Abstract
In this work, we calculate the sub-leading power contributions to radiative leptonic decay. For the first time, we provide the analytic expressions of next-to-leading power contributions and the error estimation associated with the power expansion of . In our calculation, we adopt two different models of the D-meson distribution amplitudes and . Within the framework of QCD factorization as well as the dispersion relation, we evaluate the soft contribution up to the next-to-leading logarithmic accuracy and also consider the higher-twist contribution from the two-particle and three-particle distribution amplitudes. Finally, we find that all the sub-leading power contributions are significant at MeV, and the next-to-leading power contributions lead to 143% in and 120% in corrections to leading power vector form factors with GeV. As the corrections from the higher-twist and local sub-leading power contributions are enhanced with increasing inverse moment, it is difficult to extract an appropriate inverse moment of the D-meson distribution amplitude. The predicted branching fractions are for and for .
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