Fat penguins and PQCD

1. Fat penguinsand PQCD A.I. Sanda Nagoya University Collaborators: Y. Keum, E. Kou, T. Kurimoto, H-n. Li, C. D. Lu, N. Shinha, R. Shinha, K. Ukai, T. Yoshikawa M. Yang

2. My friend and I

3. π＋π― can be in I=0 or in I =2 rule But π＋π０can only be in I=2 Bit of history Bose statistics: S wave ππstate I=0, 2 Gell-Man and Pais 50 years ago

4. u c t s d g Penguins came to save the day SVZ Penguin can not cause ΔI=2 transitions

5. Chiral perturbation theory Factorizationapproximation Ffactor of 10 enhancement

6. π K σ penguin π My understanding of theΔI=1/2 rule

7. Penguins play important role in the ΔI=1/2 rule For B physics it also play important role Rare decays give us chance to hunt for physics beyond the standard model But, they pollute CP asymmetries

8. c What we have leaned Ratio is independent of strong interaction if: • Penguin and Tree have same KM phase 2. Penguin is absent

9. * * V V V f = tb td cb sin( 2 ) Im[ ] 1 * V V V tb td cb ππ Nearly100%ＣＰＶ Bj notation Rosner&AIS Fermilab proeedings

10. sin = 0.82±0.12(stat)±0.05(syst) Belle sin = 0.75±0.09(stat)±0.04(syst) Babar Large CP Violation has been discovered! Where do we go from here?

11. If T dominated over P, We expected Fat penguins Penguins seems to be large in B decays

12. s b u b d T u u d s Pure P Pure T P

13. Babar With an assumption that |q/p|=1:

14. Belle Babar

15. 3 unknowns Lots of observables

16. We have learned that Penguins are large! Model independent measurement is difficult Dynamical calculation of P and T Should be used as guide lines In digging for physics beyond the SM

17. Nonleptonic 2 body decays Over 70 decay modes

18. History of pQCD approach • Brodsky Lepage PR D22,2157(80) • Isgar Llewellynsmith NPB317,526(89) • Botts Sterman NP B325, 62(89) • Li and his collaborators • Kroll Eur.Phys.J.C12,99(00) • Li, Keum, AIS hep-ph/0004173 PR • hep-ph/0004004 PL

19. Probability of finding a parton near Wee’s don’t know which way they are moving Wee parton Depends on wee dynamics Cannot be computed by perturbative QCD Feynman’s Mistake? Pion form factor

20. Infrared singularity! Infrared singularity! • Isgar Llewellynsmith NPB317,526(89) Isgar Llewellynsmith NPB317,526(89) Feynman’s reasoning – Naive QCD

21. Sudakov Factor in QED

22. Feynman says small x and small dominates The quark and anti-quark are far apart in space Sudakov factor suppress these regions x b This is not so in QCD!

23. Gluon PQCD approach to pion form factor

24. π π Color Singlet state does not radiate Pion form factor Sudakov factor

25. Factorization Theorem H H H H H Brodsky Lepage PR D22,2157(80) Botts Sterman NP B325, 62(89) Li and his collaborators This is a divergent operator But it is multiplicative and can be absorbed into the wave function = + X 1+ + - This is free of infrared and linear divergences

26. Pion wave function Pion formfactor

27. b quark decay b d d B

28. Gluon d d PQCD approach

29. B b d X u transition form factor

30. transition form factor

31. We now know Why FA works

32. ππ branching ratio would agree better if penguins are larger

33. CP asymmetry

34. The diagram which produces strong interaction phase -> CP violation

35. CP asymmetries will become smaller if penguins are larger We should not worry about the disagreement until K０π± asymmetry is settled

36. d u Pure P s b P d

39. Conclusion • PQCD is at its infant stage • Seems very promising • Predicts 2 body decay rates • Input: wave function • Predicts strong interaction phase • Existence of CP violation at 10-20% level for some channels

40. Summary 2 • Are large CPV inconsistent with experiment? • May be, but can’t say until K+π0 CP asymmetry is in order ∼0