In this paper we study the semileptonic decays of B + c → D(s) (l + ν l , l + l − , νν) (here l stands for e, µ, or τ ). After evaluating the B + c → (D (s) , D * (s) ) transition form factors F 0,+,T (q 2 ) and V (q 2 ), A 0,1,2 (q 2 ), T 1,2,3 (q 2 ) by employing the perturbative QCD factorization approach, we calculate the branching ratios for all these semileptonic decays. Our predictions for the values of the B + c → D (s) and B + c → D * (s) transition form factors are consistent with those obtained by using other methods. The branching ratios of the decay modes withνν are almost an order of magnitude larger than the corresponding decays with l + l − after the summation over the three neutrino generations. The branching ratios for the decays with b → d transitions are much smaller than those decays with the b → s transitions, due to the Cabibbo-Kobayashi-Maskawa suppression. We define ratios R D and R D * for the branching ratios with the τ lepton versus µ, e lepton final states to cancel the uncertainties of the form factors, which could possibly be tested in the near future.

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In this paper, we calculate the next-to-leading-order (NLO) twist-3 contribution to the form factors of B → π transitions by employing the k T factorization theorem. All the infrared divergences regulated by the logarithms ln(k 2 iT ) cancel between those from the quark diagrams and from the effective diagrams for the initial B meson wave function and the final pion meson wave function. An infrared finite NLO hard kernel is therefore obtained, which confirms the application of the k T factorization theorem to B meson semileptonic decays at twist-3 level. From our analytical and numerical evaluations, we find that the NLO twist-3 contributions to the form factors f +,0 (q 2 ) of B → π transition are similar in size, but have an opposite sign with the NLO twist-2 contribution, which leads to a large cancelation between these two NLO parts. For the case of f + (0), for example, the 24% NLO twist-2 enhancement to the full LO prediction is largely canceled by the negative ( about −17% ) NLO twist-3 contribution, leaving a small and stable 7% enhancement to the full LO prediction in the whole range of 0 ≤ q 2 ≤ 12 GeV 2 . At the full NLO level, the perturbative QCD prediction is F B→π (0) = 0.269 +0.054 −0.050 . We also studied the possible effects on the pQCD predictions when different sets of the B meson and pion distribution amplitudes are used in the numerical evaluation.

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