1.  3 measurements by Belle Pavel Krokovny KEK Introduction Introduction Apparatus Apparatus Method Method Results Results Summary Summary

2. Measurements of  3 by Belle P. Krokovny ICHEP 2006, Moscow Unitarity Triangle Using unitarity requirement: φ 1 is measured with a high accuracy (~1º) at B-factories. φ 3 is the most challenging angle to measure. Measurement of all the angles needed to test SM.

3. Measurements of  3 by Belle P. Krokovny ICHEP 2006, Moscow Constraints of the Unitarity Triangle World average as of summer 2005 from GLW, ADS, Dalitz and sin( 2 φ 1 + φ 3 ) : γ / φ 3 = 70 -14 ° +12

4. Measurements of  3 by Belle P. Krokovny ICHEP 2006, Moscow KEKB and Belle KEKB Collider 3.5 GeV e + & 8 GeV e – beams 3 km circumference, 11 mrad crossing angle L = 1.65 x 10 34 cm –2 s –1 (world record) L dt = 630 fb –1 @ Υ(4S) +off(~10%)

5. Measurements of  3 by Belle P. Krokovny ICHEP 2006, Moscow Relative phase: ( B –  DK – ), ( B +  DK + ) includes weak ( γ/φ 3 ) and strong ( δ ) phase. B +  D 0 K + decay If D 0 and D 0 decay into the same final state, Need to use the decay where V ub contribution interferes with another weak vertex. B –  D 0 K – : Amplitude ratio:

6. Measurements of  3 by Belle P. Krokovny ICHEP 2006, Moscow GLW method M. Gronau and D. London, PLB 253, 483 (1991); M. Gronau and D. Wyler, PLB 265, 172 (1991) СР eigenstate of D -meson is used ( D CP ). CP-even : D 1  K + K –, π + π – CP-odd : D 2  K S π 0, K S ω, K S φ, K S η … for D 1 for D 2 4 equations (3 independent: ), 3 unknowns Additional constraint: СР-asymmetry:  A 1,2 of different signs

7. Measurements of  3 by Belle P. Krokovny ICHEP 2006, Moscow Belle results (253 fb -1 ) BD1KBD1K 1.13 ±0.16±0.05 0.06±0.14±0.05 BD2KBD2K 1.17±0.14±0.14-0.12±0.14±0.05 BD*1KBD*1K 1.41±0.25±0.06-0.20±0.22±0.04 BD*2KBD*2K 1.15±0.31±0.12 0.13±0.30±0.08 B ±  DK ± B ±  D*K ± B +  D 1 K + B -  D 1 K - B +  D 2 K + B -  D 2 K - GLW analyses alone do not constrain γ/φ 3 significantly yet, but can be combined with other measurements and provide information on r B Phys. Rev. D 73, 051106(R) (2006) GLW method

8. Measurements of  3 by Belle P. Krokovny ICHEP 2006, Moscow ADS method D. Atwood, I. Dunietz and A. Soni, PRL 78, 3357 (1997); PRD 63, 036005 (2001) Enhancement of СР-violation due to use of Cabibbo-suppressed D decays B –  D 0 K – - color allowed D 0  K + π – - doubly Cabibbo-suppressed B –  D 0 K – - color suppressed D 0  K + π – - Cabibbo-allowed Interfering amplitudes are comparable 

9. Measurements of  3 by Belle P. Krokovny ICHEP 2006, Moscow Belle results (357 fb -1 ) hep-ex/0508048 Suppressed channel not visible yet: Using r D =0.060±0.003, for maximum mixing ( φ 3 =0, δ=180° ): r B <0.18 (90% CL) ADS method

10. Measurements of  3 by Belle P. Krokovny ICHEP 2006, Moscow If is known, parameters are obtained from the fit to Dalitz distributions of D  K s π + π – from B ±  DK ± decays Dalitz analysis method Using 3-body final state, identical for D 0 and D 0 : K s π + π -. Dalitz distribution density: (assuming СР-conservation in D 0 decays) A. Giri, Yu. Grossman, A. Soffer, J. Zupan, PRD 68, 054018 (2003) A. Bondar, Proc. of Belle Dalitz analysis meeting, 24-26 Sep 2002.

11. Measurements of  3 by Belle P. Krokovny ICHEP 2006, Moscow Dalitz analysis : D 0  K s π + 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 D 0 decay strong phase are essential Use the model-dependent fit to experimental data from flavor-tagged D *  D 0 π sample. Model is described by the set of two-body amplitudes + nonresonant term. As a result, model uncertainty in the γ/φ 3 measurement.

