Direct CP Asymmetries in hadronic D decays

1. Direct CP Asymmetries in hadronic D decays Cai-Dian Lü(吕才典) IHEP, Beijing Based on work collaborated with Hsiang-nan Li, Fu-Sheng Yu, arXiv:1203.3120, accepted by PRD

2. Outline • Motivation, CPV • Branching Ratios, study decay mechanism • Factorization, with QCD dynamics • Penguin parameterization • Use hadronic parameters fixed by data of BRs • Combine short-distance dynamics of penguin • Predict direct CP asymmetries in SM • Summary CD Lu

3. Introduction: Evidence of CPV • First evidence of CP violation in charmed meson decays by LHCb, with 3.5 σ[arXiv:1112.0938] • Confirmed by CDF , with 2.7 σ[CDF note 10784] • Naively expected much smaller in the SM • Necessary to predict more precisely in the SM. CD Lu

4. Introduction: Dynamics of D decays • To predict CPV, we have to well understand the important decay mechanism. • At first, branching ratios should be well explained — not trivial • A long-standing puzzle: • R=1 in the SU(3) flavor symmetry limit Large SU(3) breaking effects CD Lu

5. 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 CD Lu

6. Annihilation contributions • Pure annihilation process • It vanishes in the SU(3) symmetry limit • But experimentally, • Large annihilation-type contributions • Large SU(3) breaking effects in annihilation processes CD Lu

7. Must Explain BRs wellotherwise, some important dynamics may be missedpenguin parameterization related to tree as much as possible and predict direct CP asymmetries CD Lu

8. 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 CD Lu

9. Guidelines • However, topology diagrams in SU(3) symmetry cannot predict right CP asymmetry • We apply factorization hypothesis: so that to include SU(3) breaking effect • Short-distance dynamics: Wilson coefficients • Long-distance dynamics: hadronicmatrix elements of four-fermion operators • Charm Perturbation in coupling constant and 1/mc is not reliable • mass just above 1 GeV. Introduce important non-perturbative parameters CD Lu

10. Emission amplitudes T&C • Factorization: • Scale-dependent Wilson coefficients: • Nonfactorizable contributions • Relative strong phase , due to inelastic FSI • They are universal, to be determined by data CD Lu

11. Evolution scale • Important flavor SU(3) breaking effects • Non-negligible mass ratios • Suggested by the PQCD approach, the scale is set to the energy release depending on masses of final states • : the momentum of soft degrees of freedom, a free parameter to be determined CD Lu

12. Exchange(E) vs Annihilation (A) • Life time of D mesons • E contributes to decays • A contributes to decays • It is also obtained from global fits [1001.0987, 1101.4714] • In factorization, |E|<| A|. But, factorizable contributions are helicity-suppressed, and can be neglected • We consider only nonfactorizable contributions for annihilation-type amplitudes CD Lu

13. Parameterization of E and A • b’s represent the involved matrix elements, nonfactorizable contributions • The superscripts q,sdifferentiate light quarks and strange quarks strongly produced in pairs, requested by SU(3) symmetry breaking. To explain • and are universal and to be fitted CD Lu

14. So far, the SU(3) breaking is not enough to explain the difference • NLO diagrams related to nonfactorizable amplitudes contributing to Glauber divergence CD Lu

15. Mode-dependent dynamics • Glauber strong phase associated with pionin nonfactorizable amplitudes [H.n Li, S. Mishima, 09] • Pion : massless Goldstone boson, and bound state? • Masslessboson => huge spacetime => large separation between qqbar => high mass due to confinement => contradiction! • Reconciliation : Tight bound qqbar, but multi-parton => soft could (Lepage, Brodsky 79; Nussinov, Shrock 08; Duraisamy, Kagan 08) • Glauber phase corresponds to soft could[H.n Li, S. Mishima, 09] CD Lu

16. Glauber phase for pion in E & A • Glauber phase: only in nonfactorizable contribution • Introduce a phase factor for each pion involved in the amplitudes E and A, which are dominated by nonfactorizable contributions • For ππ final state, • We don’t introduce Glauber phase to emission amplitudes which are dominated by factorizable contributions CD Lu

17. Summary of SU(3) breaking effects • In emission amplitudes • Evolution of Wilson coefficients • Transition form factors • Decay constants • In annihilation amplitudes • Evolution of Wilson coefficients • Decay constants • Matrix elements and phases • Glauber phase for pion CD Lu

18. Global fit • 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 asymmetries in this mode [H.n Li, S. Mishima, 0901.1272] CD Lu

19. Cabibbo-favored branching ratios(%), well consistent with data CD Lu

20. Singly Cabibbo-suppressed decays(10-3), better agreement with data CD Lu

21. Improvement of BRs involving η’ • Benefited from the scale-dependent Wilson coefficients, predictions on all the η’ involved modes are improved, compared to the pole model and diagrammatic approach CD Lu

22. Direct CP asymmetry • Definition: • Occurs only in singly Cabibbo-suppressed decays • Interference of Tree and Penguin contributions CD Lu

23. Penguin parameterization • Use the long-distance hadronic parameters fixed by the data of branching ratios • Try to formulate penguin contribution without introducing additional free parameters • The tree operators are all (V-A)(V-A) • For penguins, the hadronic matrix elements with (V-A)(V-A) operators are the same as tree level operators CD Lu

24. Those with (V-A)(V+A) or (S-P)(S+P) are different • They can be related to tree matrix elements by chiral enhancement, or neglected by power suppression • Unambiguous predictions of direct CP asymmetries CD Lu

25. Penguin topologies • All topological penguin diagrams for D->PP CD Lu

26. Penguin operators CD Lu

27. Color-suppressed Penguin emission amplitude PT • Directly related to tree amplitudes T, by replacing short-distance Wilson coefficients CD Lu

28. Penguin emission amplitude PC • Large contribution from the enhancement by the chiral factor CD Lu

29. Penguin annihilation amplitude PA • Factorizable contribution is neglected • Consider only nonfactorizable contributions from O4 and O6 • For O6, we have the following equality from PQCD • Because only the vector current V contributes to the production of two pseudoscalar mesons CD Lu

30. Penguin exchange amplitude PE • Helicity suppression doesn’t apply for O5,O6 in PE • (S-P)(S+P) contributes to factorizable amplitude • Under factorization hypothesis — It is new • Assume the scalar matrix element is dominated by the lowest scalar resonances • Breit-Wigner propagator • Scalar decay constant CD Lu

31. Predictions of Direct CP asymmetries CD Lu

32. Difference of CP asymmetries • The prediction in the SM • LHCb • CDF • The prediction is much smaller than experimental measurements • If we vary the strong phases arbitrarily, it could be at most CD Lu

33. Summary • Predict penguin contributions, related to tree-level amplitudes under factorization hypothesis • Fix hadronic parameters using data of branching ratios • Combine short-distance dynamics associated with penguin operators • Unambiguous predictions of direct CP asymmetries in D->PP in the SM • Especially • Much smaller than LHCb and CDF measurements CD Lu

34. THANK YOU! CD Lu