In this paper, we calculate the Brightarrow D transition form factors (TFFs) within the light-cone sum rules (LCSRs) and predict the ratio mathcal {R}(D). More accurate D-meson distribution amplitudes (DAs) are essential to get a more accurate theoretical prediction. We construct a new model for the twist-3 DAs phi ^p_{3;D} and phi ^sigma _{3;D} based on the QCD sum rules under the background field theory for their moments as we have done for constructing the leading-twist DA phi _{2;D}. As an application, we observe that the twist-3 contributions are sizable in whole q^2-region. Taking the twist-2 and twist-3 DAs into consideration, we obtain f^{Brightarrow D}_{+,0}(0) = 0.659^{+0.029}_{-0.032}. As a combination of the Lattice QCD and the QCD LCSR predictions on the TFFs f^{Brightarrow D}_{+,0}(q^2), we predict mathcal {R}(D) = 0.320^{+0.018}_{-0.021}, which is about 1.5sigma deviation from the HFAG average of the Belle and BABAR data. At present the data still have large errors, and we need further accurate measurements of the experiment to confirm whether there is a signal of new physics from the ratio mathcal {R}(D).
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