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

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

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.

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

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!

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”

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)

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.

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

 (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)

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 

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

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.

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!

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]

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

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.

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

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

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

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

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 )

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.

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

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

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.

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.

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

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

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)