QCD factorization in B decays ten years later

Transcription

1 QCD factorization in B decays ten years later M. Beneke (RWTH Aachen) Flavianet meeting in honour of Chris Sachrajda on the occasion of his 60th birthday Southampton, England, December 14/15, 2009 Early years of QCD factorization Outline MB, G. Buchalla, M. Neubert and C.T. Sachrajda, Phys.Rev.Lett.83: ,1999 [hep-ph/ ]; Nucl.Phys.B591: ,2000 [hep-ph/ ]; Nucl.Phys.B606: ,2001 [hep-ph/ ] The next order: Tree-dominated decays at NNLO MB, T. Huber, X.Q. Li, [hep-ph]; also: G. Bell, [hep-ph] and [hep-ph]; G. Bell and V. Pilipp [hep-ph] M. Beneke (RWTH Aachen) Southampton, December 15, / 26

2 15 years of common scientific interests Renormalons ( ) M. Beneke (RWTH Aachen) Southampton, December 15, / 26

3 15 years of common scientific interests Renormalons ( ) Exclusive B decays and QCD factorization ( ???) MB, G. Buchalla, M. Neubert and C.T. Sachrajda, QCD factorization for B ππ decays: Strong phases and CP violation in the heavy quark limit, Phys.Rev.Lett.83: ,1999 [hep-ph/ ] QCD factorization for exclusive, nonleptonic B meson decays: General arguments and the case of heavy light final states, Nucl.Phys.B591: ,2000 [hep-ph/ ] QCD factorization in B πk, ππ decays and extraction of Wolfenstein parameters, Nucl.Phys.B606: ,2001 [hep-ph/ ] Comment on B M 1 M 2 : Factorization, charming penguins, strong phases, and polarization, Phys.Rev.D72:098501,2005 [hep-ph/ ] Penguins with Charm and Quark-Hadron Duality, Eur.Phys.J.C61: ,2009 (arxiv: [hep-ph]) M. Beneke (RWTH Aachen) Southampton, December 15, / 26

4 QCD factorization for exclusive B decays M. Beneke (RWTH Aachen) Southampton, December 15, / 26

5 QCD factorization for exclusive B decays M. Beneke (RWTH Aachen) Southampton, December 15, / 26

6 QCD factorization for exclusive B decays M. Beneke (RWTH Aachen) Southampton, December 15, / 26

7 The beginnings Chris, 25 Apr 1998 M. Beneke (RWTH Aachen) Southampton, December 15, / 26

8 The beginnings MB, 26 Apr 1998 Chris, 25 Apr 1998 M. Beneke (RWTH Aachen) Southampton, December 15, / 26

9 The beginnings MB, 26 Apr 1998 Chris, 25 Apr 1998 MB, 29 Apr 1998 M. Beneke (RWTH Aachen) Southampton, December 15, / 26

10 M. Beneke (RWTH Aachen) Southampton, December 15, / 26

11 M. Beneke (RWTH Aachen) Southampton, December 15, / 26

12 M. Beneke (RWTH Aachen) Southampton, December 15, / 26

13 M. Beneke (RWTH Aachen) Southampton, December 15, / 26

14 Factorization in higher orders (2 loops) 8a 9a 10a b 11a 12a 13a b 14a 15a 16a 17a 18a 19a Completed early September 1999 M. Beneke (RWTH Aachen) Southampton, December 15, / 26

15 Many questions and further theoretical developments All-order proofs, especially for light-light Is hard-scattering enough? Role of Sudakov suppression S. Descotes-Genon and C.T. Sachrajda, Sudakov effects in B πlν(l) form-factors, Nucl.Phys.B625: ,2002 M. Beneke (RWTH Aachen) Southampton, December 15, / 26

