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

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• Electroweak interaction
• Particle decays
• Quark model
• Form factors