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

Abstract

The Brightarrow D transition form factor (TFF) f^{Brightarrow D}_+(q^2) is determined mainly by the D-meson leading-twist distribution amplitude (DA) , phi _{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 phi _{2;D} and its impact on f^{Brightarrow D}_+(q^2). In this paper, we calculate the moments of phi _{2;D} with the QCD sum rules under the framework of the background field theory. New sum rules for the leading-twist DA moments leftlangle xi ^nrightrangle _D up to fourth order and up to dimension-six condensates are presented. At the scale mu = 2 ,mathrm{GeV}, the values of the first four moments are: leftlangle xi ^1rightrangle _D = -0.418^{+0.021}_{-0.022}, leftlangle xi ^2rightrangle _D = 0.289^{+0.023}_{-0.022}, leftlangle xi ^3rightrangle _D = -0.178 pm 0.010 and leftlangle xi ^4rightrangle _D = 0.142^{+0.013}_{-0.012}. Basing on the values of leftlangle xi ^nrightrangle _D(n=1,2,3,4), a better model of phi _{2;D} is constructed. Applying this model for the TFF f^{Brightarrow D}_+(q^2) under the light cone sum rules, we obtain f^{Brightarrow D}_+(0) = 0.673^{+0.038}_{-0.041} and f^{Brightarrow D}_+(q^2_{mathrm{max}}) = 1.117^{+0.051}_{-0.054}. The uncertainty of f^{Brightarrow D}_+(q^2) from phi _{2;D} is estimated and we find its impact should be taken into account, especially in low and central energy region. The branching ratio mathcal {B}(Brightarrow Dlbar{nu }_l) is calculated, which is consistent with experimental data.