Right-handed current with $CP$ violation in the $b\to u$ transition

Abstract

We show that the experimental data on $|V_{ub}|$ in various $B$ meson decay modes suggest a possibility of $CP$-violating right-handed current in the $b\to u$ transition. Its consequences in $B\to \pi \pi ,\rho \rho ,DK$ are examined and compared with experimental results in order to clarify possible signals of the $CP$ violation in these decay modes. As a result, we find that the $CP$-violating right-handed current is consistent with current experimental data. Its signal might be discovered by precise $CP$ measurements in future experiments.

Comments: 26 pages, 8 figures, a reference added