Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2007-05-11
Commun.Theor.Phys.49:707-716,2008
Physics
High Energy Physics
High Energy Physics - Phenomenology
21pages,5 figures,3 tables, typos corrected and numerical result for one of decay channels is improved
Scientific paper
10.1088/0253-6102/49/3/39
The branching ratios and CP violations of the $B\to D\pi$ decays, including both the color-allowed and the color-suppressed modes, are investigated in detail within QCD framework by considering all diagrams which lead to three effective currents of two quarks. An intrinsic mass scale as a dynamical gluon mass is introduced to treat the infrared divergence caused by the soft collinear approximation in the endpoint regions, and the Cutkosky rule is adopted to deal with a physical-region singularity of the on mass-shell quark propagators. When the dynamical gluon mass $\mu_g$ is regarded as a universal scale, it is extracted to be around $\mu_g = 440$ MeV from one of the well-measured $B\to D\pi$ decay modes. The resulting predictions for all branching ratios are in agreement with the current experimental measurements. As these decays have no penguin contributions, there are no direct $CP$ asymmetries. Due to interference between the Cabibbo-suppressed and the Cabibbo-favored amplitudes, mixing-induced CP violations are predicted in the $B\to D^{\pm}\pi^{\mp}$ decays to be consistent with the experimental data at 1-$\sigma$ level. More precise measurements will be helpful to extract weak angle $2\beta+\gamma$.
Su Fang
Wu Yue-Liang
Yang Ya-Dong
Zhuang Ci
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