B S Mixing at Tevatron Donatella Lucchesi University and INFN of Padova On behalf of the CDF&D0 Collaborations First Workshop on Theory, Phenomenology and Experiments in Heavy flavour physics May , Capri, Italy

Donatella Lucchesi2 May 31, 2006 B s Mixing in The Standard Model In the ratio uncertainties cancels:   = (M. Okamoto, hep-lat/ ) Big uncertainties

Donatella Lucchesi3 May 31, 2006 Measurement Principle in a Perfect World B s vs. B d oscillation B lifetime Rather than fit for frequency perform a ‘Fourier transform’  m s [ps -1 ]  A

Donatella Lucchesi4 May 31, 2006 Road Map to  m s Measurement 1. Final state reconstruction 2. High resolution on proper decay length 3. Tag B flavor at production time Opposite Side fragmentation particle: , K… ,K

Donatella Lucchesi5 May 31, 2006 Adding all the realistic effects Proper time resolution Flavor tagging power

Donatella Lucchesi6 May 31, 2006 Road Map to  m s Measurement 1. Final state reconstruction 2. High resolution on proper decay length 3. Tag B flavor at production time Opposite Side fragmentation particle: , K… ,K measure efficiency  and dilution D:  D 2 gives the “effective” number of events

Donatella Lucchesi7 May 31, 2006 Primary Vertex Secondary Vertex d = impact parameter B Decay Length L  ~ 48  m includes 33  m of beam spot Triggers Used CDF: Two tracks displaced from PV D0:  Single inclusive muons o Pt>3,4,5 GeV  Dimuons: o Other muon for flavor tagging

Donatella Lucchesi8 May 31, 2006 B s Data sample B s  D s  D s   KK D s  K *0 K K *0  K  D s  3  B s  D s 3  D s  D s  K *0 K Signal B s  D s  D s  Partially reconstructed B mesons Combinatorial background B0 D-B0 D-

Donatella Lucchesi9 May 31, 2006 CDF Hadronic B s yields summary Decay channelYield B s  D s  D s  1570±43 B s  D s  D s  K *0 K857±32 B s  D s  D s  3  612±37 B s  D s 3  D s  493±37 B s  D s 3  D s  K *0 K204±26 Total3736±79 B +  D 0  ~ 26,000 B 0  D -  ~ 22,000

Donatella Lucchesi10 May 31, 2006 CDF Semileptonic samples B s  D s l X D s   KK D s  K *0 K K *0  K  D s  3  D s l ~ 53,000

Donatella Lucchesi11 May 31, 2006 Decay channel: B s  + D s - X D s -  - and  K + K - Cuts selected maximize N Bs = 26,710 ± 556(stat) +D-+D- +Ds-+Ds- D0 Semileptonic samples

Donatella Lucchesi12 May 31, 2006 Road Map to  m s Measurement 1. Final state reconstruction 2. High resolution on proper decay length 3. Tag B flavor at production time Opposite Side fragmentation particle: , K… ,K

Donatella Lucchesi13 May 31, 2006 Proper decay time reconstruction  Semileptonic decay ct = L xy lD M B /P t lD  K  Fully reconstructed events ct = L xy B M B /P t B CDF K=  P t lD /P t B  L xy B /L xy lD  It is needed to:  Measure the lifetime to establish the time scale  Determine the time resolution D0 K=  P t lD /P t B 

Donatella Lucchesi14 May 31, 2006 B Lifetime measurement c  (B s )=1.538±0.040(stat) ps Central value c  (B s )=  m Statistical error ~10  m

Donatella Lucchesi15 May 31, 2006 Proper time resolution,  t  Lifetime measurement not very sensitive  In the  m s fit each event weighted by its resolution  Dedicated calibration needed Prompt Charm + track sample J/  +  - sample

Donatella Lucchesi16 May 31, 2006 Proper time resolution,  t

Donatella Lucchesi17 May 31, 2006 Road Map to  m s Measurement 1. Final state reconstruction 2. High resolution on proper decay length 3. Tag B flavor at production time Opposite Side fragmentation particle: , K… ,K measure efficiency , dilution D  D 2 gives the “effective” number of events N right -N wrong N right +N wrong D=D= = 2 P right -1

Donatella Lucchesi18 May 31, 2006 +D-+D- +Ds-+Ds- N = 5601 ± 102 (stat) -lepton (electron or muon) - Secondary Vertex - Event Charge Tags combined Opposite Side Taggers  Use data to calibrate the taggers and to evaluate D  Fit semileptonic and hadronic B d sample to measure: D,  m d  D 2 =2.48  0.21(stat.) (syst.)%

Donatella Lucchesi19 May 31, 2006 Same Side Tagger B 0 s likely to have K B 0 /B ± likely to have  nearby Use PID to separate pion from kaon Tune Monte Carlo to reproduce B 0,B - distributions then apply to B s

