QCD Approach to B->D \pi Decays and CP Violation

TL;DR

This paper uses a QCD framework with an introduced dynamical gluon mass to accurately predict branching ratios and CP violation effects in B→Dπ decays, aligning well with experimental data and providing insights into weak angles.

Contribution

It presents a detailed QCD-based analysis of B→Dπ decays incorporating a dynamical gluon mass to handle infrared divergences, leading to predictions consistent with experiments.

Findings

Predicted branching ratios agree with measurements.

No direct CP asymmetries due to lack of penguin contributions.

Predicted mixing-induced CP violations align with data.

Abstract

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 $2\beta+\gamma$.