1. Puzzles in B physics Recent development in PQCD, QCDF, SCET Hsiang-nan Li Academia Sinica, Taiwan presented at Whepp9 Bhubaneswar Jan. 07, 2006

2. Outlines Introduction QCDF, PQCD, and SCET B! VV polarizations B! K  direct CP asymmetries B!  branching ratios Mixing-induced CP asymmetries in b! s penguin Conclusion

3. Introduction Missions of B factories: Constrain standard-model parameters Explore heavy quark dynamics Search for new physics Entering the era of precision measurement, puzzles have appeared. Critical examination of QCD effects is necessary for confirming new physics.

4. Naïve power counting Estimate order of magnitude of B decay amplitudes in power of the Wolfenstein parameter » 0.22 It is not a power counting from any rigorous theory Amplitude» (CKM) (Wilson coefficient) Induced by O 2 =(su)(ub) / C 2,s

5. CKM matrix elements Wilson coefficients |  -i  |¼ 0.4 a 1 =C 2 +C 1 /N c a 2 =C 1 +C 2 /N c

6. Quark amplitudes b u s u Color-allowed tree TColor-suppressed tree C QCD penguin PElectroweak penguin P ew s u u s u u s u u g  Z W

7.  parameterization (C 4 /C 2 )(V td V tb /V ud V ub )/1» ( 2 /1)( 3 / 4 )» Tree-dominant

8. B(B 0 !  0  0 ) P, C, and P ew in  0  0 are all subleading. We should have Br(  0  0 )¼ O( 2 )Br(  +  - ) Data show Br(  0  0 )¼ O( )Br(  +  - ) The B!  puzzle! Large P and/or C?

9. K  parameterization (C 2 /C 4 )(V us V ub /V ts V tb )» (1/ 2 )( 5 / 2 )»

10. Direct CP in B! K  K +  - and K +  0 differ by subleading amplitudes, P ew /P » C/T». Their CP are expected to be similar. Their data differ by more than 3  !

12. sin 2  1 /sin 2  1 decay amplitude, f CP =exp(-2i  1 ) Measure S f CP / Im f CP ) measure sin(2  1 ) Either pure-tree or pure-penguin modes serve the purpose Tree-dominant B! J/  K S, penguin pollution: P/T» (C 4 /C 2 )(V ts V tb /V cs V cb )» 2 » 5% Penguin-dominant b! s, tree pollution: C’/P’ » 2 » 5%

13. 4S  0 by about 1  A puzzle? Penguin-dominated Tree-dominated

14. QCD-improved Factorization (Beneke, Buchalla, Neubert, Sachrajda) Perturbative QCD (Keum, Li, Sanda) Soft-collinear Effective Theory (Bauer, Pirjol, Rothstein, Stewart)

15. QCDF Based on collinear factorization (Brodsky and Lepage 80). Compute correction to naïve factorization (NF), ie., the heavy-quark limit. Divergent like s 0 1 dx/x (end-point singularity) in collinear factorization nonperturbative perturbative

16. Hard kernels T I comes from vertex corrections T II comes from spectator diagrams Magnetic penguin O 8g q 1 x

17. End-point singularity Singularity appears at O(1/m b ), twist-3 spectator and annihilation amplitudes, parameterized as X=(1+  e i  )ln(m b /  ) For QCDF to be predictive, O(1/m b ) corrections are better to be small ¼ FA. Data show important O(1/m b ). Different free ( ,  ) must be chosen for B! PP, PV, VP.

18. PQCD End-point singularity means breakdown of collinear factorization Use more “conservative” k T factorization (Li and Sterman 92) Parton k T smear the singularity Same singularity in form factor is also smeared No free parameters

19. Factorization picture Sudakov factors S, summation of  s ln 2 (m b /k T ) to all orders, describe parton distribution in k T k T accumulates after infinitely many gluon exchanges, similar to DGLAP evolution up to k T ~Q Large k T Small b Always collinear gluons g g

20. SCET I Two scales in B decays: m b  and m b 2 Full theory! SCET I : integrate out the lines off-shell by m b 2 C(  )J (0) (  )! C(  )  (  ) J (0) Hard-collinear gluon, mass O(m b  ) T(  0 )J (1) (  0 ) b W mb2mb2 Wilson coeff of SCET I 22 1/m b suppressed current g

21. SCET II SCET I ! SCET II : integrate out the lines off- shell by m b  Compared to QCDF, T II ! T(  0 )J(  0,  ) J(  0,  )O(  ) 22 Jet=Wilson coeff of SCET II ! T(  0 )J(  0,  )  M (  )  B (  )

