  m s in   need to resolve oscillation  need good time resolution now: Bd mixing fully resolved Bd mixing first observed by measuring  d (UA1, ARGUS 1987) mt PP PP A mixumix mixumix     cos asymmetry

9. Aart Heijboer 9 July 7, nikhef colloquium Amplitude scan Experimental effects dampen the asymmetry ● A is known as the Amplitude: the size of the asymmetry, corrected for detector effects. ● A=1 means mixing ● A=0 means data is compatible with no mixing ● knowledge about detector is put into likelihood, to 'correct' for damping of the asymmetry

10. Aart Heijboer 10 July 7, nikhef colloquium What we know already all data before 2004 LEP + SLD World average before Tevatron run II Amplitude scan: fix  m s and measure the amplitude of the corresponding frequency component (Fourier) Recent D0 result ● 17 <  ms <21 ps-1 at 90% CL ● p-value = 5%

11. Aart Heijboer 11 July 7, nikhef colloquium Outline of the measurement Need to: 1) collect a lot of B s decaysTrigger/reconstruction 2) determine the flavor of B s at production'flavor tagging' 3) measure the proper decay time of B s measure L xy p p Bs/BsBs/Bs L xy

12. Aart Heijboer 12 July 7, nikhef colloquium Getting the B s signals

13. Aart Heijboer 13 July 7, nikhef colloquium The Tevatron 1.2 fb -1 collected, 1 fb -1 in 'good' runs my office CDF ~2/3 of the data collected in 2005

14. Aart Heijboer 14 July 7, nikhef colloquium The CDF detector

15. Aart Heijboer 15 July 7, nikhef colloquium The CDF detector

16. Aart Heijboer 16 July 7, nikhef colloquium The signals we are looking for Semileptonic Hadronic B s Momentum is measured B s mass used for good S/N Small branching ratio: low yield Missing momentum ( ) Need to rely on D s mass Large branching ratio: high yield

17. Aart Heijboer 17 July 7, nikhef colloquium A typical B event at a hadron collider => look for displaced tracks Trigger on events with two displaced (d>120  m) tracks d very fast reconstruction of silicon data at L2 (20  s latency) by dedicated hardware: SVT cdf d (  ) Displaced track trigger

18. Aart Heijboer 18 July 7, nikhef colloquium Hadronic signals ● low background under the B s peak ● P T (B s ) 'perfectly' measured ● mixing fit in range > 5.3 GeV to remove partially reconstructed 'satellites' high statistics 'light B' samples: ● B +  D 0  (26 k events)  B 0  D-  (22 k events)

19. Aart Heijboer 19 July 7, nikhef colloquium Semileptonic signals ~36.000 Bs  l D s signal events (and ~1M in B 0 /B + ) missing particles ( ): no B-mass peak, but mass of lepton+D s gives discriminating power.

20. Aart Heijboer 20 July 7, nikhef colloquium Proper decay time and resolution

21. Aart Heijboer 21 July 7, nikhef colloquium Sources of uncertainty: L xy Lxy is biased because of the SVT trigger how to measure  (L xy ) contributions from primary and secondary vertex improved recently by using EBE primary P T Negligible uncertainty in hadronic Important for semileptonic (missing momentum) Only have lepton and D s Determine k  P T (l+D)/P T (B) from MC Proper time reconstruction: hadronic  Hadronic: ●  ct 0 : ~ 30  m (100 fs) ●  p /p < 1%  Semileptonic ●  ct 0 : ~ 50  m (167 fs) ●  p /p ~ 15% (K factor) Bs/BsBs/Bs L xy piece of cake!

22. Aart Heijboer 22 July 7, nikhef colloquium Sources of uncertainty: L xy Lxy is biased because of the SVT trigger how to measure  (L xy ) contributions from primary and secondary vertex improved recently by using EBE primary P T Negligible uncertainty in hadronic Important for semileptonic (missing momentum) Only have lepton and D s Determine k  P T (l+D)/P T (B) from MC Proper time: Semileptonic  Hadronic: ●  ct 0 : ~ 30  m (100 fs) ●  p /p < 1%  Semileptonic ●  ct 0 : ~ 50  m (167 fs) ●  p /p ~ 15% (K factor) Bs/BsBs/Bs L xy ● k-factor obtained from Monte Carlo ● Take advantage of variation in k-factor distribution with l D s mass. (high m lDs means small missing p T ) ● can not measure p T for semileptonic ● correct for missing p T on average

23. Aart Heijboer 23 July 7, nikhef colloquium Proper time reconstruction ● Displaced track trigger sculpts proper decay length distribution ● Modeled by efficiency function  (t) ● Derived from MC ● Not crucial for mixing measurement, but important for lifetimes

