1 33 rd 33 rd International Conference in High Energy Physics (Jul 26 th – Aug 2 nd, Moscow, Russia) Tania Moulik (Kansas University) presented by Andrei Nomerotski (Fermilab/Oxford)

2 Mass eigenstates are a mixture of flavor eigenstates: B H and B L have a different mass and may have different decay width.   m = M H – M L = 2|M 12 |,  =  H -  L = 2|  12 | Mass eigenstates are a mixture of flavor eigenstates: B H and B L have a different mass and may have different decay width.   m = M H – M L = 2|M 12 |,  =  H -  L = 2|  12 | B mixing Time evolution follows the Schrodinger equation Dominant Diagram for the transition :

3 In an Ideal Scenario.. In an Ideal Scenario.. “ Opposite sign ” “ Same sign ” Oscillations with amplitude = 1.0 and Frequency =  ms.

4 DZero Detector Spectrometer : Fiber and Silicon Trackers in 2 T Solenoid Energy Flow : Fine segmentation liquid Ar Calorimeter and Preshower Muons : 3 layer system & absorber in Toroidal field Hermetic : Excellent coverage of Tracking, Calorimeter and Muon Systems Spectrometer : Fiber and Silicon Trackers in 2 T Solenoid Energy Flow : Fine segmentation liquid Ar Calorimeter and Preshower Muons : 3 layer system & absorber in Toroidal field Hermetic : Excellent coverage of Tracking, Calorimeter and Muon Systems SMT H-disksSMT F-disksSMT barrels

5 Analysis outline μ + /e +  - - K+K+ K-K- φ D-SD-S μ(e) B X Signal Selection Look for tracks displaced from primary vertex in same jet as  /electron  Two tracks should form a vertex and be consistent with  mass (   K K  ) or K* mass (K*K  KK  )  KK  invariant mass should be consistent with Ds mass  Identify e/  P T (e/  ) > 2.0 |  | (e/  ) < 1.0/2.0

6 Signal Selection μ (e) + π -π - K+K+ K-K- φ D-SD-S μ(e) B ν X Muons were selected by triggers without lifetime bias = no online/offline Impact Parameter cuts Trigger muon can be used as tag muon : gives access to eD s sample with enhanced tagging purity

7 Signal Selection μ+μ+ π -π - K+K+ K-K- φ D-SD-S μ(e) B ν X PV L T (D S ) Ds lifetime is used to have non-zero selection efficiency at Interaction Point  Bs can decay at IP and be reconstructed Eff=30%

8 Effect of Neutrino Need to correct Decay Length for relativistic contraction  need to know B s momentum Can estimate B s momentum from MC (through so called k-factor) at expense of additional uncertainty  k/k uncertainty causes additional smearing of oscillations Only few first periods are useful for semileptonic channels Sensitivity at DL=0 is crucial All above represents the main difference wrt hadronic channels Need to correct Decay Length for relativistic contraction  need to know B s momentum Can estimate B s momentum from MC (through so called k-factor) at expense of additional uncertainty  k/k uncertainty causes additional smearing of oscillations Only few first periods are useful for semileptonic channels Sensitivity at DL=0 is crucial All above represents the main difference wrt hadronic channels 200 micron # of periods

9 Flavor Tagging and dilution calibration Identify flavor of reconstructed B S candidate using information from B decay in opposite hemisphere. a) Lepton Tag : Use semileptonic b decay : Charge of electron/muon identifies b flavor Ds cos  (l, Bs) < 0.8 Bs  e  /   b) Secondary Vertex Tag : Search for secondary vertex on opposite Side and loop over tracks assoc. to SV. c) Event charge Tag: All tracks opposide to rec. B Secondary Vertex

10 Dilution in Δm d measurement Combine all tagging variables using likelihood ratios B d oscillation measurement with combined tagger  m d =  0.030±0.016ps -1 Combine all tagging variables using likelihood ratios B d oscillation measurement with combined tagger  m d =  0.030±0.016ps -1 Combined dilution: εD 2 =2.48±0.21±0.08 % Input for Bs measurement

11 Bs decay samples after flavor tagging N Bs (  ) = 5601  102 N Bs (  + e) = 1012  62 (Muon tagged) N Bs (K*K +  ) = 2997  146 N Bs (  ) = 5601  102 N Bs (  + e) = 1012  62 (Muon tagged) N Bs (K*K +  ) = 2997  146 Bs  Ds e X Ds   Ds  K*K Bs  Ds  X Ds  

