By YU Fusheng (于福升)
2011 Cross Strait Meeting on Particle Physics and Cosmology
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 Introduction
• phenomenology
• heavy flavor physics
 Generalized
 Pole
Factorization Approach
Dominance Model


 Summary
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
Effective Hamiltonian: basic tool to study the
hadronic decay of heavy flavor mesons
are Wilson coefficients and
are four quark operators:
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
The amplitude of

The key is to tackle :
is
Naïve factorization
Generalized Factorization
Pole dominance model
QCD factorization (QCDF)
Perturbative QCD approach (PQCD)
Soft-collinear effective theory (SCET)
…
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

Assumption: the matrix element is factorized
into two parts,
Neglect the annihilation and nonfactorization
contributions
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for color-favored (T) and color-suppressed (C)
processes.

are universal and process independent.

Difficulties:

are renormalization scale and
scheme
dependent
fail to describe the color-suppressed decay modes
due to the smallness of
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
Consider non-factorization contributions

In the large-Nc approach,
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A large relative strong phase between diagrams
is induced by final-state interactions
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

Annihilation diagrams are neglected as an
approximation in the factorization model.
We will calculate considerable resonant
effects of annihilation diagrams in a single
pole dominance model.
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Only consider the lowest lying poles
 Example:

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
The weak matrix element is evaluated in the
vacuum insertion approximation,

The effective strong coupling

Inserting the propagator of intermediate state,
the decay amplitude is
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



Annihilation
Emission diagrams
Pole Model
Approach
Generalized Factorization
Consider relative strong phases between
topological diagrams
Calculate the branching ratios of
and
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
, large annihilation type contributions
agree with the experiment data better than
that of the diagrammatic approach.
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

Large annihilation type contributions agree
with the experiment data.
The single pole resonance effect dominates
the annihilation type contribution in most
decay modes.
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Small annihilation contributions in this model
 Due to the smallness of decay constants of
intermediate scalar mesons.

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
and
are studied on the basis
Generalized factorization for emission diagrams
Pole model for resonance effect of annihilation
diagrams
Relative strong phases between topological
diagrams


Our results agree with experimental data
Annihilation contributions in pole model
small to
, but large to
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
The
amplitudes satisfy the isospin
triangle relation
but

Besides, importance of inelastic final state
interactions of D meson decays in which onshell intermediate states will contribute
imaginary parts.
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