Left-right mixing on leptonic and semileptonic $b\to u$ decays

It has been known that there exists a disagreement emerged between the determination of $|V_{ub}|$ from inclusive $B \to X_u\ell\nu$ decays and exclusive $B \to \pi\ell\nu$ decays. In order to solve the mismatch, we investigate the left-right (LR) mixing effects, denoted by $\xi_u$, in leptonic and semileptonic $b \to u$ decays. We find that the new interactions $(V+A)\times (V-A)$ induced via the LR mixing can explain the mismatch between the values of $|V_{ub}|$ if Re$(\xi_{u})=-(0.14 \pm 0.12)$. Furthermore, we also find that the LR mixing effects can enhance the branching fractions for $B \to \tau\nu$ and $B \to \rho\ell\nu$ decays by 30% and 17%, respectively, while reducing the branching fraction for $B \to \gamma\ell\nu$ decays by 18%.