|Vcb| from the semileptonic decay B → Dl(vl) over bar 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 -> D TFF f(+) (q(2)) 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 (phi(3D)), whose longitudinal behavior is dominantly determined by a parameter B. Moreover, we find its second Gegenbauer moment a(2)(D) similar to 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 -> 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(+) (q(2)), we study the CKM matrix element vertical bar V-cb vertical bar together with its uncertainties by adopting two types of processes, i.e. the B-0 / B-0-type and the B-+/--type. It is noted that a smaller B less than or similar to 0.20 shows a better agreement with the experimental value on vertical bar V-cb vertical bar. For example, for the case of B = 0.00, we obtain vertical bar V-cb vertical bar (B-0 / B-0 - type) = (41.28(-4.82-1.16)(+5.68+1.13)) x 10(-3) and vertical bar V-cb vertical bar (B-+/- - type) = (40.44(-4.72 -1.00)(+5.56 +0.98)) x 10(-3), whose first (second) uncertainty comes from the squared average of the mentioned theoretical (experimental) uncertainties.