Hadronic B/D decays in factorization assisted topology diagram approach

Transcription

1 Hadronic B/D decays in factorization assisted topology diagram approach Cai-Dian Lü( 吕才典 ) CFHEP, Institute of High Energy Physics, Beijing Based on work collaborated with Hsiang-nan Li, Ying Li, F-S. Yu, Qin Qin, X.-X. Wang, S-H. Zhou, Y.-B. Wei arxiv: , PRD84 (2011) 0719 arxiv: , PRD86 (2012) arxiv: , PRD89 (2014) 0506 arxiv: , PRD92 (2015)

2 Outline n Introduction/Motivation n Factorization assisted topological diagram approach for hadronic B/D decays n Use hadronic parameters fixed by data of BRs Predict BRs of other channels and direct CP asymmetries in SM n Summary 2

3 Flavor physics is important 3

4 CKM triangle measurement 4

5 5

6 Rich physics in hadronic B decays π (K) b W u B b B W π d(s) π (K) t π The standard model describes interactions amongst quarks and leptons In experiments, we can only observe hadrons How can we test the standard model without solving QCD? 6

7 Perturbative calculations n In principle, all hadronic physics should be calculated by QCD n In fact, you can always use QCD to calculate any process, provided you can renormalize the infinities and do all order calculations. 7

8 Divergences n Perturbation calculation means order by order n Involving loop diagrams n Therefore divergences unavoidable n Ultraviolet divergences à renormalization n Infrared divergences? Infrared divergence in virtual corrections should be canceled by real emission n In exclusive QCD processes à factorization 8

9 Factorization can only be proved in power expansion by operator product expansion. To achieve that, we need a hard scale Q In the certain order of 1/Q expansion, the hard dynamics characterized by Q and the soft dynamic factorize The former into hard kernel H and the latter into distribution amplitude ϕ Factorization theorem holds up to all orders in α s, but to certain power in 1/Q H is process-dependent, but calculable ϕ are universal (process-independent) predictive power of factorization theorem In B decays the hard scale Q is just the b quark mass 9

10 Hadronic matrix elements calculations QCD-methods based on factorization work well for many processes Perturbative QCD approach based on kt factorization [Keum, Li, Sanda, 00 ; Lu, Ukai, Yang, 00 ] collinear QCD Factorization approach [Beneke, Buchalla, Neubert, Sachrajda, 99 ] Soft-Collinear Effective Theory [Bauer, Pirjol, Stewart, 01 ] Unavailable for 1/mb power corrections Topological diagrammatic approach [Chau, Cheng, et al, 91 ; Chiang, Rosner, et al, 04 ] Work well for most of charmless B decays, except for pi K puzzle etc.

11 Hadronic decays with charm quark in the final states or initial state n High precision measurements of B/D decays already by BaBar, Belle, BESIII and LHCb, and to be pushed by LHCb upgrade and Belle-II. n High precision in theoretical calculation is urged n Theore&cally, it is not sa&sfied, since there are mostly model calcula/ons, some QCD sum rules calcula/on or rely on La6ce QCD: an ul/mate tool but a formidable task now n Charm quark mass is not large enough for heavy quark expansion 11

12 Topological diagrammatic approach [Chiang, Senaha, 07 ] T C n Distinct by weak interaction and flavor flows with all strong interaction encoded, including non-perturbative ones. Model-independent n Based on flavor SU(3) symmetry. Amplitudes with strong phases extracted from data. SU(3) breaking was lost. n DP, D*P and DV fitted separately, 5 parameters for each category of decay modes. Less predictive. E A 12

13 Ø Effective Hamiltonian: For the color favored diagram (T), it is proved factorization to all order of α s expansion in soft -collinear effective theory, The decay amplitudes is just the decay constants and form factors times Wilson coeficients of four quark operators. The SU(3) breaking effect is automatically kept No free parameter 13

14 Ø Effective Hamiltonian: For other diagrams, we extract the amplitude and strong phase from experimental data by χ 2 fit We factorize out the decay constants and form factor to keep the SU(3) breaking effect 14

