1. Nonleptonic Two Body Decays of Charmed Mesons
By YU Fusheng (于福升)
2011 Cross Strait Meeting on Particle Physics and Cosmology

2. Outline Introduction Generalized Factorization Approach
phenomenology
heavy flavor physics
Generalized Factorization Approach
Pole Dominance Model
Summary

3. Topological diagrams

4. Introduction
Effective Hamiltonian: basic tool to study the hadronic decay of heavy flavor mesons
are Wilson coefficients and are four quark operators:

5. The amplitude of is The key is to tackle : Naïve factorization
Generalized Factorization
Pole dominance model
QCD factorization (QCDF)
Perturbative QCD approach (PQCD)
Soft-collinear effective theory (SCET) …

6. Naïve Factorization
Assumption: the matrix element is factorized into two parts,
Neglect the annihilation and nonfactorization contributions

7. Wilson coefficients
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

8. Generalized Factorization
Consider non-factorization contributions
In the large-Nc approach,
A large relative strong phase between diagrams is induced by final-state interactions

9. Annihilation contributions
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.

10. Pole Model
Only consider the lowest lying poles
Example:

11. Pole Model
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

12. Framework Annihilation Emission diagrams
Pole Model Generalized Factorization Approach
Consider relative strong phases between topological diagrams
Calculate the branching ratios of and

13. Free Parameters (Wilson Coefficients)

20. Phenomenological Analysis
, large annihilation type contributions agree with the experiment data better than that of the diagrammatic approach.

22. Large annihilation type contributions agree with the experiment data.
The single pole resonance effect dominates the annihilation type contribution in most decay modes.

23. Small annihilation contributions in this model
Due to the smallness of decay constants of intermediate scalar mesons.

24. Summary 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

25. Thank you !

26. Backup

27. Decay constants and form factors

28. Amplitudes

29. Strong Phase 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.

30. Pole Model for D to PP