The $B\to D^{(\ast )}l{\nu }_l$ decays in the pQCD approach with the Lattice QCD input

Abstract

In this paper, we studied the semileptonic decays $B\to D^{(\ast )}{l}^{-}{\bar{\nu }}_l$ by using the "pQCD+Lattice QCD" method. We made the extrapolation for the six relevant form factors by using the input values obtained from the pQCD factorization approach in the low $q^2$ region of $0\le q^2\le m_{\tau }^2$, and the Lattice QCD input at the end-point $q^2=q_{\max }^2$. We then calculated the ratios $R(D)$ and $R(D^{\ast })$ of the branching ratios $\mathcal{B}(B\to D^{(\ast )}{l}^{-}{\bar{\nu }}_l)$, and found numerically that (1) the "pQCD+Lattice QCD" predictions for the branching ratios $\mathcal{B}(B\to D^{(\ast )}{l}^{-}{\bar{\nu }}_l)$ agree well with the measured values within one standard deviation, and (2) the "pQCD+Lattice QCD" predictions for the ratios $R(D^{(\ast )})$ are $R(D)=0.337_{-0.037}^{+0.038}$ and $R(D^{\ast })=0.269_{-0.020}^{+0.021}$, they agree with the data within $2\sigma$ deviation, in other words, one can explain the "$R(D^{(\ast )})$-puzzle" in the framework of the standard model.

Comments: 11 pages, 3 ps figures. Add a new figure and more discussions