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

Unitarity Triangle Using unitarity requirement: φ1 is measured with a high accuracy (~1º) at B-factories. φ3 is the most challenging angle to measure. Measurement of all the angles needed to test SM.

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

KEKB and Belle KEKB Collider L= 1.65 x 1034 cm–2s–1 L dt = 655 fb–1 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

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

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-body final state, identical for D0 and D0: Ksπ+π-. Dalitz distribution density: (assuming СР-conservation in D0 decays) If is known, parameters are obtained from the fit to Dalitz distributions of D Ksπ+π– from B±DK± decays

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 phase θ) Large variations of D0 decay 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.

D0  Ksπ+π– decay model Intermediate state Amplitude Phase, ° Fit fraction KS σ1 (M=520±15 MeV, Γ=466±31 MeV) KS ρ(770) KS ω KS f0(980) KS σ2 (M=1059±6 MeV, Γ=59±10 MeV) KS f2(1270) KS f0(1370) KS ρ(1450) K* (892)+π– K*(892)–π+ K*(1410)+π– K*(1410)–π+ K*0(1430)+π– K*0(1430)–π+ K*2(1430)+π– K*2(1430)–π+ K*(1680)+π– K*(1680)–π+ Nonresonant 1.43±0.07 1 (fixed) 0.0314±0.0008 0.365±0.006 0.23±0.02 1.32±0.04 1.44±0.10 0.66±0.07 1.644±0.010 0.144±0.004 0.61±0.06 0.45±0.04 2.15±0.04 0.47±0.04 0.88±0.03 0.25±0.02 1.39±0.27 1.2±0.2 3.0±0.3 212±4 0 (fixed) 110.8±1.6 201.9±1.9 237±11 348±2 82±6 9±8 132.1±0.5 320.3±1.5 113±4 254±5 353.6±1.2 88±4 318.7±1.9 265±6 103±12 118±11 164±5 9.8% 21.6% 0.4% 4.9% 0.6% 1.5% 1.1% 61.2% 0.55% 0.05% 0.14% 7.4% 0.43% 2.2% 0.09% 0.36% 0.11% 9.7%

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

Dalitz analysis: sensitivity to f3

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

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 +0.072 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 +0.167 +0.249 +0.093 +0.172 +0.440 +0.069 +0.120 +0.177 +0.090 +0.137 +0.164

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+

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

Dalitz analysis φ3=66-20 °(stat) φ3=86-93°(stat) φ3=11-57°(stat) +19 Phys. Rev. D 73, 112009 (2006) BDK BDK* BD*K φ3=66-20 °(stat) φ3=86-93°(stat) φ3=11-57°(stat) +19 +37 +23 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

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’’ D0 D0 , where tag-side D0 decays into CP-eigenstate) phase difference can be measured:

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.

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

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