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γ/φ 3 model-independent Dalitz analysis (Dalitz+CP tagged Dalitz plots and γ/φ 3 extraction)

γ/φ 3 model-independent Dalitz analysis (Dalitz+CP tagged Dalitz plots and γ/φ 3 extraction). Alex Bondar, Anton Poluektov Budker Institute of Nuclear Physics Novosibirsk, Russia. The relative phase γ ( φ 3 ). Interference between tree-level decays; theoretically clean.

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γ/φ 3 model-independent Dalitz analysis (Dalitz+CP tagged Dalitz plots and γ/φ 3 extraction)

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  1. γ/φ3 model-independentDalitz analysis(Dalitz+CP tagged Dalitz plots and γ/φ3 extraction) Alex Bondar, Anton Poluektov Budker Institute of Nuclear Physics Novosibirsk, Russia Charm 2007, Cornell University

  2. The relative phase γ (φ3) Interference between tree-level decays; theoretically clean Favored:VcbVus* Vcs*Vub: suppressed u s Common final state K(*)- K(*)- s u u b B- B- b c c u f D(*)0 D(*)0 u u Parameters:f3, (rB, δ) per mode • Three methods for exploiting interference (choice of D0 decay modes): • Gronau, London, Wyler (GLW): Use CP eigenstates of D(*)0 decay, e.g. D0 Ksπ0, D0  π+ π- • Atwood, Dunietz, Soni (ADS): Use doubly Cabibbo-suppressed decays, e.g. D0  K+π- • Giri, Grossman, Soffer, Zupan (GGSZ) / Belle: UseDalitz plot analysis of 3-body D0 decays, e.g.Ks π+ π- Charm 2007, Cornell University

  3. Dalitz analysis method • Measure B+/B- asymmetry across Dalitz plot • Includes GLW (D0  Ks ρ0, CP eigenstate)and ADS (D0  K*+π-, DCS 2-body decay) regions amplitude decay Mirror symmetry between D0 and D0 Dalitz plots Sensitivity to f3 in interference term Determine fin flavor-tagged D*+D0π+ decays 2-fold ambiguity on f3: (f3, δ)→ (f3+π, δ+π) Model uncertainty ~ 100 Charm 2007, Cornell University

  4. M (GeV 2 ) Ksπ – 2 D0 Ksπ+π–decay model Doubly Cabibbo suppressed K* ρ-ω interference Charm 2007, Cornell University

  5. 2f3 rB Belle/Babar model-dependent results • HFAG averages for x± = rB cos( δ± f3 ) , y± = rB sin( δ± f3 ) • Belle/Babar measurements in good agreement • Note: σ(f3) depends significantly on the value of rB Contours do not include Dalitz model errors Contours do not include Dalitz model errors Charm 2007, Cornell University

  6. Model-independent analysis Model-independent way: obtain D0 decay strong phase fromψ(3770)DDdata (1) where Free parameters Unknown, can be obtainedfrom charm data: DCPKSπ+π–: (2) (3) ψ(3770)(KSπ+π–)D (KSπ+π–)D : Charm 2007, Cornell University

  7. Model-independent analysis • CLEO-c with 750 pb-1 (estimated numbers) ~ 1000 DCPKSπ+π–decays with CP-eigenstate tag. • ~ 2000 correlated D0 decays: ψ(3770)(KSπ+π–)D (KSπ+π–)D • ψ(3770)(KLπ+π–)D (KSπ+π–)D • We need to find a way: • how to use this data most efficiently • how to combine the results of two experiments • Binned approach: • Divide Dalitz plots into bins • Solve the system of equations with constraints Charm 2007, Cornell University

  8. Binned analysis: DCP [A. Giri, Yu. Grossman, A. Soffer, J. Zupan, PRD 68, 054018 (2003)] Number of events in D0-plot: -i Number of events in B-plot (4) i Number of events in DCP-plot (5) ( =1 if bin size is small enough) • ci , si can be obtained from B data only • ci from DCP, si from B data • si constrained as  Very poor sensitivity  Poor sensitivity fory  Bias if bin size is large Charm 2007, Cornell University

