$D^*$ jet fragmentation function paradox and combination mechanism


 In the framework of the perturbative Quantum Chromodynamics factorization, the production of a hadron includes contributions from fragmentation as well as combination, with the latter is of higher twist. In particular, the heavy meson production can be via the combination of a heavy quark with a light one, and the cross section can be factorized to be the convolution of the combination matrix element, the light quark distribution function, and the hard partonic sub-cross section of the heavy quark production. The partonic distribution and the combination matrix element are functions of a scaling variable, respectively, which is the momentum fraction of the corresponding quark with respect to the heavy meson. We studied the $D^{*\pm}$ production in jet via combination in pp collision at the LHC. The total result is comparable with the experimental data. The combination matrix elements can be further studied in various hadron production processes.