Theories of exclusive B meson decays

1. Theories of exclusive B meson decays Hsiang-nan Li Academia Sinica Presented at Mini-workshop Nov. 19, 2004

2. Outlines • Naïve factorization and beyond • QCDF vs. PQCD • Parton kT? • Scales and penguin enhancement • Strong phase and CP asymmetry • SCET • Remarks

3. Naïve factorization and beyond Naïve factorization (BSW) Color-allowed Color-suppressed : universal Wilson coefficients

4. Success due to “color transparency” D B Lorentz contraction Small color dipole Decoupling in space-time From the BD system To be quantitative, nonfactorizable correction? Large correction in color-suppressed modes due to heavy D, large color dipole

5. Exp shows that the Wilson coefficients are not really universal Generalized naïve factorization Due to nonfactorizable correction? Fine tune the mode-dependent parameters to data Equivalently, effective number of colors in Not very helpful in understanding decay dynamics

6. Strong phase and CP asymmetry When entering the era of B factories, CP asymmetries in charmless decays can be measured Tree Penguin Interference of T and P Data Extraction Theory

7. In naïve factorization, strong phase comes from the BSS mechanism Only source? Important source? Nonfactorizable correction, strong phase,… Need a systemic, sensible, and predictive theory Expansion in Factorization limit… Predict not yet observed modes Explain observed data

8. QCDF vs. PQCD • OCD-improved factorization=naïve factorization + QCD correction Factorizable emission Leading Vertex Non-spectator Exchange & correction Annihilation Sub-leading

9. QCDF amplitude: Two questions: The emission diagram is certainly leading…. But why must it be written in the BSW form ? Has naïve factorization been so successful that what we need to do is only small correction ? Both answers are “No” There is another option for factorizing the leading term, and naïve factorization prediction could be modified.

10. However, the subleading calculation shows an end-point singularity in twist-3 nonspectator and in annihilation Need to introduce arbitrary cutoffs Same singularity appears in the form factor This is the reason the form factor is not factorizable (calculable), and treated as a soft object (BSW form) Curiosity: Why are the form factor and the annihilation , though none is calculable ?

11. Want to calculate subleading correction?..... An end-point singularity means breakdown of simple collinear factorization Use more conservative kT factorization Include parton kT to smear the singularity The same singularity in the form factor is also smeared Then the form factor also becomes factorizable Perturbative QCD approach

12. Parton kT? Beneke’s 6 comments (ICHEP, Osaka, 2000) 1.Parton kT must be small, no help 2.kT breaks gauge invariance 3.kT factorization needs a proof 4.Twist-3 contribution is not complete 5.DA models should come from sum rules 6…..Could not remember all of them

13. 1.Parton kT must be small, no help? Sudakov factors S Describe the parton Distribution in kT kT accumulates after infinitely many gluon exchanges Similar to the DGLAP evolution up to kT~Q

14. 2.kT breaks gauge invariance? • kT factorization still starts with on-shell external particles • Decay amplitudes are gauge invariant • Parton kT is gained by exchanging gluons • Try to construct a gauge-invariant kT-dependent wave function • Then hard kernels H are gauge-invariant • Convolution of H with WF models (prediction) is gauge-invariant

15. 3.kT factorization needs a proof • Have proved it for semileptonic decays • Leading-power proof is easy: dynamics of different scales decouples • Proof for nonleptonic decays follows • Learned how to construct a gauge-invariant kT-dependent WF from proof • …….

16. Scales and penguin enhancement Fast partons In QCDF this gluon is off-shell by In PQCD this gluon is off-shell by Slow parton Fast parton For penguin-dominated modes, PQCD QCDF

18. Strong phase and CP asymmetry

19. Annihilation is similar to BSS mechanism Loop line can go on-shell kT Sudakov gluons Strong phase kT: loop momentum with the weight (Sudakov) factor

20. Pinch-induced strong phase=FSI? Inclusive decay ~ Cut quark diagram ~ Sum over final-state hadrons Off-shell hadrons On-shell

21. Our concerns in 2000 • Is kT factorization an appropriate theory? • Is a pinched singularity the correct way to produce the strong phase? • Is the annihilation the only important source of strong phases? • Do we have the guts to present the prediction, large CP asymmetries with definite signs?

22. Soft-collinear Effective Theory • An effective theory at large energy E • Effective degrees of freedom: collinear fields, soft fields,… • Expansion of Lagrangian in 1/E in terms of effective operators • Wilson coefficients: hard kernels • Convenient for factorization proof. Effective operators define nonlocal matrix elements (wave functions)

23. At lower energy, detailed structure of form factor can be seen Effective (soft) operator for energy <

24. nonpert

25. SCET • SCET is more careful in scale separation. • A form factor is split into two pieces: soft and hard contributions. • No annihilation contribution. • Need Acc (nonperturbative charming penguin) to introduce large strong phases. • All the above parameters are from fitting.

26. T can be chosen to be real, and C is assumed to be real.

27. 0.016-0.064 BBNS 04

28. In fact, charming penguin is factorizable (no IR divergence) and small Li, Mishima 04 BBNS 04 Acc is large

29. My personal comments • A bit disappointed by that SCET was led to this direction. • I can get the same “prediction” using T, C, P, assuming C to be real---4 parameters with 4 inputs. • The pi0pi0 amplitude is fixed by the isospin relation. • A stringent test will be Kpi modes. Need more parameters. pi+pi-: T+P pi0pi0: C-P pi+pi0: T+C

30. Amplitude topologies

31. Remarks • Compard to HQET, exclusive theories are still not yet well established: Matrix elements (wave function) not known Subleading corrections not clear Mechanism not explored completely ……… • It is definitely a much richer and challenging field.

32. Experimental data Exact solution PQCD pi0pi0 branching ratio gets smaller. P/T approaches theory.

33. New data: ~0.38

34. B->K pi amplitudes and data

35. K pi data imply large Pew ? • The updated data imply a large C, instead of a large Pew. T exp(i phi3) K+pi- P Large strong phase between P and T is confirmed T exp(-i phi3) (T+C) exp(i phi3) Pew K+pi0 (T+C) exp(-i phi3)

36. Buras’s picture T exp(i phi3) K+pi0 P T exp(-i phi3) Pew This is a possible solution, but ruled out by the pi pi data

38. Charming penguin: need many Acc for each polarization and for each mode. • Rescattering: hard to accommodate rho K*, phi K* simultaneously. • b->sg: negligible due to G parity. • Annihilation: not sufficient for phi K*, but able to explain rho K*. • rho+ K*0: P rho0 K*+: P+T • Interference between P and T enhances the longitudinal polarization