1. 1 Enhanced KL to pi0 nu nubar from Direct CP Violation in B to K pi Direct CP Violation in B to K pi with Four Generations with Four Generations Makiko Nagashima (NTU) ICFP2005, Oct. 3-8 NCU

2. 2 Contents Paper hep-ph/0508237 (W.S.Hou, M.N, A. Soddu) 4th generation scenario and Implications for K and B physics Paper hep-ph/0503072 (W.S.Hou, M.N, A. Soddu) to appear in Phys. Rev. Lett. Impact of 4th generation on B to K pi Direct CPV b → s s → d b → d motivated by extend our study to

3. 3 3 generation Standard Model and CKM mechanism SU(2) doublet SU(2) singlet Quark sector 3 mixing angles 1 CP phase CKM matrix Unitarity Triangle Study of CPV / Test of SM / Search for NP

4. 4 Direct CP Violation (DCPV) Difference of Yields vs given by single term no relative phases DCPV goes away CP

5. 5 TREE and PENGUIN diagrams Tree diagram s u u dd b W b u u u u s W > 1/Nc b d W g u s d u Penguin diagram b d u s d u W Z,γ > sub-dominant

6. 6 Result on DCPV in Kπ PUZZLE

7. 7 The puzzle still persists It calls for New Physics ?

8. 8 K pi DCPV riddle QCDF (BBNS) SM3 kT PQCD (KLS) away sub-dominant If one neglects EWP and C, No phase differences Theoretical expectations within different treatment of the hadronic matrix element (2003) (2001) contradiction up to LO calculation

9. 9 We call for Large with an extra weak phase We employ kTPQCD approach must not be negligible Assemble 4 th generation scenario consistent with ~12% The deviation

10. 10 kTPQCD approach Large strong phase comes from annihilation process a hard gluon kicks spectator At leading process is introduced to cure the endpoint singularities

11. 11 A. Arhrib and W-S. Hou, EPJC27,555 T. Yanir, JHEP06, 044 Simple parameterization 4 th generation scenario A sequential 4 th generation in addition to the SM particles well-known unknown same quantum number follows WS parameterization

12. 12 Remind Our assumption Neither Scalar OPE nor Tensor OPE. R.H. dynamics is suppressed by ms/mb The low energy operators are the same as the SM New physics enters though loop processes, and changes the short distance effects

13. 13 Effective Hamiltonian Tree QCD Penguin EW/EM Penguin t' effects well-satisfy b → sγrate and DCPV Large enhancement Wilson coefficient Dividing ΔCi by QCD penguin Natural ability of 4 th generation to large enhancement of EWP

14. 14 Constraint PDG04 Belle(04) B(b→sll) gets greatly enhanced Δm is lower than EXP. bound 4 th generation effects are not excluded!!

15. 15 Result kTPQCD in the SM 4 th generation + sizable splitting between Roughly, described as It naturally generates the phase diff. and sizable mag. of the extra term

16. 16 Our result is at leading order in kTPQCD. A recent result finds a much larger color-suppressed tree (C) at next-to-leading order. is less negative (H-n. Li, S. Mishima and A.I. Sanda, hep-ph/0508041) Remark Comparably large C would allow more parameter space for the 4 th generation

17. 17 Naively assumed did not care about One may have suspicion that b→s would spill over into s→d is not necessarily ~ 0

18. 18 should be all intertwined … PLB 192 441 (1987) by W.S. Hou et al. Precisely, should be written by 6 mixing angles and 3 CP phases

19. 19 Be moderate From K pi study, we learned Keep We have some constraint on from Impose be close to the Cabibbo angle

20. 20 Allowed region from K processes standard (1) is less stringent (simulated dots) (shaded region) (elliptic rings) depends on hadronic parameter R6 and R8 Bijnens (2) We found (1) (2)

21. 21 Outcome for Current Upper Bound It is very hard to measure but challenging… We find enhancing to or even higher !! It might be even larger than !! we take

22. 22 Impact on Bd and D system

23. 23 Summary Starting point → Direct CP Violation in B→Kπ 4 th generation is possible to generate Large EWP Extend our study to Bd and K system ( to, phenomenologically, understand the possibilities of having still fourth generation ) ( )

24. 24 BACKUP SLIDE

25. 25 2D plots in different way

26. 26 FROM PDG04 Our anxiety

27. 27 We now know neutrinos have mass, will have CPV, and more to be revealed. # of neutrino =3 is just one piece of info. The rho parameter is less of a problem. The S parameter is the real problem (it ‘s so for most NP models.) What the situation changes if the Higgs is not seen and actually heavy ?

28. 28 Extra generation vs. EW precision data V.A. Novikov et al., PLB529, 111 Ng Δm=sqrt(mU^2-mD^2) [GeV] mH>113 GeV, mD=130 GeV mN [GeV] Ng mD=200, mU=220, mE=100 [GeV]

29. 29 Some Curiosities

30. 30 MICPV is rather little sensitive to strong phases Specially, MICPV due to b→s transition behaves like naïve factorization + 4 th gene.

31. 31 No Rescattering Another framework: extra strong phase from Final State Interaction Naïve Factorization ⊗ Final State Rescattering Otherwise Double Counting George W.S. Hou, BCP JC, Oct. 14 (2002)

32. 32 We followed Mod.Phys.Lett. A18,1763 by C-K. Chua, W-S. Hou and K-C. Yang It accounts for (strong phase) ICHEP04 (strong phase) problem

33. 33 This FSI picture doesn’t help for resolving the puzzle There is no solution We performed analysis by incorporating t’ effects re-scattering happens between EW penguin would be brought into amplitude from