16 Many questions and further theoretical developments All-order proofs, especially for light-light Is hard-scattering enough? Role of Sudakov suppression S. Descotes-Genon and C.T. Sachrajda, Sudakov effects in B πlν(l) form-factors, Nucl.Phys.B625: ,2002 Hard-spectator-scattering: role of the intermediate scale m b Λ? What is the B meson LCDA? Does one need transverse-momentum dependence? S. Descotes-Genon and C.T. Sachrajda, Factorization, the light cone distribution amplitude of the B meson and the radiative decay B γlν(l), Nucl.Phys.B650: ,2003, Universality of nonperturbative QCD effects in radiative B decays, Phys.Lett.B557: ,2003, Spectator interactions in B Vγ decays and QCD factorization, Nucl.Phys.B693: ,2004. M. Beneke (RWTH Aachen) Southampton, December 15, / 26

17 Many questions and further theoretical developments All-order proofs, especially for light-light Is hard-scattering enough? Role of Sudakov suppression S. Descotes-Genon and C.T. Sachrajda, Sudakov effects in B πlν(l) form-factors, Nucl.Phys.B625: ,2002 Hard-spectator-scattering: role of the intermediate scale m b Λ? What is the B meson LCDA? Does one need transverse-momentum dependence? S. Descotes-Genon and C.T. Sachrajda, Factorization, the light cone distribution amplitude of the B meson and the radiative decay B γlν(l), Nucl.Phys.B650: ,2003, Universality of nonperturbative QCD effects in radiative B decays, Phys.Lett.B557: ,2003, Spectator interactions in B Vγ decays and QCD factorization, Nucl.Phys.B693: ,2004. Eventually the relevance of collinear modes (rather than soft only as in HQET) played an important role in the development of soft-collinear effective theory. M. Beneke (RWTH Aachen) Southampton, December 15, / 26

18 First data failures and successes Talks in 1999 concluded with statements like Let s hope that the heavy quark limit is good enough for the real world with m b = 5 GeV and Λ = 500 MeV. M. Beneke (RWTH Aachen) Southampton, December 15, / 26

19 First data failures and successes Talks in 1999 concluded with statements like Let s hope that the heavy quark limit is good enough for the real world with m b = 5 GeV and Λ = 500 MeV. Problems 2001: First measured direct CP asymmetries (π + K, then π + π in 2002) opposite in sign to perturbative prediction. Annihilation? Other power corrections? Or NNLO? A CP = [c α s] NLO + O(α 2 s, Λ/m b ) M. Beneke (RWTH Aachen) Southampton, December 15, / 26

20 First data failures and successes Talks in 1999 concluded with statements like Let s hope that the heavy quark limit is good enough for the real world with m b = 5 GeV and Λ = 500 MeV. Problems 2001: First measured direct CP asymmetries (π + K, then π + π in 2002) opposite in sign to perturbative prediction. Annihilation? Other power corrections? Or NNLO? A CP = [c α s] NLO + O(α 2 s, Λ/m b ) 2003: Colour-suppressed mode π 0 π 0 larger than prediction Input parameters (λ B )? Power corrections? Or NNLO?» rsp n C a 2 (ππ) = [ i] NLO + [0.123] LOsp + [0.072] tw3o r sp = 9f M1 ˆf B m b f Bπ + (0)λ B M. Beneke (RWTH Aachen) Southampton, December 15, / 26

21 Successes Colour-allowed and penguin-dominated branching fractions are usually quantitatively ok PP vs PV vs VP (with some reservations), η ( ) K ( ) CP asymmetries would have no reason to be small, if the amplitudes were completely long-distance dominated γ (70 ± 5) from time-dependent CP asymmetries Small V ub Qualitative explanation of the absence of longitudinal polarization in B VV decays M. Beneke (RWTH Aachen) Southampton, December 15, / 26

