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J/  K * wrong flavor decays Discussions of some common analysis techniques in BaBar by Max Baak.

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Presentation on theme: "J/  K * wrong flavor decays Discussions of some common analysis techniques in BaBar by Max Baak."— Presentation transcript:

1 J/  K * wrong flavor decays Discussions of some common analysis techniques in BaBar by Max Baak

2 Outline Why look at J/  K * wrong flavor decays?Why look at J/  K * wrong flavor decays? -Theoretical introduction BaBar in a nutshellBaBar in a nutshell Analysis StrategyAnalysis Strategy BaBar data sampleBaBar data sample Fit & SystematicsFit & Systematics ConclusionConclusion

3 CP Violation via the CKM matrix The CKM matrix is a complex unitary matrix, coupling between quark generations and W bosons. With 3 quark generations, it allows for 4 independent, physical parameters: –3 real numbers & 1 complex non-trivial phase The existence of the complex coupling (phase) gives rise to CP violation. All CP violating observables are possible due to interference between different decay amplitudes involving a weak phase.

4 The CKM Matrix: Wolfenstein parameterization Complex phase λ =V us = sin(  cabbibo ) = ± A =V cb / λ 2 = 0.83±0.06 Out of 6 unitarity triangles, this one practically interesting: It has all sides O( 3 ) Large phases  potentially large CP asymmetries = Wolfenstein parameterization uses the observed hierarchy of the CKM elements and pushes the complex phase to the smallest elements Unitarity

5 CP violation in the inference between mixing and decay Amplitude ratio Mixing Phase In order to have CP Violation: Time evolution of initial B 0 (or B 0 ) mesons into a final CP eigenstate A single decay amplitude is sufficient -Mixed decay serves as 2 nd amplitude -Thus, amplitudes comparable by construction -Large CP asymmetries are possible!

6 Golden Decay Mode: B 0 J/y K 0 S Golden Decay Mode: B 0  J/y K 0 S Theoretically clean way (1%) to measure the phase of (i.e. sin2  ) Clean experimental signature Branching fraction: O(10 -4 ) - “large” compared to other CP modes Time-dependent CP asymmetry u,c,tu,c,t u,c,tu,c,t WW WW K 0 mixing   CP = +1 B 0  J/  K 0 L   CP = -1 B 0  J/  K 0 S B 0   (2s) K 0 S B 0   c1 K 0 S “Golden Modes”

7 Can sin2  L and sin2  S be different? * Normal assumption is that sin2b L =-sin2b S. This holds to 1% in the Standard Model - Corrections from    q/p  and suppressed penguins. Current value is: S(J/  K s ) + S(J/  K L ) = 0.04 ± Consistent with SM, but statistics limited. Can one do better? Yes! Violation of sin2b L =-sin2b S requires (different) “wrong-flavor” amplitudes, forbidden in the Standard Model. How to check for these? Practically K 0 mixes into CP states. At first order underlying physics for wrong-flavor K and K * decays assumed to be similar. Use high-statistics sample to tag K *0.  Model-independent search for new physics. * hep-ph/ (Y. Grossman, A. Kagan, Z. Ligeti)

8 J/   Mixing pdf’s Assume wrong-flavor decays are allowed. How do the pdf’s change? Define the ratios:, For final state J/  K *0 this results in the mixing equations - Where again:,. For final state simply replace by. One gets and. Equations add up to pure exponential  need to determine initial flavor (t=0 ps) of B meson to differentiate between mixed & unmixed states. Time-dependent analysis gives coefficients at few % level.

9 B meson production at BaBar Off On PEP-II B A B AR Electron-Positron collider: e + e -   (4s)  B 0 B 0 –Only  (4s) resonance can produce B meson pair –Low B 0 production cross-section: ~1 nb (total hadron ~4 nb) –Clean environment, coherent B 0 B 0 production B-Factory approach B 0 B 0 threshold BB threshold 81.3 /fb of BaBar data  88 million B’s

10  (4S): Coherent B 0 B 0 production B 0 B 0 system evolves coherently until one of the particles decays –Mixing-oscillation clock only starts ticking at the time of the first decay  relevant: time difference parameter  t –B mesons have opposite flavour at time  t=0 –Half of the time B of interest decays first (where  t<0) Integrated sine asymmetry is 0: Coherent production requires time dependent analysis At t cp =0 B0B0 B0B0 At t=0 B0B0 B0B0 t = t B1 – t B2 Coherent (BaBar) Incoherent (LHCb) -- ++ ++ --  t(ps) t(ps)

