Semi-leptonic decays $B\to D^{(\ast )}(1S,2S)\ell {\nu }_{\ell }$ within the covariant light-front approach

Abstract

We present a systematic analysis of the semi-leptonic decays $B_{(s)}\to D_{(s)}(1S,2S)\ell {\nu }_{\ell }$ and $B_{(s)}\to D_{(s)}^{\ast }(1S,2S)\ell {\nu }_{\ell }$ with $\ell =e,\mu ,\tau$ within the covariant light-front quark model (CLFQM). Using the form factors of the transitions $B_{(s)}\to D_{(s)}(1S,2S)$ and $B_{(s)}\to D_{(s)}^{\ast }(1S,2S)$, we calculate the branching ratios of the relevant semi-leptonic decays and find that $Br(B_{(s)}\to D_{(s)}{\ell }^{\prime }{\nu }_{{\ell }^{\prime }})$ and $Br(B_{(s)}\to D_{(s)}^{\ast }{\ell }^{\prime }{\nu }_{{\ell }^{\prime }})$ with ${\ell }^{\prime }=e,\mu$ are agree well with the data, while $Br(B_{(s)}\to D_{(s)}\tau {\nu }_{\tau })$ and $Br(B_{(s)}\to D_{(s)}^{\ast }\tau {\nu }_{\tau })$ are systematically smaller than the experimental measurements. This naturally gives rise to the so-called $\mathcal{R}(D)$ and $\mathcal{R}(D^{\ast })$ anomalies. Our predictions $\mathcal{R}(D)=0.261\pm 0.013$ and $\mathcal{R}(D^{\ast })=0.228\pm 0.026$ show $3.1\sigma$ and $2.1\sigma$ deviations from the current experimental world averages compiled by the Heavy Flavor Averaging Group (HFLAV), respectively, yet only deviate by $0.16\sigma$ and $1.5\sigma$ from the latest LHCb measurements. For the decays $B_{(s)}\to D_{(s)}(2S)\ell {\nu }_{\ell }$ and $B_{(s)}\to D_{(s)}^{\ast }(2S)\ell {\nu }_{\ell }$, their branching ratios lie in the range $10^{-4}\sim 10^{-3}$, which are much larger than the results from the Bethe Salpeter (BS) equation , but agree with the relativistic quark model (RQM) calculations. Furthermore, we also calculate the forward-backward asymmetries ${\mathcal{A}}_{FB}$ and longitudinal polarization fractions $f_L$ for the corresponding decays. Our predictions are consistent with most other theoretical results and experimental data

Comments: 25 pages, 6 figures