24. Aart Heijboer 24 July 7, nikhef colloquium Lifetime measurement (hadronic) N

25. Aart Heijboer 25 July 7, nikhef colloquium Proper time resolution Effect of non-zero ct error asymmetry: attenuation of the oscillation Smearing of decay time causes attenuation of asymmetry signal: Have to know  ct to measure the mixing amplitude How to measure  ct ? 2 2 )( t t m eD     

26. Aart Heijboer 26 July 7, nikhef colloquium Measuring the proper time resolution Cannot measure the ct resolution directly on data (no prompt peak in the B s signal due to trigger) Solution: construct events that look like a B but are known to come from the PV.. real D some pion from the underlying event (i.e. from PV) True must be zero; compare error with predicted error from the vertex fit. And study dependence on kinematic variables, isolation,  2 of fit etc..

27. Aart Heijboer 27 July 7, nikhef colloquium proper time resolution

28. Aart Heijboer 28 July 7, nikhef colloquium 3) Flavour tagging

29. Aart Heijboer 29 July 7, nikhef colloquium Flavour tagging Bs/BsBs/Bs LxyLxy We need to know the flavor of the B s at production. Opposite side tag: look at the decay products of the other b quark in the event: Leptons charge of the b-'jet' the two b quarks fragment independently: can calibrate opposite side taggers with B d & B u other B often outside acceptance Same side tag: look at particles produced in B meson formation (K in case of Bs) Very powerful (high acceptance) but cannot calibrate on B d & B u Need to rely on MC need to identify Kaons K e/ 

30. Aart Heijboer 30 July 7, nikhef colloquium A tagger is characterized by  : efficiency D: dilution = 1-2 x mistag rate (large dilution is good) Dampens asymmetry: Figure of merit:  D 2 x D We must know what D is to measure A D<1 dampens the oscillation signal Flavor tagging II

31. Aart Heijboer 31 July 7, nikhef colloquium Opposite side taggers Measure opposite side tagger dilutions Simultaneous fit to lD +, lD 0 and lD* modes predicted dilution dilution scale factor Dilution predicted on event-by-event basis (based on P T rel, lepton-id etc). how to check/calibrate the prediction is correct? Aart Heijboer 31 May 25, Brookhaven, particle physics seminar

32. Aart Heijboer 32 July 7, nikhef colloquium ● Fragmentation into B s tends to produce an additional kaon. ● Charge of K identifies B s flavor at production ● B 0 and B + mostly accompanied by pions ● Use combined likelihood from time-of-flight detector and dE/dx in COT identify Kaons Same side kaon tagging

33. Aart Heijboer 33 July 7, nikhef colloquium ● resolution ~ 100 ps ● separates kaons from pions up to 1.5 GeV ● crucial for SSKT Time of flight detector

34. Aart Heijboer 34 July 7, nikhef colloquium Same side kaon tagging tagger not optimized for these modes, but valuable check that MC predicts the right dilution

35. Aart Heijboer 35 July 7, nikhef colloquium Flavor tagging: results ● Exclusive combination of opposite side taggers ● Same side combined with opposite side assuming independence ● Recently added kaon tagger increases effective statistics by a factor 3.5!

36. Aart Heijboer 36 July 7, nikhef colloquium 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

37. Aart Heijboer 37 July 7, nikhef colloquium Amplitde scan: B d Verify validity of procedure fitted value of  m d agrees with world average.

38. Aart Heijboer 38 July 7, nikhef colloquium Results

39. Aart Heijboer 39 July 7, nikhef colloquium Amplitude scan: hadronic Aart Heijboer 39 July 7, nikhef colloquium

40. Aart Heijboer 40 July 7, nikhef colloquium Amplitude scan: semileptonic

41. Aart Heijboer 41 July 7, nikhef colloquium Amplitude scan: combined July 7, nikhef colloquium Aart Heijboer 41

42. Aart Heijboer 42 July 7, nikhef colloquium Amplitude scan without the yellow and green stuff Aart Heijboer 42 July 7, nikhef colloquium

43. Aart Heijboer 43 July 7, nikhef colloquium Significance of the result ● Amplitude scan not used for significance evaluation, instead: ● Look at -  log( L ) = - log( L mixing /L no mixing ) = - log( L A=1 /L A=0 ) ● gives better discriminating power than A/  (A) ● no search window needed Minimal value observed -  log( L )=-6.76 What is the probability that happens as result of fluctuation if  m s =very large?