11 A(-)symmetric collider for will (not) work … A(-)symmetric collider for  (4S) will (not) work … Asymmetry is a time-dependent process –  t between two B decays of O(ps) –In reality one measures decay distance between two B decays In symmetric energy e + e - collider, where  (4S) produced at rest, daughter B’s travel ~ 20  m  too small a distance to discern. Solution: boost the CMS to increase distances in lab frame. Build an asymmetric collider! For BaBar: -High energy e - beam: 9.0 GeV -Low energy e + beam: 3.1 GeV 

12 Coherent BB pair Start the Clock This can be measured using a silicon vertex detector! (  )  (4S) = 0.56 Z In pictures:

13 Experimental technique Inclusive B-Flavor Tagging & Vertex Reconstruction Exclusive B Meson & Vertex Reconstruction Key strategies: Exclusive B-reco for 1 meson Use other B to determine flavor-tag at  t=0. Determine vertices to get  z. Question: How to handle mistags? Limited vertex resolution  need to disentangle resolution from physics.

14 True  t distributions of mixed and unmixed events perfect flavor tagging & time resolution realistic mis-tagging & finite time resolution w: the fraction of wrongly tagged events  m d : oscillation frequency Mistag rates need to be disentangled from C & S coefficients!

15 Splitting the Dilutions from the Coefficients To disentangle mistag fractions from (co)sine coefficients, a second, large data-sample is needed, having known coefficients. In BaBar uses the “Breco” sample, described with basic pdf: Including the mistags the asymmetry then turns out as: Sensitive to mistag fraction measurement because the mixing has not started yet At t=0 the observed ‘mixed’ events are only due to wrongly tagged events Folded raw asymmetry |  t| [ps]

16 Methods of B flavor tagging (1) In BaBar tagging is handled with Neural Nets. Many different physics processes can be used for tagging, primary information is listed below: Secondary lepton Kaon(s) Soft pions from D * decays Fast charged tracks Primary lepton

17 B flavor tagging performance (2) 9 sub-taggers, using combinations of the various inputs, are combined in the Tagging Neural Network. The NN ‘spits out’ 4 physics categories in which the data is cate- gorized, all with different tagging efficiencies and mistag-fractions. Tagging category Fraction of tagged events  (%) Wrong tag fraction w (%) Mistag fraction difference  w (%) Q =  (1-2w) 2 (%) Lepton 9.1     0.3 Kaon+Kpi 16.7     0.4 Kaon+Spi 19.8     0.4 Inclusive 20.0     0.2 ALL 65.6   0.7 B A B AR 81.3 fb  B A B AR 81.3 fb  Errors on C and S depend on the “quality factor” Q as: Why? Number of events is prop. to . Multiplication of C&S with  gives another factor to Q.

18 Vertex and  z reconstruction B rec vertex B rec daughters z 1.Reconstruct B rec vertex from B rec daughters Beam spot Interaction Point B rec direction B tag direction 2.Reconstruct B tag direction from B rec vertex & momentum, beam spot, and  (4S) momentum = pseudotrack B tag Vertex tag tracks, V 0 s 3.Reconstruct B tag vertex from pseudotrack plus consistent set of tag tracks 4.Convert from Δz to Δt, accounting for (small) B momentum in  (4S) frame Note: event multiplicity Result: σ ( Δz) rms ~ 180μm (Δt=0.6ps) versus ~ βγcτ = 260μm

19 Actual  t signal resolution function Actual  t signal resolution function high flexibility zz Signal MC (B 0 )  t  (meas-true)   t event-by-event  (  t) from vertex errors Resolution Function (RF): –Sum of 3 Gaussians (mixing + CP analyses) –Core: correct vertex (90%). Error systematically underestimated, so scaled up with S core (~1.1). –Tail: nearly correct vertex (10%). Reco. vertex picked up (a) track(s) from the tag B. –Outliers (< 0.1%): wrong vertex. Outlier component serves as a “vacuum cleaner”. ~0.6 ps tracks from long-lived D’s in tag vertex  asymmetric RF

