1. WIN-03, Lake Geneva, WisconsinSanjay K Swain Hadronic rare B decays Hadronic rare B-decays Sanjay K Swain Belle collaboration B - -> D cp K (*)- B - -> D(K S  +  -) K - Dalitz analysis B ->  B ->  K (*) Conclusion V ud V ub V cd V cb V td V tb * * * 3()3() 2()2() 1()1()

2. WIN-03, Lake Geneva, WisconsinSanjay K Swain Hadronic rare B decays Using B -  D CP K - mode (GLW method) B -  D CP K - where D CP = (D 0  D 0 ) A(B -  D CP K - )  |A(B -  D 0 K - )|+|A(B -  D 0 K - )|e i  e i  A(B +  D CP K + )  |A(B +  D 0 K + )|+|A(B +  D 0 K + )|e -i  e i  When D 0 D 0 CP-even states (D 1 ): K + K -,  +  - CP-odd states (D 2 ): K S  0, K S , K S , K S , K S  ’ ¯ 3 3 common final state ¯ ¯ PLB 253(1991)483 PLB 265(1991)172 } Color-favored b uu c u K D B - - -- - o } uu c K D B - -- - Color-suppressed V cb V ub - s } s o }  3 =arg(V ub ) u - * b

3. WIN-03, Lake Geneva, WisconsinSanjay K Swain Hadronic rare B decays GLW method cont….. 33   A(B +  D 0 K + )A(B -  D 0 K - ) A(B +  D 0 K + ) A(B -  D 0 K - ) A(B +  D CP K + ) A(B -  D CP K - ) = Reconstruct the two triangles   3 — -3-3 One can measure  3 even if  =0( without strong phase) Non vanishing strong phase (   0)  Direct CP violation

4. WIN-03, Lake Geneva, WisconsinSanjay K Swain Hadronic rare B decays GLW method cont… Solution: One can instead measure R 1,2 = R /R D CP D non-CP = 1 + r 2  2r cos(  )cos(  3 ) where R D CP B (B -  D 1,2 K - ) + C.C B (B -  D 1,2  - ) + C.C = A 1,2 = B (B -  D 1,2 K - )B (B +  D 1,2 K + ) B (B -  D 1,2 K - ) - +  2r sin(  )sin(  3 ) 3 independent measurements  3 unknowns r, ,  3 (solve it) But A 1 R 1 = - A 2 R 2 1 + r 2  2r cos(  )cos(  3 ) B (B +  D 1,2 K + ) = Amp(B -  D 0 K - )  0.1 x Amp(B -  D 0 K - ) Also B -  D 0 [K +  - ]K - has same final state as B -  D 0 [K +  - ]K - (DCSD) But _ _ r = |B  KD|/|B  KD| _

5. WIN-03, Lake Geneva, WisconsinSanjay K Swain Hadronic rare B decays Kinematics to identify signal Candidates are identified by two kinematic variables Beam constrained mass (M bc )=  (E 2 beam -p B 2 ) Energy difference (  E) = E B - E beam But @  (4S) peak energy: 24% BB 76% Continuum (qq, q =u, d, c or s) KEKB operates here  – We use continuum suppression variables -> LR( Cos  B, Fisher) -

6. WIN-03, Lake Geneva, WisconsinSanjay K Swain Hadronic rare B decays Results (78 fb -1 ) B  D  B  D K Flavor specific CP even CP odd 6052  88 683.4  32.8 648.3  31 347.5  21 47.3  8.9 52.4  9 134.4  14.7 15.6  6.4 6.3  5.0 EE EE

7. WIN-03, Lake Geneva, WisconsinSanjay K Swain Hadronic rare B decays Double ratios( R 1,2 ) and asymmetries( A 1,2 ) R 1 = 1.21  0.25  0.14 and R 2 = 1.41  0.27  0.15 A 0 = 0.04  0.06(stat)  0.03 (sys) ( non-CP mode) A 1 = +0.06  0.19(stat)  0.04 (sys) ( CP + mode) A 2 = - 0.18  0.17 (stat)  0.05(sys) ( CP – mode) We cannot constrain  3 with these statistics. 25.0  6.522.1  6.1 20.5  5.6 29.9  6.5 EEEE CP even CP odd ( r 2 = 0.31 ± 0.21, just 1.5  away from physical boundary) r = |B  KD|/|B  KD| _

