Calculation of branching fraction and $CP$ violation in $B^-\rightarrow D_s^-D^0$ decay

TL;DR

This paper calculates the $CP$ violation and branching ratio in the decay $B^- ightarrow D_s^-D^0$ using a theoretical factorization approach, providing results consistent with experimental measurements.

Contribution

The study introduces a detailed calculation of $CP$ violation considering both tree and penguin diagrams with phase considerations, advancing theoretical understanding of this decay mode.

Findings

Calculated $CP$ asymmetry of (-0.35±0.03)% consistent with experimental data.

Estimated total amplitude yields a branching ratio matching observed values.

Provided a comprehensive theoretical framework for analyzing $CP$ violation in this decay.

Abstract

The most precise measurement of the $CP$ asymmetry in the decay $B^-\rightarrow D_s^-D^0$ has been reported by LHCb collaboration with the value of $(-0.4\pm0.5\pm0.5)\%$. In this study, the $CP$ violation in the decay $B^-\rightarrow D_s^-D^0$ has been calculated under the factorization approach. This decay mode includes current-current tree and penguin diagrams and their amplitudes are considered separately. In each of the tree and penguin amplitudes, the strong and weak phases have been introduced. The $CP$ asymmetry has been calculated in this work to be $(-0.35\pm0.03)\%$. Finally, from the sum of the amplitudes, we have calculated the total amplitude and obtained comparable results with experimental value for the branching ratio of $B^-\rightarrow D_s^-D^0$ decay.