22 Successes Colour-allowed and penguin-dominated branching fractions are usually quantitatively ok PP vs PV vs VP (with some reservations), η ( ) K ( ) CP asymmetries would have no reason to be small, if the amplitudes were completely long-distance dominated γ (70 ± 5) from time-dependent CP asymmetries Small V ub Qualitative explanation of the absence of longitudinal polarization in B VV decays 12 Branching fraction Π K 0 2 Π K 2 Η K 0 10 Η K Π Π 0 Π Π Π 0 Π 0 Π Η Π Η Π 0 Η ΗΗ Η Η K 0 K 0 ΗΗ Π 0 K K 0 Η K K Π 0 K 2 Π 0 K 0 2 ΗK ΗK M. Beneke (RWTH Aachen) Southampton, December 15, / 26

23 Π Π 0 ACP % Π Π Π 0 Π 0 Π Η S Π 0 Π 0 S Π Π Π 0 Η Π Η Π0 Η ΗΗ ΗΗ Η Η K K 0 Π K 0 K K Π 0 K K 0 K 0 Π K S Π 0 K 0 Π 0 K 0 ΗK S Η K 0 ΗK 0 Η K Η K ACP % Π K 0 Π 0 K Π K Π 0 K 0 Ρ K 0 Ρ 0 K Ρ K Ρ 0 K 0 ΩK ΩK 0 S ΩK 0 ΦK ΦK 0 S ΦK 0 ΗK ΗK 0 Η K Η K M. Beneke (RWTH Aachen) Southampton, December 15, / 26

24 Why NNLO? Basic question: «Λ O(α s) vs O m b Recall: problems with direct A CP and some colour-suppressed modes are based on comparison to (essentially) leading order QCD predictions Can never exlcude large sizeable power corrections theoretically. M. Beneke (RWTH Aachen) Southampton, December 15, / 26

25 Why NNLO? Basic question: «Λ O(α s) vs O m b Recall: problems with direct A CP and some colour-suppressed modes are based on comparison to (essentially) leading order QCD predictions Can never exlcude large sizeable power corrections theoretically. NNLO or fit! M. Beneke (RWTH Aachen) Southampton, December 15, / 26

26 Understanding hard spectator-scattering M. Beneke (RWTH Aachen) Southampton, December 15, / 26

27 M. Beneke (RWTH Aachen) Southampton, December 15, / 26

28 M. Beneke (RWTH Aachen) Southampton, December 15, / 26

29 M. Beneke (RWTH Aachen) Southampton, December 15, / 26

30 The next order Back to MB, GB, MN and C.T. Sachrajda, Nucl.Phys.B591: ,2000 [hep-ph/ ]. Two-loop correction to form factor term: 8a 9a 10a b 11a 12a 13a 1a 2a 3a b b 14a 15a 4a 5a 6a 7a 16a 17a b b b b 18a 19a M. Beneke (RWTH Aachen) Southampton, December 15, / 26

31 One-loop correction to T II i (u, z): (a) (b) (c) (d) (e) (f) A.1 A.2 A.3 A.4 B.1 B.2 B.3 B.4 M. Beneke (RWTH Aachen) Southampton, December 15, / 26

32 One-loop correction to J(z; ω, v) (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) M. Beneke (RWTH Aachen) Southampton, December 15, / 26

33 NNLO Status Spectator-scattering One-loop J II : (Becher et al. 04; MB, Yang 05; Kirilin 05) One-loop T II tree amplitudes: (MB, Jäger, 05; Kivel, 06; Pilipp 07) One-loop T II penguin amplitudes: (MB, Jäger, 06) Vertex term Two-loop T II tree amplitudes: (MB, Huber, Li 09; Bell 09) Two-loop T II penguin amplitudes: (in progress) Tree-dominated decays complete at NNLO. No NNLO result yet on direct CP asymmetries. M. Beneke (RWTH Aachen) Southampton, December 15, / 26

34 Size of the 2-loop vertex correction Re Α 1 V 1.04 Re Α 2 V Μ GeV Μ GeV Im Α 1 V Μ GeV Im Α 2 V Μ GeV M. Beneke (RWTH Aachen) Southampton, December 15, / 26