44. Aart Heijboer 44 July 7, nikhef colloquium probability to see such a large value of  log(L) as result of a statistical fluctuation (aka p-value) = 0.2 % Significance of the result Repeat likelihood scan many times while randomizing the tagger decisions

45. Aart Heijboer 45 July 7, nikhef colloquium Measurement of  m s ● Decided (a-priory) to extract  m s if the p-value < 1% ● it's 0.5%, so here we go... ● systematics on A are unimportant for  m s. only lifetime scale matters. ● effect considered: Si alignment, bias from ct-curvature correlations, primary vertex

46. Aart Heijboer 46 July 7, nikhef colloquium Measurement of |V td |/|V ts | now again limited by theory error

47. Aart Heijboer 47 July 7, nikhef colloquium Effect on unitarity triangle Before 2006 Including CDF and D0 now again limited by theory

48. Aart Heijboer 48 July 7, nikhef colloquium Conclusions Experimentally challenging... made possible by Tevatron: ~only place where B s is made B-physics trigger: CDF has displaced track trigger Good lifetime resolution to resolve fast oscillations: SVX (L00) Flavor tagging (time-of-flight detector for SSKT)

49. Aart Heijboer 49 July 7, nikhef colloquium Systematics on the amplitude systematics on amplitude scale: both A and  A

50. Aart Heijboer 50 July 7, nikhef colloquium

51. Aart Heijboer 51 July 7, nikhef colloquium

52. Aart Heijboer 52 July 7, nikhef colloquium Triggering on B decays Level 1: (396 ns) Reconstruct COT tracks (!) on dedicated hardware: XFT require pair of tracks Level 2 (20  s): Add Silicon information to XFT tracks.. look for: two displaced tracks or lepton+displaced track Detector Raw Data Level 1 pipeline: 42 clock cycles Level 1 Trigge r L1 Accep t Level 2 Trigg er Level 2 buffer: 4 events L2 Accep t DAQ buffers L3 Farm Level 1 7.6 MHz Synchromous Pipeline 5.5  s Latency 45 kHz accept rate Level 2 Asynchromous 2 Stage Pipeline 20  s Latency 300 Hz accept rate Mass Storage (50~100 Hz) 7.6 MHz Crossing rate SVX read out after L1

53. Aart Heijboer 53 July 7, nikhef colloquium Proper time reconstruction Bs/BsBs/Bs L xy Three problems... Lxy distribution is biased by the trigger P T is not measured accurately in semi-leptonic modes How do we measure our ct resolution? In principle, measing the proper time at decay is easy

54. Aart Heijboer 54 July 7, nikhef colloquium

55. Aart Heijboer 55 July 7, nikhef colloquium Coupled oscillators coupling induces splitting in energy levels (not only in QM) oscillation pattern is made up of two fundamental frequencies: the red and blue oscillator eigen-frequencies are no longer eigen-frequency of the system two different eigenfrequencies, split by small value size of splitting proportional to the amount of coupling between red and blue oscillation (envelope) between pure blue and pure red time

56. Aart Heijboer 56 July 7, nikhef colloquium

57. Aart Heijboer 57 July 7, nikhef colloquium 76 people from 24 institutions

58. Aart Heijboer 58 July 7, nikhef colloquium Coupled oscillators coupling induces splitting in energy levels (not only in QM) oscillation pattern is made up of two fundamental frequencies: the red and blue oscillator eigen-frequencies are no longe eigen-frequency of the system two different eigenfrequencies, split by small value size of splitting proportional to the amount of coupling between red and blue oscillation (envelope) between pure blue and pure red time introducing a coupling introduces splitting in the energy levels; we've seen that before.....

59. Aart Heijboer 59 July 7, nikhef colloquium Datasets with high tagging efficiency Bs/BsBs/Bs LxyLxy e/  Default: trigger or decay products of the reconstructed B and hope for a tag 'New' idea: trigger on tagged events muon (tag) + two displaced tracks (B-decay) Di-lepton trigger one lepton from semi-leptonic decay one for OST trigger already existed (used for SUSY searches) modest yield, but very high  D 2 : Adding this data in next round of analysis. D s ->  pi  D 2 from lepton taggers measured on B 0 and B + in this sample: 4.5% ! (compare with 1.5 for other samples)

60. Aart Heijboer 60 July 7, nikhef colloquium The Future Many improvements on the way: ● more data ● factor 2-3 more already collected ● Tevatron Luminosity going up ● Same Side Kaon tagging ● Additional trigger paths ● Use satellites in hadronic modes ● Improve ct resolution ● Reoptimize event selection (NN)  D 2 = 5% & improve  ct) by 10%  D 2 = 3.5%  D 2 = 1.55% Mode Yield. 1600. 800. 600 500. 200 3700 events in total

61. Aart Heijboer 61 July 7, nikhef colloquium