In this paper, we present a set of charmed-meson $D^{*}$ at next-to-leading order (NLO) and, for the first time, at next-to-next-to-leading order (NNLO) accuracy.
This new sets of charmed-meson $D^{*}$ FFs are obtained through global QCD fits to all relevant data sets from single-inclusive $e^{+}e^{-}$ annihilation.
The ``Hessian approach'' are applied for the determination of FFs uncertainties as well as the corresponding observables.
We compared the resulting $D^{*}$ FFs with the results in the litrature. The theory predition using the extracted FFs are also compared with the available data sets for single-inclusive $D^{*\pm}$-meson production in electron-positron annihilation.