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Independent quark/antiquark fragmentation to massive particles in proton-proton collisions

We critically discuss fragmentation of quark or antiquark to massive particles (mesons or baryons) in proton-proton collisions. Both heavy and light quark/antiquark fragmentations are discussed using universal $z$-dependent fragmentation functions. Different scenarios how to define the $z$ variable are considered: as a fraction of energy, momentum or light-cone momentum of the parent quark/antiquark. Also a choice of the direction of motion of hadron with respect to the parent parton must be made in the simplest approach. Energy and flavour violation is discussed for the region of small $p_t$ and/or center-of-mass $y \sim$ 0. Results of different approaches are compared. We show that at the LHC energies all schemes become consistent for $D$-meson transverse momenta larger than $2$ GeV. Relations to results from the literature are made. We present some examples for production of D mesons from light and charm quarks/antiquarks. Emission with respect to the direction of motion lowers the cross section of $D$ mesons at larger rapidities compared to the traditional approach ($y_D = y_{q/\bar q}$). As illustrated here the effect of using different prescriptions is particularly large at low energies (fixed target experiments).