1 Disclaimer This talk is not for B physics experts. Taipei101 If you did it, you may check s during my talk. B0B0 B0B0

 2 (  and  3 (  ) Masashi Hazumi (KEK) 3 rd International Conference on Flavor Physics (ICFP2005), October 3-8, 2005  1 “beam”  2 “banana”  3 “fan”

3 Motivation for  2 and  3 measurements Overconstrain the CKM unitarity triangle –important test of Kobayashi-Maskawa mechanism of CP violation –one of the main physics goals of BaBar and Belle Overconstrain the CKM unitarity triangle –important test of Kobayashi-Maskawa mechanism of CP violation –one of the main physics goals of BaBar and Belle  1 “beam”  2 “banana”  3 “fan”

4 Principle of measurement  2 from time-dependent CP asymmetries  3 from direct CP asymmetries  1 “beam”  2 “banana”  3 “fan” (other methods exist but are not competitive)

5 Methods Interestingly, at present best results on  2 and  3 are obtained by methods proposed after B factories started taking data. In reality, you need two diagrams with different weak phases (CP-odd phases) and strong phases (CP-even phases) two amplitudes with similar size ( |A 1 /A 2 | = r > O(0.1) ) precise measurements (knowledge) on  and r sufficient signal yields with good (tolerable) background level A 1 /A 2 =|A 1 /A 2 |exp(i  )exp(i  )  CP  |A 1 /A 2 |exp(  i  )exp(i  )

6 Mixing-induced CP violation (CPV) and  2 (  ) 11 33 22 V ud V * ub V td V * tb V cd V * cb B0B0 d b – d – bt – t B0B0 – V * tb V td V * tb V td Mixing diagramDecay diagram (tree) B0B0 b – d d u – d – u // // V ud V * ub

7 Mixing-induced CP violation (CPV) and  2 (  ) B 0      B 0  (             B 0       E (GeV) Events/(0.02GeV) 666±43 signals from 275 million BB pairs Small |V ub | = (4.38  0.19  0.27 )  10  3  measurements still limited by statistics B0B0 b – d d u – d – u // // V ud V * ub

8 Mixing-induced CP violation (CPV) and  2 (  ) B 0      B 0  (             B 0      Small |V ub | = (4.38  0.19  0.27 )  10  3  measurements still limited by statistics 617±52 signals from 232 million BB pairs signal-enhanced region B0B0 b – d d u – d – u // // V ud V * ub

9 made by H. Miyake Time-dependent CP violation in B 0      ( A =  C ) (CP = +1) Mixing-induced CPVDirect CPV With the tree diagram only S     = sin2  2 A     = 0

10 Tough (  ) bananas: penguin pollution Compelling evidence for direct CPV Large penguin diagram (P) ~ Tree diagram (T) Large strong phase difference between P and T B 0d0d d b d u u W g ++ -- V td V * tb t d A  S  4.0  direct CPV 4.0  direct CPV

11 Isospin analysis: flavor SU(2) symmetry Model-independent (symmetry-dependent) method SU(2) breaking effect well below present statistical errors

12  2 (  ) from B   inputs B (  +  0 ) = (5.5  0.6) B (  +  - ) = (5.0  0.4)  B (  0  0 ) = (1.5  0.3) A (  0  0 ) =  0.4 S (  +  - ) =  0.50  0.12 A (  +  - ) =  0.10 inputs B (  +  0 ) = (5.5  0.6) B (  +  - ) = (5.0  0.4)  B (  0  0 ) = (1.5  0.3) A (  0  0 ) =  0.4 S (  +  - ) =  0.50  0.12 A (  +  - ) =  0.10 larger than expected  big impact on  2 determination larger than expected  big impact on  2 determination

13 Isospin analysis with B 0       Even worse on first sight... –Dirty final state:              –Mixture of CP = +1 and  1: need to know each fraction (A + +A - )/√2 A || (A + -A - )/√2 A⊥A⊥ A0A0 + + A0A0 A+A+ A-A-     +1  1  1 CP vector

14 B 0      longitudinal polarization from helicity distribution total background f L =   f L =   CP (A + +A - )/√2 A || (A + -A - )/√2 A⊥A⊥ A0A0 + + A0A0 A+A+ A-A-     +1  1  1 ~purely CP = +1 ! ~purely CP = +1 !

15  2 (  ) from B   22 A 00 A +- / 2 squashed triangle  small  Inputs to isospin analysis B (  +  0 ) = (26  6) B (  +  - ) = (26  4)  B (  0  0 ) < 1.1 A (  0  0 ) = N.A. S (  +  - ) =  0.22  0.22 A (  +  - ) =  0.02  0.17 Inputs to isospin analysis B (  +  0 ) = (26  6) B (  +  - ) = (26  4)  B (  0  0 ) < 1.1 A (  0  0 ) = N.A. S (  +  - ) =  0.22  0.22 A (  +  - ) =  0.02  0.17 the best mode now !  2 = (96  13)º (triangle not closed with present central values)

16 Time-dependent Dalitz analysis with B 0         A rE to try even more involved analysis s  = m(     ) 2 s + =m(     ) 2 ++ ++ ++ Isospin analysis  isolate penguin and restore the simplicity Dalitz analysis  accept complication and dare to utilize Breit-Wigner phases Isospin analysis  isolate penguin and restore the simplicity Dalitz analysis  accept complication and dare to utilize Breit-Wigner phases  is for strong/CP-even phase difference.  Breit-Wigner phases from             . A mplitudes should be large enough for good statistics.  similar to  r atios between amplitudes  Determined by Dalitz fit E xperimentally favored (e.g. high efficiency, small background)  Not so great but tolerable Snyder-Quinn 1993

17  2 = (113  6)º +27  17  2 (  ) from B 0        No discrete ambiguity in deg. ! Important in the future.

