1. ϕ 3 measurements at B factories Yasuyuki Horii Kobayashi-Maskawa Institute, Nagoya University, Japan Epiphany Conference, Cracow, 9th Jan. 2012 1

2. Experiments Contributing to ϕ 3 Determination Belle e + e − collision at 10.6 GeV BaBar e + e − collision at 10.6 GeV _ CDF pp collision at 1.96 TeV LHCb pp collision at 7 TeV With charm inputs by CLEO, etc. 2

3. CKM Matrix and Unitary Triangle  Charged-current interaction Lagrangian:  CKM matrix and unitary triangle: orthogonal 3

4. CKM Parameters and ϕ 3  Precision on ϕ 3 has been improved in recent years (20°  10°).  Good agreement with measurements of other CKM parameters. Recent Result by CKMfitter Full Frequentist Method Recent Result by UTfit Bayesian Method ϕ 3 = 68° +10° −11° ϕ 3 = 74°±11° 4

5. Definition and Golden Mode for ϕ 3  Definition:  Golden mode: B  DK Color allowed. Final state contains D. Color suppressed. Final state contains D. _ ϕ 3 ~ −arg(V ub ) Only large complex element. L. Wolfenstein, PRL 51, 1945 (1983) 5 Tree processes

6. Method of ϕ 3 Measurement  Exploit the interference between the decay chains through D and D. – Angle ϕ 3 (as well as strong phases) appears in the decay rates.  Several choices of the D decays: – D  KK, ππ, K S π 0, K S φ, K S ω, … (Gronau, London, and Wyler) – D  Kπ, Kππ 0, … (Atwood, Dunietz, and Soni) – D  K S ππ, K S KK, … (Bondar, Giri, Grossman, Soffer, and Zupan) 6 B-D0K-B-D0K- B-D0K-B-D0K- _ D0fD0f D0fD0f _ B-B- f K - 33 ① ② Decay rate ∝ |A(①) + A(②)| 2 _ If no interference, angle disappears.

7.  Current constraint on ϕ 3 mainly obtained by GGSZ while additional improvement is provided by GLW and ADS. 7

8. GLW: Amplitude Triangles and Observables  Amplitude triangles:  Usually-measured observables: Magnitude of one side is ~0.1 of the others while relative magnitude of the others help ϕ 3 constraint. 8

9. B -  D CP+ K - B +  D CP+ K + B -  D CP- K - B +  D CP- K + GLW by Belle Red: signal Magenta: B  Dπ Green: BB BG Blue: qq BG (q=u, d, s, c) Light blue: peaking BG Significant CP asymmetry for CP+ mode. Opposite asymmetry btw CP+ and CP−. LP 2011 preliminary, 772M BB CP+ (K + K −, π + π − ): 582 ± 40 eventsCP− (K S π 0, K S η): 476 ± 37 events Systematics dominated by peaking BG. 9

10. GLW by LHCb  Result obtained by using data taken in 2010. EPS 2011 preliminary, 35.6 pb -1 Signal clearly seen. Promising result for obtaining nice R CP+ /A CP+ at higher statistics. 10

11. GLW up to 2010 BaBar, 467M BB, PRD82, 072004 (2010) D CP− K − D CP− K + D CP+ K − D CP+ K + CDF, 1 fb -1, PRD81, 031105(R) (2010) Opposite asymmetry btw CP+ and CP−. Consistent with the results of Belle. Good agreement with other measurements. 11 D (ππ) K − D (ππ) K + D (KK) K − D (KK) K +

12. Summary for GLW  All results for B  D CP K obtained in 2010-2011.  Good agreement in measurements by different experiments.  CP violation clearly established for CP+ ( ϕ 3 information). 12

13. ADS: Amplitude Triangles and Observables  Amplitude triangles:  Usually-measured observables: Magnitudes of the sides are small relatively to the GLW ones (small signal) while three sides of the triangles have similar magnitudes (large CPV). Additional parameters: Inputs from charm factories. Larger contribution from continuum BG. 13

14. ADS by Belle PRL106, 231803 (2011), 772M BB  First evidence is reported by Belle with significance of 4.1σ.  Improved continuum suppression with NeuroBayes neural network.  Observables:  Indication of important information for ϕ 3 measurement: R ADS and A ADS varies in [0.2, 2.5] x 10 -2 and [-0.9, 0.9], respectively, depending on ϕ 3 and strong phases (assuming r B = 0.1). continuum Signal Dπ BB 14

15. ADS by LHCb  LHCb also obtain evidence of ADS signal: EPS 2011 Preliminary, 343 pb -1 4.0σ significance Good agreement with the results of Belle. 15

