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
been well understood 5CD Lu
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
processes6CD Lu
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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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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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
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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