Donatella Lucchesi20 May 31, 2006 Flavor Taggers performances  Exclusive combination of tags in OST  SSTK-OST combination assumes independent tagging information

Donatella Lucchesi21 May 31, 2006 Amplitude Scan notation  A is introduced:  A=1 when  m s measured =  m s true B 0 mixing in hadronic decay In the figure:  Points: A±  (A) from Likelihood fit for different  m  Yellow band: A±1.645  (A)  Dashed line:  (A) vs.  m   m excluded at 95% C.L. if A±1.645  (A)<1  Measured sensitivity:  (A)=1

Donatella Lucchesi22 May 31, 2006 D0 Results “favored value’’ = 19 ps -1 17<  m s <21 ps -1 at the 90% C.L.  m  19 ps -1 : A/  A=2.5 and A-1/  A=1.6 Sensitivity = 14.1ps -1  m s >14.8 at the 95% C.L.

Donatella Lucchesi23 May 31, 2006 Choice of Procedure Before un-blinding: p-value probability that observed effect is due background fluctuation. No search window. p-value<1%? make double sided confidence interval from  (ln( L )), measure  m s set 95% C.L. based on Amplitude Scan yes no ln[ L (A=1)/ln L (A=0)] Probability of random tag fluctuation estimated on data (randomized tags) and checked with toy Monte Carlo

Donatella Lucchesi24 May 31, 2006 CDF Amplitude Scans Sensitivity: 17.3 ps -1  m s > 15.9 ps 95% CL Sensitivity: 25 ps -1  m s > 16.7 ps 95% CL

Donatella Lucchesi25 May 31, 2006 CDF Combined Amplitude Scan Sensitivity better than the W.A ps -1 Rare case!!

Donatella Lucchesi26 May 31, 2006 Likelihood Profile & significance How often random tags produce a likelihood deep this dip? Probability of fake: p-value=0.5% Measure  m s !!!

Donatella Lucchesi27 May 31, 2006 Measurement of  m s  m s = ± 0.07 ps <  m s <17.91 ps -1 at 90% C.L <  m s <17.97 ps -1 at 95% C.L.

Donatella Lucchesi28 May 31, 2006 |V td |/|V ts | Determination Used as inputs:  m Bs /m Bd = PDG 2006   2 = ( M. Okamoto, hep-lat/ )   m d = 0.507±0.005 PDG |V td |/|V ts |= (stat.+syst.) |V td |/|V ts | = (stat) (syst) Latest Belle result b  s  ( hep-ex/ ):

Donatella Lucchesi29 May 31, 2006 Conclusions  1 fb -1 of data used for Bs oscillation study  D0:  2.5  deviation from 0 in the Amplitude Scan at  m s =19 ps -1  90% C.L. interval for  m s : ps -1 o For the summer: Include D s  K*K, D s  K s K D s  3  and e+D s Include hadronic decays Include Same Side Tagging

Donatella Lucchesi30 May 31, 2006 Conclusions cont’d  CDF:  experimental signature for B s -B s oscillations  Probability of random fluctuation is 0.5%  First direct measurement of:  m s = ± 0.07 ps |V td |/|V ts |= (stat.+syst.) o Future: Include other decays (Partially recon. D s *  D s  /  ) Combine efficiently flavor tags Improve ct resolution

Donatella Lucchesi31 May 31, 2006 BACKUP

Donatella Lucchesi32 May 31, 2006 The Accelerator

Donatella Lucchesi33 May 31, 2006 Detector for the measurement: CDF Trigger: displaced tracks (SVT) Tagging Power: TOF & dE/dX (COT) Proper time Resolution: SVX and L00

Donatella Lucchesi34 May 31, 2006 Detector for the measurement: D0 Fiber and Silicon trackers in 2T Solenoid field Fine segmentation Liquid Ar Calorimeter & Preshower Three layers system & absorber Hermetic detector

Donatella Lucchesi35 May 31, 2006 Tevatron Luminosity 1fb -1 Used in the analysis

Donatella Lucchesi36 May 31, 2006 Parametrizing tag decision

Donatella Lucchesi37 May 31, 2006 Calibrating SSTK

Donatella Lucchesi38 May 31, 2006 Calibrating SSTK Tune MC to reproduce B 0/± dilution and then measure it for SSTK

Donatella Lucchesi39 May 31, 2006 D0 Procedure Correction factor due to missing neutrino Several effects taken into account:  Resolution scale factor for detector mismodeling  Reconstruction efficiency as function of decay length  Physical and combinatorial background contributions

Donatella Lucchesi40 May 31, 2006 Systematic Uncertainties Amplitude Scan Related to absolute value of A important when setting a limit Cancel out in A/  A Very small compared to statistical error

Donatella Lucchesi41 May 31, 2006 Combined Amplitude Scan: an other view

Donatella Lucchesi42 May 31, 2006 Systematic Uncertainties on  m s Fit Model: negligible Relevant only lifetime scale