Using hadron-in-jet data in a global analysis of $D^{*}$ fragmentation functions

We present a novel global QCD analysis of charged $D^{*}$-meson fragmentation functions at next-to-leading order accuracy. This is achieved by making use of the available data for single-inclusive $D^{*}$-meson production in electron-positron annihilation, hadron-hadron collisions, and, for the first time, in-jet fragmentation in proton-proton scattering. It is shown how to include all relevant processes efficiently and without approximations within the Mellin moment technique, specifically for the in-jet fragmentation cross section. The presented technical framework is generic and can be straightforwardly applied to future analyses of fragmentation functions for other hadron species, as soon as more in-jet fragmentation data become available. We choose to work within the Zero Mass Variable Flavor Number Scheme which is applicable for sufficiently high energies and transverse momenta. The obtained optimum set of parton-to-$D^{*}$ fragmentation functions is accompanied by Hessian uncertainty sets which allow one to propagate hadronization uncertainties to other processes of interest.