1. 1 CP Violation and Final State Interactions in Hadronic Charmless B Decays Hai-Yang Cheng Academia Sinica FSIs DCPV in B  K , ,  Polarization anomaly in B  K * FPCP2004, October 4-9, 2004, Daegu, Korea

2. 2 Why FSI in charmless B decays? Direct CPV (5.7  ) in B 0  K +  - was established by BaBar and Belle Combined BaBar & Belle data  3.6  DCPV in B 0  -  + For DCPV in B  +  -, 5.2  effect claimed by Belle, not confirmed by BaBar Expt(%) QCDF PQCD QCDF predictions seem not consistent with experiment ! FSI may play an essential role as DCPV  sin  sin   : weak phase,  : strong phase

3. 3 “Simple” CP violation from perturbative strong phases: penguin (BSS) vertex corrections (BBNS) annihilation (pQCD) “Compound” CP violation from LD rescattering: [Atwood,Soni] weak strong

4. 4 Other possible hints at large FSI effects in B physics: Some decay modes do not receive factorizable contributions e.g. B  K  0c with sizable BR, though  0c |c   (1-  5 )c|0  =0. Color-suppressed B 0  D 0 h 0 (h 0 =  0, ,  0, ,  ’) measured by Belle, CLEO, BaBar are larger than theoretical expectations. Br(B 0   0  0 )  1.5  10 -6 cannot be explained by QCDF or PQCD. and likewise for B 0  0  0 Longitudinal fraction f L  50% for B   K* by Belle & BaBar  in sharp contrast to the scaling law: for factorizable amplitudes in B decays to light vector mesons,  rescattering effect or new physics ?

5. 5  Regge approach [Donoghue,Golowich,Petrov,Soares] FSI phase is dominated by inelastic scattering and doesn’t vanish even in m b  limit  QCDF [Beneke,Buchalla,Neubert,Sachrajda] strong phase is O(  s,  /m b ): systematic cancellation of FSIs in m b   Charming penguin [Ciuchini et al.] [Colangelo et al.] [Isola et al.] long distance in nature, sources of strong phases, supported by SCET  Quasi elastic scattering model [Chua,Hou,Yang] Consider MM  MM (M: octet meson) rescattering in B  PP decays  One-particle-exchange model for LD rescattering has been applied to charm and B decays [Lu,Zou,..], [Du et al.]  Diagrammatic approach [Chiang et al.] … Approaches for FSIs in charmless B decays

6. 6 Diagrammatic Approach All two-body hadronic decays of heavy mesons can be expressed in terms of six distinct quark diagrams [Chau, HYC(86)] All quark graphs are topological and meant to have all strong interactions included and hence they are not Feynman graphs. And SU(3) flavor symmetry is assumed.

7. 7 Global fit to B , K  data (BRs & DCPV) based on topological diagrammatic approach yields [Chiang et al.] consistent with that determined from B  D  decays

8. 8 quark exchange quark annihilation meson annihilation possible FSIs  W exchange Color suppressed C  At hadron level, FSIs manifest as resonant s-channel & OPE t-channel graphs. B0D00B0D00

9. 9 FSI as rescattering of intermediate two-body states [HYC, Chua, Soni; hep-ph/0409317]  FSIs via resonances are assumed to be suppressed in B decays due to the lack of resonances at energies close to B mass.  FSI is assumed to be dominated by rescattering of two-body intermediate states with one particle exchange in t-channel. Its absorptive part is computed via optical theorem: Strong coupling is fixed on shell. For intermediate heavy mesons, apply HQET+ChPT (for soft Goldstone boson) Cutoff must be introduced as exchanged particle is off-shell and final states are hard Alternative: Regge trajectory [Nardulli,Pham][Falk et al.] [Du et al.] …

10. 10 Dispersive part is obtained from the absorptive amplitude via dispersion relation  = m exc + r  QCD (r: of order unity)  or r is determined form a  2 fit to the measured rates  r is process dependent  n=1 (monopole behavior), consistent with QCD sum rules Once cutoff is fixed  CPV can be predicted subject to large uncertainties and will be ignored in the present work Form factor is introduced to render perturbative calculation meaningful

11. 11 B   K SD PQCD Direct CPV in B 0  K +  - was reported by BaBar & Belle for F 0 B  (0)=0.25 from covariant LF model [HYC,Chua,Hwang(04)]

12. 12 All rescattering diagrams contribute to penguin topology fit to rates  r D = r D*  0.69  predict direct CPV

13. 13 BR SD (10 -6 ) BR with FSI (10 -6 ) BR Expt (10 -6 ) DCPV SD DCPV with FSI DCPV Expt BB 17.8 23.3 +4.6 -3.7 24.1  1.3 0.010.024 +0.00 -0.001 -0.02  0.03 B0+B0+ 13.9 19.3 +5.0 -3.1 18.2  0.8 0.04-0.14 +0.01 -0.03 -0.11  0.02 B0B0 9.7 12.5 +2.6 -1.6 12.1  0.8 0.08 -0.11 +0.02 -0.04 0.04  0.04 B0B0 6.3 9.1 +2.5 -1.6 11.5  1.0 -0.040.031 +0.008 -0.014 0.02  0.14  Sign of  + K - CP asymmetry is flipped after rescattering and is in agreement with experiment.  K  rates are enhanced by (30-40)% via FSI  Isospin sum rule relation [Atwood,Soni] can be used to test the presence of EWP

14. 14 B    A f =-C f : direct CP asymmetry; S f : mixing-induced CP violation A(  +  - )=0.58  0.17 by Belle, 0.09  0.16 by BaBar SD PQCD

