By YU Fusheng (于福升 )
2011 Cross Strait Meeting on Particle Physics and Cosmology1
Introduction
• phenomenology
• heavy flavor physics
Generalized Factorization Approach
Pole 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 is
The key is to tackle :
Naïve factorizationGeneralized FactorizationPole dominance modelQCD 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
dependentfail 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,
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 Generalized Factorization Approach
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 basisGeneralized factorization for emission diagramsPole model for resonance effect of annihilation
diagramsRelative strong phases between topological
diagrams
Our results agree with experimental data
Annihilation contributions in pole modelsmall 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 on-shell intermediate states will contribute imaginary parts. 29
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