  9. Binned analysis: DCP [A. Bondar, A.Poluektov, Eur. Phys. J. C47 347-353 (2006), hep-ph/0510246] 50 ab-1 (50000 ev.) at SuperB should be enough for model-indep. φ3 measurement with accuracy 2-3° ~10 fb-1 (10000 ev.) at ψ(3770) needed to accompany this measurement. Nearest future: ~1000 DCP events at CLEO. Bin size should be large  bias due to rB=0.2 Charm 2007, Cornell University

  10. Binned analysis: DCP [A. Bondar, A.Poluektov, hep-ph/0703267] • To use the limited CLEO-c data: • Find binning with optimal sensitivity • Get rid of bias due to Satisfy simultaneously for binning with Good approximation: uniform binning in ΔδD But the optimal binning depends onD0 model.  bias if it differs from the actual one (~10° by toy MC). causes unavoidablemodel sensitivity. Reduces as data increases (by applying finer binning). Charm 2007, Cornell University

  11. Binned analysis: (KSπ+π–)2 2 correlated Dalitz plots, 4 dimensions: (6) Can use maximum likelihood technique: (7) with ci and si as free parameters. For the same binning as in DCP, number of bins is N2 (instead of N), but the number of unknowns is the same. With Poisson PDF, it’s OK to have Nij<1. Can obtain both ci and si. Charm 2007, Cornell University

  12. Binned analysis: (KSπ+π–)2 [A. Bondar, A.Poluektov,hep-ph/0703267] • Can use the same binning as in DCP • ci ,simeasured independently  no model uncertainty due to constraint • Only 4-fold ambiguity: ci -c-i or si -s-i.reduces to 2-fold if DCP data are used with the same binning. • Stat. sensitivity comparable to DCP ci ,simeasured in toy MC (points) and calculated (crosses) for ΔδD-binning Charm 2007, Cornell University

  13. MC simulation of the bias in f3 measurement Model dependence for 2x8 bins in Dcp case: Model dependence for 2x8 bins in (Ksp+p-)2 case: Charm 2007, Cornell University

  14. Summary of stat. sensitivity Errors corresponding to 1000 events in B, DCP and (Kππ)2 samples Expected charm data contribution for 750 fb-1 at CLEO-c: (1000 DCP and 2000 (Kππ)2) σx=0.003, σy=0.007 σ(φ3)~3° with rB=0.1 Charm 2007, Cornell University

  15. Conclusion • Several approaches are proposed for model-independent analysis: • Binned with DCP (original GGSZ): implemented, studied. Bias with limited statistics. • Binned with (KSπ+π–)2: Twice as much data, similar to DCP sensitivity. No bias, less ambiguity. • Getting ready for model-independent measurement together with CLEO. Analysis strategy needs to be discussed C/t factory BaBar Super HFAG Super B factory Belle HFAG CLEO Super Babar/Belle Charm 2007, Cornell University

  16. Backup slides Charm 2007, Cornell University

  17. Dalitz analysis method A. Giri, Yu. Grossman, A. Soffer, J. Zupan, PRD 68, 054018 (2003) A. Bondar, Proc. of Belle Dalitz analysis meeting, 24-26 Sep 2002. Using 3-bodyfinalstate, identical for D0and D0: Ksπ+π-. Dalitz distribution density: (assuming СР-conservationin D0 decays) If is known, parameters are obtained from the fit to Dalitz distributionsof DKsπ+π–fromB±DK±decays Charm 2007, Cornell University

  18. D0 Ksπ+π–decay Statistical sensitivity of the method depends on the properties of the 3-body decay involved. (For|M|2=Const there is no sensitivity to the phaseθ) Large variations ofD0decay strong phase are essential Use the model-dependent fit to experimental data from flavor-tagged D* D0π sample. Model is described by the set of two-body amplitudes + flat non-resonant term. As a result, model uncertainty in the γ/φ3 measurement (~10° currently). Charm 2007, Cornell University

  19. Binning optimization  Maximizing “binning quality” function allows to find a binning with the B-stat. sensitivity close to unbinned approach. Charm 2007, Cornell University

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