15. 15 Long-distance contributions to B    Cutoff scale is fixed by B  K  via SU(3) symmetry  too large  +  - (  9  10 -6 ) and too small  0  0 (  0.4  10 -6 ) A dispersive part unique to  but not available to K  is needed to suppress  +  - and enhance  0  0 D+(+)D+(+) D-(-)D-(-) ++ -- same topology as vertical W- loop diagram V

16. 16 BR SD (10 -6 ) BR with FSI (10 -6 ) BR Expt (10 -6 ) DCPV SD DCPV with FSI DCPV Expt B0+B0+ 7.6 5.0 +1.3 -0.9 4.6  0.4 -0.05 0.64 +0.03 -0.08 0.37  0.24 B000B000 0.3 1.3 +0.3 -0.2 1.5  0.3 0.61-0.30 +0.01 -0.04 0.28  0.39 B0B0 5.1 4.8  0.1 5.5  0.6 5  10 -5 -0.009  0.001-0.02  0.07 Charming penguin alone doesn’t suffice to explain  0  0 rate Sign of direct CP asymmetry is flipped after rescattering ! DCPV in  -  0 mode is very small even after inclusion of FSI. It provides a nice way to search for New Physics SU(3) relation:  (  +  - )=-  (  + K - ) [Deshpande,He]  A(  +  - )  -4.0 A(  + K - ) can be used to predict DCPV in  +  -

17. 17 B  W-exchange can receive LD contributions from FSI |P/T| is of order 0.30, smaller than some recent claims Define T eff =T+E+V, C eff =C-E-V  C eff /T eff =0.71 exp[i72  ] B  K  C/T is similar to the  case

18. 18 BR SD (10 -6 ) BR with FSI (10 -6 ) BR Expt (10 -6 ) DCPV SD DCPV with FSI DCPV Expt B 0  +   7.9 8.4  0.3 10.1  2.0 -0.01 -0.43  0.11 -0.48  0.14 B 0    + 18.4 18.8 +0.3 -0.2 13.9  2.1 -0.03 -0.24  0.06 -0.15  0.09 B 0  0  0 0.6 1.3 +0.4 -0.3 1.9  1.2 0.01 0.57 +0.01 -0.03 B     0 12.8 14.0 +0.7 -0.4 12.0  2.0 -0.04 0.36  0.10 0.16  0.13 B      6.8 7.5 +0.6 -0.3 9.1  1.3 0.06 -0.56 +0.14 -0.15 -0.19  0.11 B   DCPV in  +  - mode is well accounted for Br(  0  0 )  1.3  10 -6, recalling BaBar upper limit, 2.9  10 -6, and Belle result of (5.1  1.8)  10 -6. Discrepancy between them should be clarified. We use F 1 B  (0)=0.30 [HYC,Chua,Hwang]. If F 1 B  (0)=0.37 is employed, the     will become too large ﹣ ﹣ _ _

19. 19 Expt(%) QCDF PQCD Summary for DCPV

20. 20 Expt(%) QCDF+FSI PQCD Summary for DCPV pQCD and FSI approaches for DCPV can be discriminated in  0  0 and  +  - modes

21. 21 Short-distance induced transverse polarization in B  V 1 V 2 (V: light vector meson) is expected to be suppressed Polarization anomaly in B   K *,  K * Scaling law obeyed by  modes is violated in  K * and  K * (except  0 K *+ ) decays

22. 22  Anomaly can be accommodated in QCDF via large penguin-induced annihilation by adjusting endpoint divergence [Kagan] BR is enhanced by a factor of 2 via annihilation, too large ?  Transverse gluon in b  sg chromodipole operator  transversely polarized  [Hou & Nagashima]   Similar behavior for  K *, but no polarization anomaly in  K * modes ?

23. 23  Get large transverse polarization from B  D s * D * and then convey it to  K * via FSI [Colangelo, De Fazio, Pham] f T (D s * D * )  0.51 contributes to A  only f ||  0.41, f   0.08  Regge analysis of FSI [Ladisa,Laporta,Nardulli,Santorelli] elastic FSI: Pomeron exchange (see also Chua,Hou,Yang) inelastic FSI: use Regge trajectory method to evalute charming penguins

24. 24  very small perpendicular polarization, f   2%, in sharp contrast to f   15% obtained by Colangelo et al. ＋  0 ! We found large cancellation occurs in B  { D s * D,D s D*}  K* processes. This can be understood as CP & SU(3) symmetry While f T  0.50 is achieved, why is f  not so small ?

25. 25  Cancellation in B  {VP,PV}  K * can be circumvented in B  {SA,AS}  K *. For S,A=D **,D s **, it is found f L : f || : f  = 0.71: 0.06 : 0.22 However,  K * rate gets only a small enhancement so that effect of sizable f  will be washed out by intermediate states from V,P  Strong phases in  K *  For B +  K *0  +, f L : f || : f  = 0.64: 0.35 : 0.01, f L expt =0.74  0.08 f L is indeed suppressed  For B +  K *+  0, f L : f || : f  = 0.62: 0.37 : 0.01, f L expt =0.96 +0.04 -0.16 Why is scaling law working here ?

26. 26 Conclusion  Color–suppressed modes such as B 0  D 0  0,  0  0,  0  0,K 0  0 can be substantially enhanced by LD rescattering.  DCPV in charmless B decays is significantly affected by FSI rescattering. Correct sign and right magnitude of DCPV in K -  + and  +  - are obtained after inclusion of FSI.  Large transverse polarization with f T  0.50 can be obtained from rescattering of The anomaly of not so small f  remains mysterious