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

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

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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.3CD Lu

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

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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

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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

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Must Explain BRs wellotherwise, some important dynamics may

be missed

penguin parameterization related to tree as much as possible and predict

direct CP asymmetries

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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

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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/mc is not reliable• mass just above 1 GeV. Introduce important

non-perturbative parameters

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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

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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

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Exchange(E) vs Annihilation (A)

• Life time of D mesons

E contributes to decaysA 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

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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 fitted13CD Lu

So far, the SU(3) breaking is not enough to explain the difference

• NLO diagrams related to nonfactorizable amplitudes contributing to Glauber divergence

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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

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

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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

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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, 0901.1272]

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

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

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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

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Direct CP asymmetry• Definition:

• Occurs only in singly Cabibbo-suppressed

decays

• Interference of Tree and Penguin contributions

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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

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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

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Penguin topologies

• All topological penguin diagrams for D->PP

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Penguin operators

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Color-suppressed Penguin emission amplitude PT

• Directly related to tree amplitudes T, by replacing short-distance Wilson coefficients

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Penguin emission amplitude PC

• Large contribution from the enhancement by the chiral factor

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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

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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 30CD Lu

Predictions of Direct CP asymmetries

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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

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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

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THANK YOU!

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