35 Numerical result (tree amplitudes) a 1 (ππ) = [ i] NLO + [ i] NNLO» rsp n o [0.014] LOsp + [ i] NLOsp + [0.008] tw = i i (if 2 r sp) r sp = 9f M1 ˆf B m b f Bπ + (0)λ B a 2 (ππ) = [ i] NLO [ i] NNLO» rsp n o + [0.114] LOsp + [ i] NLOsp + [0.067] tw = i i (if 2 r sp) The NNLO corrections to the vertex term and spectator scattering are significant individually (about 25% for a 2 ). But both tend to cancel too bad! Largest uncertainty is input parameter dependence: Allows C/T ππ 0.7, if λ B is small. The colour-suppressed amplitudes are probably dominated by spectator-scattering. But arg (C/T ππ) < 15. Perturbation theory works at scale m b and m b Λ. No indication of further large radiative corrections. M. Beneke (RWTH Aachen) Southampton, December 15, / 26

36 Branching fraction results (tree-dominated decays) B π π B 0 d π+ π B 0 d π0 π B π ρ B π 0 ρ B 0 π + ρ B 0 π ρ B 0 π ± ρ B 0 π 0 ρ Theory I Theory II Experiment ( ) ( ) ( ) ( ) 5.16 ± ± 0.19 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 15.7 ± 1.8 ( ) 7.3 ± ( ) 23.0 ± ± 0.5 B ρ L ρ0 L ( ) ( ) B 0 d ρ+ L ρ L ( ) ( ) B 0 d ρ0 L ρ0 L M. Beneke (RWTH Aachen) Southampton, December 15, / 26

37 Factorization test Γ(B π π 0 ) dγ( B 0 π + l ν)/dq 2 q2 =0 = 3π 2 f 2 π V ud 2 α 1 (ππ) + α 2 (ππ) 2 From semi-leptonic data [cf. Becher, Hill, 05; Ball 06, BaBar 06]: V ub f +(0) = (9.1 ± 0.7) 10 4 equivalent to α 1 (ππ) + α 2 (ππ) exp = 1.29 ± 0.11 Leading uncertainties: λ B (B LCDA), α π 2 (pion LCDA), power corrections, hard-collinear scale-dependence Good agreement of central values (λ B = 0.35 GeV) Α 1 ΠΠ Α 2 ΠΠ Λ B GeV M. Beneke (RWTH Aachen) Southampton, December 15, / 26

38 Colour-suppressed vs colour-allowed decays ΠΠ R Λ B GeV ΠΡ R Λ B GeV ΡΡ R Λ B GeV Preference for small λ B, i.e. strong spectator-scattering (as already evident in the global analysis of [MB, Neubert, 03] ). M. Beneke (RWTH Aachen) Southampton, December 15, / 26

39 Charged π ρ ± modes R 3 = Γ(B 0 π + ρ ) Γ(B 0 π ρ + ) C = 1 2 ˆC(π ρ + ) C(π + ρ ) R A BΡ 0 0 f BΠ 0 C A 0 BΡ 0 f BΠ 0 Both quantities depend mainly on Specifically, f πa B ρ 0 (0)/(f ρf B π + (0)) α 1 (ρπ)/α 1 (πρ) = R e iδ T. C = 1 R2 1 + R 2 + 4R 2 (1 + R 2 ) 2 (a cos δa + b cos δ b) cos γ +... Seems to favour slighty smaller B ρ to B π form factor ratio than QCD sum rules ( 1.25). In the future: factorization test for ρρ gives B ρ form factor directly. M. Beneke (RWTH Aachen) Southampton, December 15, / 26

40 Outlook Look forward to NLO direct CP asymmetries to complete the picture. 2-loop corrections to phases can be large. M. Beneke (RWTH Aachen) Southampton, December 15, / 26