12. Measurements of  3 by Belle P. Krokovny ICHEP 2006, Moscow ρ-ω interference Doubly Cabibbo Suppressed K * M (GeV 2 ) K s π – 2 D 0  K s π + π – Decay Model D*->D 0 π->[K S π + π - ]π

13. Measurements of  3 by Belle P. Krokovny ICHEP 2006, Moscow Dalitz analysis: sensitivity to  3

14. Measurements of  3 by Belle P. Krokovny ICHEP 2006, Moscow Fit parameters are x  = r cos(  φ 3 +δ) and y  = r sin(  φ 3 +δ) (better behaved statistically than ) are obtained from frequentist statistical treatment based on PDFs from toy MC simulation. 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 +0.093 +0.069 +0.090 +0.167 +0.172 +0.120 +0.137 +0.249 +0.440 +0.177 +0.164 Phys. Rev. D 73, 112009 (2006) Dalitz analysis B   DK  B   D*K  B   DK* 

15. Measurements of  3 by Belle P. Krokovny ICHEP 2006, Moscow Dalitz analysis Belle result (357 fb -1 ) 331±17 events 81±8 events 54±8 events B   DK  B   D*K  B   DK*  B-B- B+B+ B-B- B+B+ B-B- B+B+ Phys. Rev. D 73, 112009 (2006)

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

17. Measurements of  3 by Belle P. Krokovny ICHEP 2006, Moscow sin(2φ 1 +φ 3 ) from B 0  D * π decay where Use B flavor tag, measure time-dependent decay rates: Decay : + B  D -  + B tag  B 0 CP violation

18. Measurements of  3 by Belle P. Krokovny ICHEP 2006, Moscow sin(2φ 1 +φ 3 ) Belle result (357 fb -1 ) - full reconstruction with - partial reconstruction (reconstruct only pions) D * π full rec D * π partial rec Phys. Rev. D 73, 092003 (2006)

19. Measurements of  3 by Belle P. Krokovny ICHEP 2006, Moscow sin(2φ 1 +φ 3 ) S + (D*π)=0.049±0.020±0.011 S – (D*π)=0.031±0.019±0.011 S + (Dπ)=0.031±0.030±0.012 S – (Dπ)=0.068±0.029±0.012 Full-rec + partial-rec Full-rec |sin(2φ 1 +φ 3 )|>0.46 (0.13) |sin(2φ 1 +φ 3 )|>0.48 (0.07) at 68% (95%) CL CP violation significance : 2.5σ If R ~0.02: Phys. Rev. D 73, 092003 (2006)

20. Measurements of  3 by Belle P. Krokovny ICHEP 2006, MoscowSummary The angle φ 3 /  remains the most difficult angle of the Unitarity The angle φ 3 /  remains the most difficult angle of the Unitarity Triangle to measure, although there is a tremendous progress Triangle to measure, although there is a tremendous progress from B-factories. from B-factories. O(20º) Precision in direct measurements of φ 3 is achieved using new O(20º) Precision in direct measurements of φ 3 is achieved using new GGSZ method (B->D 0 [K S ππ]K) GGSZ method (B->D 0 [K S ππ]K) Other methods do not constrain γ/φ 3 significantly yet, but can be used in combined fit and provide information on r B The precision is statistically limited good perspectives for The precision is statistically limited  good perspectives for improving the result with larger data set improving the result with larger data set

21. Measurements of  3 by Belle P. Krokovny ICHEP 2006, Moscow Backup

22. Measurements of  3 by Belle P. Krokovny ICHEP 2006, Moscow B ±  DK ±, D  K S π + π – Dalitz plots D 0 from B +  D 0 K + D 0 from B -  D 0 K - ( π + and π - interchanged ) K * (892) bands

23. Measurements of  3 by Belle P. Krokovny ICHEP 2006, Moscow Control sample Same fit procedure was applied for the control sample: B  D ( * )  The results are consistent with r=0.01 for D (*)0 and with 0 for D *-  

24. Measurements of  3 by Belle P. Krokovny ICHEP 2006, Moscow Systematic errors Background shape: baseline – BB MC + continuum data sample, variations – continuum only, M BC sidebands. Efficiency over Dalitz plot: main fit – MC, variation – use high momentum D*[D  ]  E – M BC shape: vary shape parameters by 1   E – M BC for BB and qq: use different shape for qq and BB

25. Measurements of  3 by Belle P. Krokovny ICHEP 2006, Moscow Intermediate state Amplitude Phase, °Fit fraction K S σ 1 (M=520±15 MeV, Γ=466±31 MeV) K S ρ(770) K S ω K S f 0 (980) K S σ 2 (M=1059±6 MeV, Γ=59±10 MeV) K S f 2 (1270) K S f 0 (1370) K S 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% 0.4% 61.2% 0.55% 0.05% 0.14% 7.4% 0.43% 2.2% 0.09% 0.36% 0.11% 9.7% D 0  K s π + π – decay model

26. Measurements of  3 by Belle P. Krokovny ICHEP 2006, Moscow Model-independent approach D 0 decay amplitude : D 0 -D 0 interference from B +  D 0 K + : is measured directly, is model-dependent If CP-tagged D 0 are available (e.g. from ψ’’  D 0 D 0, where tag-side D 0 decays into CP-eigenstate) phase difference can be measured:

27. Measurements of  3 by Belle P. Krokovny ICHEP 2006, Moscow Model-independent Approach A.Bondar, A.Poluektov hep-ph/0510246 50 ab -1 at SuperB factory should be enough for model-independent γ/φ 3 Measurement with accuracy below 2° ~10 fb -1 at ψ(3770) needed to accompany this measurement. A.Giri, Yu. Grossman, A. Soffer, J. Zupan, PRD 68, 054018 (2003)

28. Measurements of  3 by Belle P. Krokovny ICHEP 2006, Moscow Dalitz analysis: sensitivity to  3

29. Measurements of  3 by Belle P. Krokovny ICHEP 2006, Moscow Constraints to r B