1 / 43

Puzzles in B physics Recent development in PQCD, QCDF, SCET

Puzzles in B physics Recent development in PQCD, QCDF, SCET. Hsiang-nan Li Academia Sinica, Taiwan presented at Whepp9 Bhubaneswar Jan. 07, 2006. Outlines. Introduction QCDF, PQCD, and SCET B ! VV polarizations B ! K  direct CP asymmetries B !  branching ratios

julius
Download Presentation

Puzzles in B physics Recent development in PQCD, QCDF, SCET

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Puzzles in B physicsRecent 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 O2=(su)(ub) / C2 ,s

  5. CKM matrix elements • Wilson coefficients |-i|¼ 0.4 a1=C2+C1/Nc a2=C1+C2/Nc

  6. Quark amplitudes s u u W u b u s Color-allowed tree T Color-suppressed tree C s s u u , Z u u g QCD penguin P Electroweak penguin Pew

  7.  parameterization Tree-dominant (C4/C2)(VtdVtb/VudVub)/1» (2/1)(3/4)»

  8. B(B0!00) • P, C, and Pew 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 (C2/C4)(VusVub/VtsVtb)» (1/2)(5/2)»

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

  11. sin 21/sin 2 • 1 decay amplitude, fCP=exp(-2i1) • Measure SfCP/ ImfCP )measure sin(21) • Either pure-tree or pure-penguin modes serve the purpose • Tree-dominant B! J/ KS, penguin pollution: P/T» (C4/C2)(VtsVtb/VcsVcb)»2» 5% • Penguin-dominant b! s, tree pollution: C’/P’ »2» 5%

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

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

  14. QCDF • Based on collinear factorization (Brodsky and Lepage 80). • Compute correction to naïve factorization (NF), ie., the heavy-quark limit. • Divergent like s01 dx/x (end-point singularity) in collinear factorization perturbative nonperturbative

  15. Hard kernels • TI comes from vertex corrections • TII comes from spectator diagrams x q 1 Magnetic penguin O8g

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

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

  18. Factorization picture Sudakov factors S, summation of sln2(mb/kT) to all orders, describe parton distribution in kT Always collinear gluons Large kT Small b g g kT accumulates after infinitely many gluon exchanges, similar to DGLAP evolution up to kT~Q

  19. SCETI • Two scales in B decays: mb and mb2 • Full theory! SCETI: integrate out the lines off-shell by mb2 Wilson coeff of SCETI W 2 b C()J(0)()!C()() J(0) g T(0)J(1)(0) mb2 Hard-collinear gluon, mass O(mb) 1/mb suppressed current

  20. SCETII • SCETI! SCETII: integrate out the lines off-shell by mb • Compared to QCDF, TII! T(0)J(0,) Jet=Wilson coeff of SCETII J(0,)O() 2 ! T(0)J(0,)M()B()

  21. B! K direct CP

  22. Large strong phase • ACP(K+-)¼ -0.115 implies sizable T» 15obetween T and P (PQCD, 00) If T=0 If T=0 T exp(i3) T exp(i3) Br P P Br = Br T exp(-i3) Br = Br Direct CP T exp(-i3)

  23. Explanation 1 • How to understand the small ACP(K+0)? • Large PEW 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) Br¼ Br PEW

  24. 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 exp(i3) (T+C) exp(i3) P Br¼ Br (T+C) exp(-i3)

  25. NLO PQCD (Li, Mishima, Sanda 05) • LO: all pieces at LO • LONLOWC: 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%

  26. Vertex correction • Vertex correction enhances C/ a2, and makes it almost imaginary. Without vertex correction Re, with vertex correction Im, with vertex correction Is negative. It rotates T!

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

  28. Hadronic uncertainty PQCD results

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

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

  31. SCET inputs

  32. SCET predictions

  33. B! branching ratios

  34. 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.

  35. SCET inputs Not a resolution

  36. 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) • LONLOWC +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00.35     0.81   0.41  0.25   0.72 NLO has saturated the 00 bound  the  puzzle is confirmed.

  37. 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 » mb h»(mb)1/2

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

  39. Check B!K,  • Large real C/T=0.72 ! • Data S4+LO jet S4+NLO jet   ACP(+K-) 4-3.5   -4.1 ACP(0K+) -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  

  40. Mixing-induced CP in b! s

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

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

More Related