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

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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

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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.

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The CKM Matrix: Wolfenstein parameterization Complex phase λ =V us = sin( cabbibo ) = 0.2205 ±0.0018 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

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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!

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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 WW WW 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”

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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 ± 0.17 - 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/0204212 (Y. Grossman, A. Kagan, Z. Ligeti)

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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.

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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

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(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)

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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

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

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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.

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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!

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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]

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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

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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 0.23.3 0.6 -0.9 0.5 7.9 0.3 Kaon+Kpi 16.7 0.29.9 0.7-0.2 0.510.7 0.4 Kaon+Spi 19.8 0.320.9 0.8-2.7 0.6 6.7 0.4 Inclusive 20.0 0.331.6 0.9-3.2 0.6 0.9 0.2 ALL 65.6 0.528.1 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.

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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 10-12 Result: σ ( Δz) rms ~ 180μm (Δt=0.6ps) versus ~ βγcτ = 260μm

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Actual t signal resolution function Actual t signal resolution function high flexibility zz 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

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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

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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

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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 )

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Example m ES EE 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.

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N tag = 30977 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

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

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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.

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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.

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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

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Systematic errors on C(C) and S(S) (preliminary!) [C] [S] Description of background events0.0140.011 (Co)sine content of background components Bkg. shape uncertainties, peak. component t resolution and detector effects 0.0190.022 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* samples0.0110.002 CKM-suppressed decays on tag-side0.0060.018 K swapping 0.0120.002 Fixed lifetime and oscillation frequency0.0080.013 Total0.0310.033

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Conclusions No conclusions yet: analysis is still blinded. (C) = (C) = 0.055 0.031 (S) = (S) = 0.094 0.033 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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