12 K*K Fit Components (Cabibbo suppressed) Difficult mode due to K* natural width and mass resolution – larger errors wrt  mode

13 Results of the Lifetime Fit From a fit to signal and background region: Decay Mode c  Bs (  m) c  bkg (  m) Bs  Ds  X, Ds   404  9627  6 Bs  Ds e X, Ds   444   18 Bs  Ds  X, Ds  K*K407   10 Bs  Ds e X Ds   Ds  K*K Bs  Ds  X

14 Amplitude Method Amplitude fit = Fourier analysis + Maximum likelihood fit often used in oscillation measurements If A=1, the Δm’ s is a measurement of Bs oscillation frequency, otherwise A=0 Need to know dilution (from Δm d analysis)

15 Cross-check on B d  XμD ± (   ) EXACTLY the same sample & tagger Amplitude Scan shows B d oscillations at correct place  no lifetime bias with correct amplitude  correct dilution calibration Same results for two other modes EXACTLY the same sample & tagger Amplitude Scan shows B d oscillations at correct place  no lifetime bias with correct amplitude  correct dilution calibration Same results for two other modes Amplitude Scan DØ Run II Preliminary

16 Measure Resolution Using Data Ultimately  m s sensitivity is limited by decay length resolution – very important issue Use J/ψ → μμ sample Fit pull distribution for J/ψ Proper Decay Length with 2 Gaussians Resolution Scale Factor is 1.0 for 72% of the events and 1.8 for the rest Cross-checked by several other methods Ultimately  m s sensitivity is limited by decay length resolution – very important issue Use J/ψ → μμ sample Fit pull distribution for J/ψ Proper Decay Length with 2 Gaussians Resolution Scale Factor is 1.0 for 72% of the events and 1.8 for the rest Cross-checked by several other methods μ PV J/ψ vertex μ L±σLL±σL DØ Run II Preliminary

17 Amplitude Scan of B s  XμD s (   ) Deviation of the amplitude at 19 ps-1 2.5σ from 0  1% probability 1.6σ from 1  10% probability Deviation of the amplitude at 19 ps-1 2.5σ from 0  1% probability 1.6σ from 1  10% probability

18 Log Likelihood Scan  m s < 21 ps 90% CL assuming Gaussian errors Most probable value of  m s = 19 ps -1 Systematic  Resolution  K-factor variation  BR (B s  D s X)  VPDL model  BR (B s  D s D s ) In agreement with the amplitude scan Have no sensitivity above 22 ps -1

19InterpretationInterpretation Results of ensemble tests: DZero result : Combined with World (before CDF measurement): Results of ensemble tests: DZero result : Combined with World (before CDF measurement):    m s (ps -1 )     m s (ps -1 ) 

20 Impact on the Unitarity Triangle Before B S mixing

21 Impact on the Unitarity Triangle With D0

22 Impact on the Unitarity Triangle With CDF

23 “Golden” Events for Visualization Period of 19ps -1 DØ Run II Preliminary Weigh events using # of periods

24 Can We See Bs Oscillations By Eye ? Weighted asymmetry This plot does not represent full statistical power of our data Weighted asymmetry This plot does not represent full statistical power of our data # of periods

25 More Amplitude Scans New results : Amplitude scans from two additional modes Ds  K*K Bs  Ds (   e X Bs  Ds  X Ds  

26CombinationCombination Amplitude is centred at 1 now, smaller errors Likelihood scan confirms 90% CL  m s limits: ps -1 Data with randomized tagger : 8% probability to have a fluctuation (5% before for  mode) Detailed ensemble tests in progress Amplitude is centred at 1 now, smaller errors Likelihood scan confirms 90% CL  m s limits: ps -1 Data with randomized tagger : 8% probability to have a fluctuation (5% before for  mode) Detailed ensemble tests in progress

