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

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

Topological diagrams

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

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) …

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

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

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

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.

Pole Model Only consider the lowest lying poles Example:

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

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

Free Parameters (Wilson Coefficients)

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

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

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

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

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Backup

Decay constants and form factors

Amplitudes

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.

Pole Model for D to PP