18  2 (  ) from B  

19  2 W.A. CKM (indirect) All W.A.

20 Direct CP violation and  3 (  ) 11 33 22 V ud V * ub V td V * tb V cd V * cb u b u u c s W B +d+d  D0D0 V cs V*ubV*ub f COM 3 u b u s u c W B +d+d D0D0 ++ V us V * cb _ f COM 3 B  D (*) K (*) Choice of f COM very imporant ! Color suppressedColor allowed

21  A rE to measure  3 (1) GLW f COM = D CP [PLB 253,483; 265,172(’91)]  +  - /  +  - (CP=+1),  S  0 / .. (CP=  1) Gronau-London-Wyler A CP= , R CP=   r B,  B,  3 need more statistics (four observables, three unknowns) O∆ ∆ O  score

22  A rE to measure  3 (2) ADS f COM = D DCSD Atwood-Dunietz-Soni Not yet observed, but important limit on r B already available Not yet observed, but important limit on r B already available OX ∆ O  score [PRL 91,171801(’03)] color suppresed Cabibbo suppresed

23  A rE to measure  3 (3) Dalitz f COM = Ks     OO ∆ O  score Giri-Grossman-Soffer-Zupan [PRD 68,054018(’03)] B+:B+: B-:B-: m + =m(K s  + ), m  =m(K s   ) CPV : Asymmetry in Dalitz dist.: r r |A 2 | |A 1 | r = obtain from tagged D 0 (D *+  D 0  + ) sample

24 Signal yields 232M BB 275M BB D 0 K* D0KD0K D* 0 K [D 0  0 ] 209 signals 58 signals 36 signals 49 signals 90 signals 282 signals [hepex/ ] [hepex/ ][hepex/ ] EE EE EE

25 Dalitz Plots: D 0 K 232M BB 275M BB B+B+ BB B+B+ BB

26  3 Fit Results  3 (deg) rBrB rBrB  3 (deg) D 0 K* D0KD0K D* 0 K [D 0  0 ] D0KD0K D* 0 K [D 0  0  ]  3 = (68  13  11 model )º +14  15  3 = (67  28  13  11 model )º  3 = (67  28  13  11 model )º [hepex/ ] [hepex/ ]

27  3 (  ) from B  D (*) K (*)  3 = (63 )º +15  12

28 Unitarity Triangle with Angle Measurements  1 = (22  1)º  2 = (99 )º  3 = (63 )º +13   12  1 +  2 +  3 = (184 )º +20  14 (naïve sum by the speaker)

29 All combined ρ = ± η = ± 0.022

30 Summary Recent remarkable progress in  2 and  3 measurements – Now overconstraining CKM just from angle measurements (i.e. from CP asymmetries alone !) O(10º) achieved using new ideas ! –  for  2, DK Dalitz for  3 – Still limited by statistics Improvements in the future guaranteed To compete with the  1 precision, we need – better understanding of hadronic uncertainties SU(2) breaking Dalitz amplitudes, amplitude ratios, etc. – much more data  LHCb, Super B factory  1 = (22  1)º  2 = (99 )º  3 = (63 )º +13   12

31 Backup Slides

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33

34 b u W B 0 ++ VudVud  VcbVcb c d D*D* d d b c W B 0 ++ V cd  V ub u d D*D* d d   (B 0 →D    ) ~ 1 + cos(  mt) – S  sin(  mt)  (B 0 →D    ) ~ 1 + cos(  mt)  S  sin(  mt)  (B 0 →D    ) ~ 1  cos(  mt)  S  sin(  mt)  (B 0 →D    ) ~ 1  cos(  mt)  S  sin(  mt)   Cabibbo favored Cabibbo suppressed CP S  = 2(  1) L R sin(2  1  3  )  : hadronic phase, R = ~0.02 A CF A DCS mixing mixing induced CPV [L=0 (D  ), 1(D   ) R,  not same for D  and D   sin(2  1 +  3 ): B 0  D (*)+  - TCPV 4 2 [I.Dunietz, PLB 427,179(’98)] B0→B0→ mixing A DCS A CF

35  t Distributions B 0  D   10.6K cand.(96% purity) B0B0 B0B0  152M BB 232M BB partial reconstruction B0B0  B0B0 D    CP Full recon  t(ps) 89.3K signals Good tag Lepton tag background D    D    [hepex/ ][PRL 93,031802(04)] D    D    D   

36 sin(2  1 +  3 ): Summary D*   DD DD (c~0 if  ~0 or 180 deg.)

37 Extraction of  3 ? estimated form B (B  D s    ) [SU(3) symmetry] No significant constraint yet ! R