27 Add Same Side Tagging Add hadronic modes triggering on tag muon Add more data (4-8 fb -1 in next 3 years) with improved detector – additional layer of silicon between beampipe and Silicon Tracker (Layer0) – better impact parameter resolution Add Same Side Tagging Add hadronic modes triggering on tag muon Add more data (4-8 fb -1 in next 3 years) with improved detector – additional layer of silicon between beampipe and Silicon Tracker (Layer0) – better impact parameter resolution Layer0 has been successfully installed in April 2006 S/N = 18:1 & no pickup noise First 50 pb -1 of data on tape, first tracks have been reconstructedOutlookOutlook

28 SummarySummary Established upper and lower limits on  m s using Bs  Ds    X mode Analysis published in PRL 97 (2006) Combined with two other channels Bs  Ds      X Bs  Ds    e X considerable improvement in sensitivity 14.1  16.5 ps -1, no improvement for  m s interval Looking forward to a larger dataset with improved vertex detection If  m s is indeed below 19 ps -1 expect a robust measurement with the extended dataset Established upper and lower limits on  m s using Bs  Ds    X mode Analysis published in PRL 97 (2006) Combined with two other channels Bs  Ds      X Bs  Ds    e X considerable improvement in sensitivity 14.1  16.5 ps -1, no improvement for  m s interval Looking forward to a larger dataset with improved vertex detection If  m s is indeed below 19 ps -1 expect a robust measurement with the extended dataset

29 BACKUP SLIDES

30 B Mesons Bu+Bu+ B0B0 Bs0Bs0 Bc+Bc+ b u b d b s b c Matter b u b c b s b d Anti-Matter

31 CKM matrix and B mixing Wolfenstein parametrisation - expansion in. complex Why are we interested to study B meson oscillations

32 B Mixing In general, probability for unmixed and mixed decays Pu,m(B)  Pu,m(B). In limit,  12 << M 12 (  <<  M) (Standard model estimate and confirmed by data), the two are equal. ~ for Bs system ~ for Bd system

33 Constraing the CKM Matrix from  m s    from Lattice QCD calculations) Ratio suffers from lower theoretical Uncertainties – strong constraint Vtd  And similar expression for  m s    CDF+D0 (2006)  m s inputs

34 Excellent Tevatron Performance Data sample corresponding to over 1 fb -1 of the integrated luminosity used for the Bs mixing analysis Full dataset is ready (85-90% DAQ efficiency) Data sample corresponding to over 1 fb -1 of the integrated luminosity used for the Bs mixing analysis Full dataset is ready (85-90% DAQ efficiency)

35 Muon Triggers Limitation of data recording. Triggers are needed to select useful physics decay modes. 396 ns bunch crossing rate ~ 2.5 MHz  ~50 Hz for data to be recorded. Single inclusive muon Trigger: |η| 3,4,5 GeV Muon + track match at Level 1 Prescaled or turned off depending on inst. lumi. We have B physics triggers at all lumi’s Extra tracks at medium lumi’s Impact parameter requirements Associated invariant mass Track selections at Level 3 Dimuon Trigger : other muon for flavor tagging e.g. at 50· cm -2 s -1, L3 trigger rate : 20 Hz of unbiased single μ 1.5 Hz of IP+μ 2 Hz of di-μ No rate problem at L1/L2 Limitation of data recording. Triggers are needed to select useful physics decay modes. 396 ns bunch crossing rate ~ 2.5 MHz  ~50 Hz for data to be recorded. Single inclusive muon Trigger: |η| 3,4,5 GeV Muon + track match at Level 1 Prescaled or turned off depending on inst. lumi. We have B physics triggers at all lumi’s Extra tracks at medium lumi’s Impact parameter requirements Associated invariant mass Track selections at Level 3 Dimuon Trigger : other muon for flavor tagging e.g. at 50· cm -2 s -1, L3 trigger rate : 20 Hz of unbiased single μ 1.5 Hz of IP+μ 2 Hz of di-μ No rate problem at L1/L2

36 μ  Sample μD s : 26,710 Opposite-side flavor tagging Tagging efficiency 21.9  0.7 % μD ± : 7,422 μD ± : 1,519 μD s : 5,601±102

37 check Using B d  XμD ± (   ) The Amplitude Scan shows Bd oscillations at 0.5 ps-1 no lifetime bias (A=1) : correct dilution calibration The Amplitude Scan shows Bd oscillations at 0.5 ps-1 no lifetime bias (A=1) : correct dilution calibration

38 Detector Effects flavor tagging power, background Decay length resolution momentum resolution  p)/p = ? %  l = ? SM prediction -  m s ~ 20 ps -1 Trying to measure : T osc ~0.3 X s ! 

