|Vcb||Vcb| from the semileptonic decay B→Dℓν¯ℓ and the properties of the D-meson distribution amplitude

The improved QCD light-cone sum rule (LCSR) provides an effective way to deal with the heavy-to-light transition form factors (TFFs). Firstly, we adopt the improved LCSR approach to deal with the B→DB→D TFF f+(q2)f+(q2) up to twist-4 accuracy. Due to the elimination of the most uncertain twist-3 contribution and the large suppression of the twist-4 contribution, the obtained LCSR shall provide us a good platform for testing the D-meson leading-twist DA. For the purpose, we suggest a new model for the D  -meson leading-twist DA (ϕ3Dϕ3D), whose longitudinal behavior is dominantly determined by a parameter B  . Moreover, we find its second Gegenbauer moment a2D∼B. Varying B within certain region, one can conveniently mimic the D-meson DA behavior suggested in the literature. Inversely, by comparing the estimations with the experimental data on the D-meson involved processes, one can get a possible range for the parameter B and a determined behavior for the D  -meson DA. Secondly, we discuss the B→DB→D TFF at the maximum recoil region and present a detailed comparison of it with the pQCD estimation and the experimental measurements. Thirdly, by applying the LCSR on f+(q2)f+(q2), we study the CKM matrix element |Vcb||Vcb| together with its uncertainties by adopting two types of processes, i.e. the B0/B¯0-type and the B±B±-type. It is noted that a smaller B≾0.20B≾0.20 shows a better agreement with the experimental value on |Vcb||Vcb|. For example, for the case of B=0.00B=0.00, we obtain |Vcb|(B0/B¯0−type)=(41.28−4.82+5.68−1.16+1.13)×10−3 and |Vcb|(B±−type)=(40.44−4.72+5.56 −1.00+0.98)×10−3, whose first (second) uncertainty comes from the squared average of the mentioned theoretical (experimental) uncertainties.