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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: , accepted by PRD

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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 2CD Lu

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Introduction: Evidence of CPV First evidence of CP violation in charmed meson decays by LHCb, with 3.5 σ [arXiv: ] 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. 3CD Lu

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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 4CD Lu

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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 5CD Lu

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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 6CD Lu

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Must Explain BRs well otherwise, some important dynamics may be missed penguin parameterization related to tree as much as possible and predict direct CP asymmetries 7CD Lu

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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 8CD Lu

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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: hadronic matrix elements of four-fermion operators Charm Perturbation in coupling constant and 1/m c is not reliable mass just above 1 GeV. Introduce important non-perturbative parameters 9CD Lu

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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 10CD Lu

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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 11CD Lu

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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 [ , ] In factorization, |E|<| A|. But, factorizable contributions are helicity-suppressed, and can be neglected We consider only nonfactorizable contributions for annihilation-type amplitudes 12CD Lu

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

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

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Mode-dependent dynamics Glauber strong phase associated with pion in nonfactorizable amplitudes [H.n Li, S. Mishima, 09] Pion : massless Goldstone boson, and bound state? – Massless boson => 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] 15CD Lu

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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 16CD Lu

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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 17CD Lu

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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, ] 18CD Lu

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

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

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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 21CD Lu

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

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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 23CD Lu

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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 24CD Lu

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

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Penguin operators 26CD Lu

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

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Penguin emission amplitude P C Large contribution from the enhancement by the chiral factor 28CD Lu

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Penguin annihilation amplitude PA Factorizable contribution is neglected Consider only nonfactorizable contributions from O 4 and O 6 For O 6, we have the following equality from PQCD Because only the vector current V contributes to the production of two pseudoscalar mesons 29CD Lu

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Penguin exchange amplitude PE Helicity suppression doesn’t apply for O 5,O 6 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 30CD Lu

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Predictions of Direct CP asymmetries 31CD Lu

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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 32CD Lu

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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 33CD Lu

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THANK YOU! 34CD Lu

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