8. WIN-03, Lake Geneva, WisconsinSanjay K Swain Hadronic rare B decays B -  D 0 K* - mode (90 fb -1 data) Signal MC data Works exactly same way as B - -> D CP K - decay Look for CP asymmetries and double ratios -> constraint  3 169.5±15.4 16  Flavor specific modes

9. WIN-03, Lake Geneva, WisconsinSanjay K Swain Hadronic rare B decays B -  D CP K* - mode Can not constraint  3 with this statistics -> need more data CP asymmetries : A 1 = -0.02 ± 0.33(stat) ± 0.07(sys) A 2 = 0.19± 0.50(stat) ± 0.04(sys) 13.1 ± 4.3 4.3  7.2 ± 3.6 2.4  CP-even CP-odd

10. WIN-03, Lake Geneva, WisconsinSanjay K Swain Hadronic rare B decays B ±  D(K S  +  - )K ± Dalitz analysis(140 fb - 1 ) In case of B -  D CP K - where D CP =(D 0  D 0 ) both D 0 and D 0 decays to CP eigenstates ( K + K -..) One can write the total amplitude for B +  DK + : Amp(B + ->DK + ) = f(m + 2,m - 2 ) + r. e i(  3 +  ) f(m - 2, m + 2 ) (B - decay amplitude can be written similar way :  -> ,  3 -> -  3 ) m + 2 (m - 2 ) -> squared of invariant mass of K S  + (  - )combinations f -> complex amplitude of D 0 -> K S  +  - decay f( m + 2,m - 2 ) =  a k. e i  A k (m + 2,m - 2 ) + b e i  -> both 2-body resonances and non-res component - - D0K0 D0K0  D0K0 D0K0  D0KS D0KS 

11. WIN-03, Lake Geneva, WisconsinSanjay K Swain Hadronic rare B decays Suppose all D 0  K 0     decays are via K*  D 0  K*    K S   D 0  K*    K S   M(K S   ) 2 M(K S   ) 2 Dalitz plot interference Simple example

12. WIN-03, Lake Geneva, WisconsinSanjay K Swain Hadronic rare B decays D 0  K S     K*  KSKS KSKS KSf2KSf2 reality is more complex(& better) many amplitudes & strong phases(13) lots of interference

13. WIN-03, Lake Geneva, WisconsinSanjay K Swain Hadronic rare B decays Fit results for D ->K S  +  - decay ResonanceAmplitudePhase K *-( 892)  + K S  0 K *+( 892)  - K S  K S f 0 (980) K S f 0 (1370) K S f 2 (1270) K * 0 - (1430)  + K * 2 - (1430)  + K *- (1680)  + K S  1 ( M=535±6 MeV,  =460±15 MeV ) K S  2 ( M=1063±7 MeV,  =101±12 MeV ) Non-resonance 1.706 ± 0.015 1.0(fixed) 0.136 ± 0.008 0.032 ± 0.002 0.385 ± 0.011 0.49 ± 0.04 1.66 ± 0.05 2.09 ± 0.05 1.2 ± 0.05 1.62 ± 0.024 1.66 ± 0.09 0.31 ± 0.04 6.51 ± 0.22 138 ± 0.9 0 (fixed) 330 ± 3 114 ± 3 214.2 ± 2.3 311 ± 6 341.3 ± 2.3 353.6 ± 1.8 316.9 ± 2.1 84 ± 10 217.3 ± 1.4 257 ± 11 149 ± 1.6

14. WIN-03, Lake Geneva, WisconsinSanjay K Swain Hadronic rare B decays BB B+B+ B ±  D(K S  +  - )K ± Dalitz analysis Fit Dalitz distributions for B + and B - decay simultaneously -> r,  3,  as free parameters Use D 0  K S     to make Dalitz-plot model fit 58K events with 13 amplitudes Select B ±  K ± D 0 (  K S      events 107 ± 12 events in 142 fb -1 Belle data Form Dalitz plots for B + & B 

15. WIN-03, Lake Geneva, WisconsinSanjay K Swain Hadronic rare B decays B ±  D(K S  +  - )K ± Dalitz analysis Weak phase  3 = 95 0 ±25 0 (stat) ±13 0 (sys)±10 0 strong phase  = 162 0 ±25 0 (stat) ±12 0 (sys) ±24 0 (3 rd error is model uncertainty) r = 0.33 ± 0.10(stat) @90% C.L : 0.15<r<0.5,61 0 <  3 <142 0, 104 0 <  <214 0 33 r  33 r = |B  KD|/|B  KD| _