15 Global Fit for all BàDP, D*P and DV decays (PRD92, 0916 (2015)) n 31 measured modes induced by b c transitions Large strong phase χ 2 is much smaller than previous topology diagram approach Topological amplitudes 15

16 BàDP X 16

17 BàD*P X 17

18 BàDV 18

19 Nonperturbative parameters χ C, φ C, χ E, φ E are universal for all the DP, D * P and DV modes factorization 19

20 SU(3) breaking effects in amplitudes to be 10~20% 20

21 SU(3) breaking (I) SU(3) breaking effects can be described by decay constants 21

22 CKM suppressed b u transitions Vub T C E A All modes predicted, with assumptions: n non-perturbative parameters are the same as those in the b c transitions n W-annihilation A diagrams calculated in the pole model [arxiv: ] 22

23 CP asymmetries FAT predictions LHCb measurement To be tested in the future 23

24 Global fit for hadronic D decays (Phys.Rev. D86 (2012) ) 12 free parameters are extracted from 28 experimental data of D->PP branching ratios Λ describes the soft momentum in D meson The value of Glauber phase is consistent with the value extracted from B->πK data, resolving the puzzle for direct CP asymmetry in this mode [H.n Li, S. Mishima, ] 24

25 Evidence of CPV in D decays n First evidence of CP viola&on in charmed meson decays by LHCb, with 3.5 σ [arxiv: ] n Confirmed by CDF, with 2.7 σ [CDF note 10784] n Naively expected much smaller in the SM n Necessary to predict more precisely in the SM. 25

26 Topology diagrams for BRs According to weak interactions and flavor flows Include all strong interaction effects, involving final state interaction (FSI) effects Magnitude and phase are introduced to each topology This is a complete set Penguins are neglected for BRs due to suppression of CKM matrix elements 26

27 Evolu/on scale n Important flavor SU(3) breaking effects n Non-negligible mass ra/os n Suggested by the PQCD approach, the scale is set to the energy release depending on masses of final states n : the momentum of sos degrees of freedom, a free parameter to be determined 27

28 Singly Cabibbo-suppressed decays (10-3 ), better agreement with data 28

29 SU(3) breaking effects In the factorization method Large SU(3) breaking effects in W exchange diagram Dynamics in the annihilation amplitudes has not yet been well understood 29

30 Phys.Rev. D89 (2014) 5,

31 Penguin parameteriza/on n Use the long-distance hadronic parameters fixed by the data of branching ra/os n Try to formulate penguin contribu/on without introducing addi/onal free parameters n The tree operators are all (V-A)(V-A) n For penguins, the hadronic matrix elements with (V-A)(V-A) operators are the same as tree level operators 31

32 Predictions of Direct CP asymmetries Δ CP = x

33 LHCb combination LHCb-PAPER LHCb-CONF Semileptonic: Semileptonic: Prompt: (preliminary) Prompt: (preliminary) The two measurement are compatible at the 3 % level The two measurement are compatible at the 3 % level χ2 = 4.85 Naive average (neglecting indirect CP violation) 33

34 Current experimental status 34

35 Current experimental status Our theoretical prediction in 2012 is x

36 Charmless B decays n Famous pi K puzzle not well explained n Tree + penguin contribution, complicated 36

37 Large color suppressed tree diagram contribution together with large strong phase also expected 37

38 Preliminary results 38

39 Summary DàPP, PV, B DP, D*P and DV decays are studied in the factorization-assisted topological-amplitude approach In D decays, we fix hadronic parameters using data of branching ratios Combine short-distance dynamics associated with penguin operators Unambiguous predictions of direct CP asymmetries in Dà PP, PV decays in the SM n n n Only four universal non-perturbative parameters to be fitted for all B DP, D*P and DV decays, more predictive than ever Results are consistent with data. SU(3) breakings are studied. Predictions to be tested by future exp. 39

40 Many Thanks for a wonderful workshop! Thanks the organizing committee, especially Eung Jin Chun and his team!