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Measurement of φ3 using Dalitz plot analysis of B+D(*)K(*)+ by Belle

This paper presents the measurement of the angle φ3, the most challenging angle to measure in the Unitarity Triangle, using the Dalitz plot analysis of the decay B+D(*)K(*)+. The results are obtained from data collected at the KEKB collider with the Belle detector.

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Measurement of φ3 using Dalitz plot analysis of B+D(*)K(*)+ by Belle

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  1. Measurement of f3 using Dalitz plot analysis of B+ D(*)K(*)+by Belle Pavel Krokovny KEK Introduction Apparatus Method Results Summary

  2. Unitarity Triangle Using unitarity requirement: φ1 is measured with a highaccuracy (~1º) atB-factories. φ3 is the most challenging angle to measure. Measurement of all the angles needed to testSM.

  3. Constraints of the Unitarity Triangle World average as of summer 2005 from GLW, ADS, Dalitz and sin(2φ1+φ3): γ/φ3=70 -14° +12

  4. KEKB and Belle KEKB Collider 3.5 GeV e+ & 8 GeV e–beams 3 km circumference, 11 mrad crossing angle L= 1.65 x 1034 cm–2s–1 L dt = 655 fb–1

  5. B+ D0K+ decay Need to use the decay whereVubcontribution interferes with another weak vertex. B– D0K–:B– D0K–: If D0 and D0decay into the same final state, Relative phase: (B– DK–), (B+ DK+) includesweak (γ/φ3) and strong (δ) phase. Amplitude ratio:

  6. 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

  7. Dalitz analysis: D0 Ksπ+π– 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 + nonresonant term. As a result, model uncertainty in the γ/φ3 measurement.

  8. D0 Ksπ+π– decay model

  9. M (GeV 2 ) Ksπ – 2 D0 Ksπ+π– Decay Model D*->D0π->[KSπ+π-]π Doubly Cabibbo Suppressed K* ρ-ω interference

  10. Dalitz analysis: sensitivity to f3

  11. Dalitz analysis Phys. Rev. D 73, 112009 (2006) Belle result (357 fb-1) BD*K BDK* BDK 81±8 events 54±8 events 331±17 events B- B+ B- B- B+ B+

  12. Dalitz analysis Phys. Rev. D 73, 112009 (2006) Fit parameters are x= r cos(φ3+δ) and y= r sin(φ3+δ) (better behaved statistically than ) are obtained from frequentist statistical treatment based on PDFs from toy MC simulation. BDK BD*K BDK* x–= 0.025-0.080 y–= 0.170-0.117 x+= –0.135-0.070 y+= –0.085-0.086 x-= –0.128-0.146 y-= –0.339-0.158 x+= 0.032-0.116 y+= 0.008-0.136 x–= –0.784-0.295 y–= –0.281-0.335 x+= –0.105-0.167 y+= –0.004-0.156 +0.072 +0.167 +0.249 +0.093 +0.172 +0.440 +0.069 +0.120 +0.177 +0.090 +0.137 +0.164

  13. Control sample Same fit procedure was applied for the control sample: B  D(*)p The results are consistent with r=0.01 for D(*)0 p+ and with 0 for D*- p+

  14. Systematic errors Background shape: baseline – BB MC + continuum data sample, variations – continuum only, MBC sidebands. Efficiency over Dalitz plot: main fit – MC, variation – use high momentum D*[D p] DE – MBC shape: vary shape parameters by 1 s DE – MBC for BB and qq: use different shape for qq and BB

  15. Dalitz analysis Phys. Rev. D 73, 112009 (2006) BDK BDK* BD*K φ3=86-93°(stat) φ3=11-57°(stat) φ3=66-20 °(stat) +23 +19 +37 Combined for 3 modes:φ3=53°+15 3° (syst)9° (model) 8°<φ3<111° (2σ interval) rDK =0.159+0.054 0.012(syst)0.049(model) CPV significance: 74% rD*K=0.175+0.108 0.013(syst)0.049(model) rDK*=0.564+0.216 0.041(syst)0.084(model) -18 -0.050 -0.099 -0.155

  16. Model-independent approach D0 decay amplitude: D0-D0 interference from B+ D0K+: is measured directly, is model-dependent If CP-tagged D0 are available (e.g. from ψ’’ D0D0 , where tag-side D0 decays into CP-eigenstate) phase difference can be measured:

  17. Model-independent Approach A.Bondar, A.Poluektov hep-ph/0510246 A.Giri, Yu. Grossman, A. Soffer, J. Zupan, PRD 68, 054018 (2003) 50 ab-1 at SuperB factory should be enough for model-independent γ/φ3 Measurement with accuracy below 2° ~10 fb-1 at ψ(3770) needed to accompany this measurement.

  18. Summary • The angle φ3/g remains the most difficult angle of the Unitarity Triangle to measure, although there is a big progress from B-factories. • O(20º) Precision in direct measurements of φ3 is achieved using Dalitz analysis method (B->D0[KSππ]K) • The precision is statistically limited  good perspectives for • improving the result with larger data set

  19. Backup

  20. Constraints to rB

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