Factorization of radiative leptonic D-meson decay with sub-leading power corrections * *Supported in part by the National Natural Science Foundation of China (1675082, 11735010), and the Natural Science Foundation of Tianjin (19JCJQJC61100)

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 .