16. WIN-03, Lake Geneva, WisconsinSanjay K Swain Hadronic rare B decays B ->  +  0 mode(first observation) data used:78 fb -1 B (B + ->  +  0 ) =(31.7  7.1(stat)  6.4(sys)  2.1(pol))x10 -6 A CP (B  ->    0 ) = (0.1 ±22.4(stat) ±2.8(sys))% First observation of charmless vector-vector mode 00 ++ 00 ++ B+B+ B+B+ u b d - W - - - u u u u u b d u u - - W Z/  EWP

17. WIN-03, Lake Geneva, WisconsinSanjay K Swain Hadronic rare B decays Helicity analysis  0 momentum requirement  final state is vector-vector system -> give S,P or D wave Both longitudinal and transverse polarization are possible  Longitudinal pol. ratio, = (94.8  10.6(stat)  2.1(sys))% LL  fit result

18. WIN-03, Lake Geneva, WisconsinSanjay K Swain Hadronic rare B decays B ->  K (*) (78 fb -1 ) BF’s - - b s u - Penguin ModeBF x 10 -6  K +  K 0  K *0  K *+ 9.4 ± 1.1 ± 0.7 9.0 ± 2.2 ± 0.7 10.0 ± 1.6 ± 0.8 6.7 ± 2.1 ± 1.0 s s u W u, c, t --- 136±15 35.6±8.4 58.5±9.1 8±4.3 11.3±4.5 V ts

19. WIN-03, Lake Geneva, WisconsinSanjay K Swain Hadronic rare B decays B ->  K * (78 fb -1 ) polarization K+K+ |A 0 | 2 = 0.43 ± 0.09 ± 0.04 |A | 2 = 0.41 ± 0.10 ± 0.04 (CP odd and CP even states) and arg(A ) = 0.48 ± 0.32 ± 0.06 arg(A ) = -2.57 ± 0.39 ± 0.09 T T = Distribution of decays ->A 0, A, A,  tr, ,  tr T = K*K* A x -> complex amplitudes Amplitudes are determined by unbinned max likelihood fit: z  tr

20. WIN-03, Lake Geneva, WisconsinSanjay K Swain Hadronic rare B decays Summary Now we have better measurement on CP asymmetries and ratio of BF’s in B - -> D CP K - mode Constrained  3 using Dalitz analysis of B - -> D(K S  +  - )K - decay Measured the branching fractions and different helicity amplitudes in B ->  mode. Measured the branching fractions and helicity amplitudes in B ->  K (*) mode Lot more other hadronic rare B-decays……..

21. WIN-03, Lake Geneva, WisconsinSanjay K Swain Hadronic rare B decays MC with  3 = 70 o B + / B 

22. WIN-03, Lake Geneva, WisconsinSanjay K Swain Hadronic rare B decays ~2.4σ separation BB B+B+ B ±  D(K S  +  - )K ± Dalitz analysis Fit Dalitz distributions for B + and B - decay simultaneously -> r,  3,  as free parameters

23. WIN-03, Lake Geneva, WisconsinSanjay K Swain Hadronic rare B decays KEKB Accelerator Two separate rings Finite crossing angle L designed = 10 34 cm -2 s -1 Achieved: L peak > 10 34 cm -2 s -1 Integrated Luminosity ~ 158 fb -1 E e = 3.5 GeV E e = 8.0 GeV + -

24. WIN-03, Lake Geneva, WisconsinSanjay K Swain Hadronic rare B decays Detector Performance K/  separation is done using: ACC, TOF, dE/dx( CDC) PID(K) = Wide momentum range L(K) L(K) + L(  )

25. WIN-03, Lake Geneva, WisconsinSanjay K Swain Hadronic rare B decays Background Suppression Variables to distinguish signal from continuum events  Cos  B Event Shape variable: (Fisher) BB : Spherical Continuum: back-to-back(jet-like) – BB e+e+ e-e- B CONTINUUM SIGNAL

26. WIN-03, Lake Geneva, WisconsinSanjay K Swain Hadronic rare B decays Cos  B Fisher Likelihood ratio Background Suppression Signal Continuum

27. WIN-03, Lake Geneva, WisconsinSanjay K Swain Hadronic rare B decays Main question: “Is V unitary” ? Three generation quark mixing matrix(V) V =  3 = arg(V * ) ub (Also known as  ) V ud V ub + V cd V cb + V td V tb = 0 Orthogonality of 1 st and 3 rd column gives: ** * a b -b   = arg( ) a -b * –  3 = arg( ) V cd V cb V ud V ub * V cd V cb V td V tb * * * 3()3() 2()2() 1()1()