20 Effect of charm tracks on  t D flight direction bias  (z tag ) Charm tracks z tag Prompt B tracks  t true  t meas z rec  t meas –  t true < 0  t > 0 z axis D flight direction bias  (z tag ) Charm tracks z tag Prompt B tracks  t true  t meas z rec  t meas –  t true < 0  t < 0 Underlying principle: tag vertex dominates resolution. tag  z ~110  m, reco  z ~65  m Bias:  core =  b core   t,  tail =  b tail   t,  outl =  0

21 Correlation:  t  residual  t bias Monte Carlo z axis z tag Prompt B tracks Charm tracks D flight direction  (  t) smallest,  t bias zero  (z tag ) D flight direction bias  (z tag ) Charm tracks z tag Prompt B tracks  (  t) largest,  t bias largest

22 B reconstruction For exclusive B reconstruction, two nearly uncorrelated kinematic variables are employed to cut on background. Both use the property that E beam is well known: Signal at  E ~ 0 Signal at m ES ~ m B Resolutions Typically,  E dominated  E (at least 5 times larger than  beam )

23 Example m ES EE sidebands signal region m ES [GeV/c 2 ]  E [MeV] Typically,  E is fit for all events with m ES > 5.27 GeV. The entire mass spectrum is then refit within the energy window to obtain bkg. probablities, to be used as inputs in the likelyhood fit.

24 N tag = Purity = 81.6% Sigma = 2.76 MeV Breco Sample – All B A B AR 81.3 fb  B A B AR 81.3 fb  m ES [GeV/c 2 ] Charm decay modes B open Charm decay modes The Breco sample contains 24 reconstructed B 0 open charm modes. Prob(sig) ~ 81.6 % Prob(sig) ~ 0 % Gaussian ARGUS function

25 Breco Sample – Per tagging category (example) Lepton Kaon Lepton NT2NT1 B A B AR 29.7 fb  B A B AR 29.7 fb 

26 J/  K * data sample Cleanest data sample in BaBar! Yield: 1641 events, Purity = 97.3 %, Mass resolution = 2.7 MeV Set ‘tight’ K and  selection, to minimize accidental swapping.

27 Fitting Technique Analysis performed blind to prevent experimenters’ bias. Simultaneous unbinned maximum log-likelihood fit to  t spectra of both Breco and J/  K * samples. (Likelihood fit accounts for Poisson stats.) Fit for cosine and sine coefficients: C, S, C, S. -Signal model: pdf for mixed and unmixed events (4) convolved with triple gaussian signal resolution function (8). Dilutions and dilution-diff’s between B 0 and B 0 tags are incorporated for each tagging category (8).  B and  m d fixed to PDG 2002 values. -Background model: prompt and lifetime components for mixed and unmixed data (5) convolved with double gaussian resolution function (5). Separate dilutions for background description (10). -Assign probabilities for individual events per tagging category to be signal (prob sig ) or bkg (1-prob sig ), based on observed m ES value and a global fit to the m ES distribution. -Likelihood function: Sum all signal and bkg pdf’s for a combined fit with a total of 40 free parameters.

28 Background description MC cocktail 4 types of background are accounted for in empirical Dt description: “Argus background” (combinatorics) Prompt background: no time dependence (70%) Lifetime 1: pure double-sided exponential Lifetime 2: exponential + mixing terms Peaking background (in ‘signal probability’) Lifetime 3: double-sided exponential, fixed to B + lifetime. peaking bkg For J/  K * data: 2.5 % Argus shape background: 1.2 % from inclusive J/  ’s Peaking background (from incl. J/  MC): 2.3 % J/  K -    (non resonant) 1.1 % J/      S

29 Systematic errors on C(C) and S(S) (preliminary!)  [C]  [S] Description of background events (Co)sine content of background components Bkg. shape uncertainties, peak. component  t resolution and detector effects Silicon detector residual misalignment  t resolution model (B reco vs B J/Y K*, tag vs mistag) Mistag diff’s B reco and B J/Y K* samples CKM-suppressed decays on tag-side K  swapping Fixed lifetime and oscillation frequency Total

30 Conclusions No conclusions yet: analysis is still blinded.  (C) =  (C) =   (S) =  (S) =  Max C correlation: 29 %max S correlation: 9 % Expected error:  (S(J/  K s ) + S(J/  K L )) = 0.14 (old: 0.17)


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