16. ADS by CDF  CDF also obtain evidence of ADS signal (3.2σ): Accepted by PRD(RC) in 2011, 7 fb -1 Good agreement with other measurements. 16

17. ADS D * K by Belle  Continuum suppression with:  Signal seen with 3.5σ significance for D*  Dγ mode.  Ratio to favored mode:  Difference between R Dπ0 and R Dγ : indication of the effect of the interference term 2r B *r D cos (δ B *+δ D ) cos ϕ 3 (opposite sign for R Dπ0 and R Dγ ). continuum Signal D*πD*π BB DK/Dπ Signal D*πD*π BB DK/Dπ continuum LP 2011 preliminary, 772M BB 17

18. ADS D * K by Belle  Asymmetry:  Indication of opposite sign for A Dπ0 and A Dγ : consistent with expectation. (Opposite strong phase between D*  Dπ 0 and D*  Dγ.)  Combining R Dπ0, R Dγ, A Dπ0, and A Dγ : indication of negative cos(δ B *+δ D )cos ϕ 3 and positive sin(δ B *+δ D )sin ϕ 3. Consistent with B  D (*) K GGSZ result. LP 2011 preliminary, 772M BB 18

19. R ADS for DK A ADS for DK Summary for ADS Signal established. Negative asymmetry. Promising for ϕ 3 determination. Signal seen also for B  D*K ADS. Encouraging for improving ϕ 3 measurement. R ADS for D * K A ADS for D * K 19

20. Additional Update: B 0  DK *0 ADS by Belle  ADS method can be extended to B 0  DK *0 by tagging B 0 from K *0.  K *0 cannot be separated by K + π − and effective parameters r S and δ S are included in ‘ADS fit’.  Result: New 772M BB Both color suppressed. No significant signal for main mode: 7.7 +10.6 -9.5. Signal seen for calibration mode: 190 +22 -21. DK *0 Dρ DK *0 Dρ (NB’: variable for continuum suppression.) Dh… qq BB 20

21. GGSZ, Model-Dependent Approach  Amplitude of B ±  DK ± process can be expressed by  Procedure of analysis: 1. Fit to m ± by M ± to obtain x ± = r B cos(± ϕ 3 +δ B ) and y ± = r B sin(± ϕ 3 +δ B ). 2. Extract ϕ 3 (as well as r B and δ B ) from x ± and y ±. Amplitude of D  K S h + h - decay determined from Dalitz plot of large continuum data (Flavor is tagged by soft-pion charge in D *±  D  ± soft ). Isobar-model assumption with BW for resonances. Example: D  K S π + π − 21

22. GGSZ by Belle  Examples of Dalitz plots and confidence contours on x and y:  Result on ϕ 3 obtained by combining DK and D * K: PRD81, 112002 (2010), 657M BB Dalitz plots for B  DK. D decay modeling (isobar model) 22 B−B− B+B+

23. GGSZ by BaBar PRL105, 121801 (2010), 468M BB B  DKBD*KBD*K B  DK * Dalitz plots for B  DK Contours for x and y 23 Effective hadronic parameters for B  DK * to take interference with other B  DK S 0 π.

24. GGSZ, Model-Independent Approach  Divide the Dalitz plot into several regions (averaged strong phase of D  K S hh obtained without assuming model). Optimal binning: uniform division of the strong phase difference. (Binning is model-dependent while result model-independent.) Number of events in i th bin is a function of x ± /y ± where Values of ϕ 3, r B, and δ B are extracted from N i ± ’s (simultaneous equations for ϕ 3, r B, and δ B ). DKSπ+π−DKSπ+π− ψ(3770) by CLEO 24

25. GGSZ Model-Independent by Belle  Result of the fit of B ±  DK ± sample in each bin:  Result on ϕ 3 as well as contours on x and y: Moriond 2011 preliminary, 772M BB Black: flavor sample Third error due to c i and s i uncertainty. Will decrease to 1° or less by BES-III. 25

26. Summary  Recent improvement on ϕ 3 (20°  10°) is achieved by updates on B  D (*) K (*) by Belle, BaBar, LHCb, and CDF. – GLW CP asymmetry for CP+ mode established by BaBar and Belle. – ADS Evidence of signal obtained by Belle, CDF, and LHCb. Evidence also obtained for D * K by Belle. – GGSZ First model-independent measurement by Belle.  Promising to obtain a precision of O(1°) in near future. 26

27. 2 ϕ 1 + ϕ 3  Result of partial reconstruction for B  D * π ± published by Belle. (Preliminary result shown in 2008.) Belle, PRD84, 021101(R) (2011), 657M BB ± Mixing-induced CP violation to extract 2 ϕ 1 + ϕ 3. 27