39 Sample Composition Estimate using MC simulation, PDG Br’s, Evtgen exclusive Br’s Estimate using MC simulation, PDG Br’s, Evtgen exclusive Br’s Signal: 85.6%

40 Flavor tag Dilution calibration B d mixing measurement using B d  D*  X, D*  D0 , D0   , and evaluate dilution in various diution bins. Follows similar analysis outline as Bs mixing. Form measured asymmetry in 7 bins in visible proper decay length ( x M ) – Count OS and SS events (compare charge of reconstructed muon with tagger decision) Fit the  2: Also include B+  D0  X decay asymmetry. B d mixing measurement using B d  D*  X, D*  D0 , D0   , and evaluate dilution in various diution bins. Follows similar analysis outline as Bs mixing. Form measured asymmetry in 7 bins in visible proper decay length ( x M ) – Count OS and SS events (compare charge of reconstructed muon with tagger decision) Fit the  2: Also include B+  D0  X decay asymmetry.

41 Dilution calibration : Results For final fit, bin the tag variable |d| in 5 bins and do a simultaneuos fit    (i) where i=1,5. Parameters of the fit :  m, fcc, 5 D d, 5 D u = 12 For final fit, bin the tag variable |d| in 5 bins and do a simultaneuos fit    (i) where i=1,5. Parameters of the fit :  m, fcc, 5 D d, 5 D u = 12  m  stat.) ps -1  D 2 = (2.48  0.21) (%) (stat.)  stat.  Increasing dilution B0 B+

42 Individual Taggers performance Tagger  D (%)  D 2 (%) Muon 6.61    0.17(stat) Electron 1.83    0.07 (stat) SV 2.77    0.11 (stat) Total OST   0.22 (stat) Note : To evaluate the individual tagger performance |d pr | > 0.3 This cut was not imposed for final combined tagger. Final eD2 is higher.

43 Likelihood minimization to get  ms Form Probability Density Functions (PDF) for each source Minimize d pr Dilution Calibration (From  m d measurement) Signal selection function (y)

44 Bs Signal and background Signal PDF: Background PDF composed of long-lived and prompt components – Evaluated from a lifetime fit. Long Lived Background – Described by exponential convoluted with a gaussian resolution function. Non-sensitive to the tagging Non-oscillating Oscillating with Δm d frequency Prompt Background – Gaussian distribution with resolution as fit parameter. Signal PDF: Background PDF composed of long-lived and prompt components – Evaluated from a lifetime fit. Long Lived Background – Described by exponential convoluted with a gaussian resolution function. Non-sensitive to the tagging Non-oscillating Oscillating with Δm d frequency Prompt Background – Gaussian distribution with resolution as fit parameter.

45 Combine individual tag informations to tag the event. Get tag on opposite side and construct PDF’s for variables discriminating b (   ) and b (  + ) (Use B+  D 0  X decays in data) Discriminating variables (x i ): Combine individual tag informations to tag the event. Get tag on opposite side and construct PDF’s for variables discriminating b (   ) and b (  + ) (Use B+  D 0  X decays in data) Discriminating variables (x i ): Combined flavor tag algorithm more pure Electron/MuonSV Tagger

46 Ensemble Tests Using data Simulate Δm s =∞ by randomizing the sign of flavour tagging Probability to observe Δlog(L)>1.9 (as deep as ours) in the range 16 < Δm s < 22 ps -1 is 3.8% 5% using lower edge of syst. uncertainties band Using MC Probability to observe Δlog(L)>1.9 for the true Δm s =19 ps -1 in the range 17 < Δm s < 21 ps -1 is 15% Many more parameterized MC cross-checks performed – all consistent with above Using data Simulate Δm s =∞ by randomizing the sign of flavour tagging Probability to observe Δlog(L)>1.9 (as deep as ours) in the range 16 < Δm s < 22 ps -1 is 3.8% 5% using lower edge of syst. uncertainties band Using MC Probability to observe Δlog(L)>1.9 for the true Δm s =19 ps -1 in the range 17 < Δm s < 21 ps -1 is 15% Many more parameterized MC cross-checks performed – all consistent with above