22. B! K  direct CP

23. Large strong phase A CP (K +  - )¼ -0.115 implies sizable   » 15 o between T and P (PQCD, 00) T exp(i  3 ) P T exp(-i  3 ) T exp(i  3 ) P T exp(-i  3 ) If  T =0 Br Br = Br If  T =0 Br = Br Direct CP

24. Explanation 1 How to understand the small A CP (K +  0 )? Large P EW to rotate P (Buras et al.; Yoshikawa; Gronau and Rosner; Ciuchini et al., Kundu and Nandi) ) new physics? (Hou’s talk) T exp(i  3 ) P T exp(-i  3 ) P EW Br¼ Br

25. Explanation 2 Large C to rotate T (Charng and Li; He and McKellar) ) mechanism missed in naïve power counting? C is subleading by itself. Try NLO PQCD. (T+C) exp(i  3 ) (T+C) exp(-i  3 ) T exp(i  3) P Br¼ Br

26. NLO PQCD (Li, Mishima, Sanda 05) LO: all pieces at LO LO NLOWC : NLO Wilson coefficients VC: vertex correction QL: quark loops MP: Magnetic penguin Corrections to form factors are not very relevant here. decrease P by 10%

27. Vertex correction Vertex correction enhances C/ a 2, and makes it almost imaginary. Without vertex correction Re, with vertex correction Im, with vertex correction Is negative. It rotates T!

28. Quark amplitudes at LO and NLO C’ is enhanced by a factor of 3, Arg(C’/T’)=-80 o C’ is still subleading. T, P’ ew are almost unchanged.

29. PQCD results Hadronic uncertainty

30. QCDF  T has a wrong sign in QCDF. C makes the situation worse. (T+C) exp(i  3 ) (T+C) exp(-i  3 ) T exp(i  3) P Br = Br

31. SCET C/T is real in leading SCET, and large from the  data. C can not reduce A CP (K +  0 ) (hep-ph/0510241). (T+C) exp(i  3 ) (T+C) exp(-i  3 ) T exp(i  3) P Br = Br

32. SCET inputs

33. SCET predictions

34. B!  branching ratios

35. Remarks It is natural to explain the  K data in PQCD. The B!  puzzle, large B(  0  0 ), remains. B(  0  0 ) is an input of SCET, not a resolution Resolution was claimed in QCDF/SCET (Beneke and Yang 05). Any proposal for the  puzzle must survive the constraint from other data.

36. SCET inputs Not a resolution

37. B!  in PQCD Data BABAR Belle Average  +  - 30± 4± 5 30± 6  +  0 22.5 +5.7 -5.4 ± 5.8 31.7±7 7.1 +3.8 -6.7 26.4 +6.1 -6.4  0  0 <1.1 <1.1 B!  L  L in NLO PQCD (Li, Mishima) LO NLOWC +VC +QL +MP +NLO  +  - 24.29 23.43 24.76 24.12 23.67  +  0 15.85 15.57 15.85 15.85 15.57  0  0 0.35 0.81 0.41 0.25 0.72 NLO has saturated the  0  0 bound  the  puzzle is confirmed.

38. QCDF The mechanism to enhance C/  2 comes from the NLO jet function in SCET. The QCDF formulas are modified: The enhancement from the jet function is about 30» 60% Jet function  » m b  h »(m b  ) 1/2

39. B!  in QCDF/SCET Branching ratios Beneke and Jager 05 Parameter sets With NLO jet

40. Check B!  K,  Large real C/T=0.72 ! Data S4+LO jet S4+NLO jet A CP (  + K - ) 4 -3.5 -4.1 A CP (  0 K + ) -11.5 -4.1 -3.9 Tendency is not favored ! Also overshoot the  data Data (£ 10 -6 ) S4+LO jet S4+NLO jet B(  0  0 ) < 1.1 0.87 1.68 Expected, because  and  factorization formulas are almost identical

41. Mixing-induced CP in b! s

42. All approaches gave consistent results, and small uncertainty. C (tree pollution) remains small even with NLO Promising new physics signal, if data stand.

43. Conclusion Many puzzles in B-factory data A CP (K +  0 ) much differs from A CP (K +  - ). new physics in P EW ? New mechanism in C? A CP (B + ) are sensitive to NLO QCD B(  0  0 ) remains as a puzzle. Wait until Babar and Belle settle down. S penguin much different from S ccs is a promising new physics signal. If we are lucky, new physics may be right at the corner, but….