Uncertainties of the B → D transition form factor from the D-meson leading-twist distribution amplitude

The B → D transition form factor (TFF) f₊^B→D(q²) is determined mainly by the D-meson leading-twist distribution amplitude (DA), φ_2;D, if the proper chiral current correlation function is adopted within the light-cone QCD sum rules. It is therefore significant to make a comprehensive study of DA φ_2;D and its impact on f₊^B→D(q²). In this paper, we calculate the moments of φ_2;D with the QCD sum rules under the framework of the background field theory. New sum rules for the leading-twist DA moments left angle ξⁿ right angle _D up to fourth order and up to dimension-six condensates are presented. At the scale μ = 2 GeV, the values of the first four moments are: left angle ξ¹ right angle _D = -0.418^+0.021_-0.022, left angle ξ² right angle _D = 0.289^+0.023_-0.022, left angle ξ³ right angle _D = -0.178 ± 0.010 and left angle ξ⁴ right angle _D = 0.142^+0.013_-0.012. Basing on the values of left angle ξⁿ right angle _D (n = 1, 2, 3, 4), a better model of φ_2;D is constructed. Applying this model for the TFF f₊^B→D(q²) under the light cone sum rules, we obtain f₊^B→D(0) = 0.673^+0.038_-0.041 and f₊^B→D(q²_max) = 1.117^+0.051_-0.054. The uncertainty of f₊^B→D(q²) from φ_2;D is estimated and we find its impact should be taken into account, especially in low and central energy region. The branching ratio B(B → Dl anti ν_l) is calculated, which is consistent with experimental data. (orig.)