A new parton fragmentation procedure for heavy hadron production in proton-proton collisions

We propose a new procedure for parton-to-hadron fragmentation in proton-proton collisions. The hadronization is considered in the parton-parton center-of-mass system and hadrons are assumed to be emitted in the direction of outgoing partons in that frame and then their four-momenta are transformed to the overall center-of-mass system using relevant Lorentz transformations and appropriate distributions are constructed. For heavy hadron production the energy-momentum condition is imposed. In many cases our procedure disagrees with the commonly used rule that rapidity of produced hadron is the same as rapidity of the parent parton. We illustrate the newly proposed scheme for production of $D$ mesons, $\Lambda_c$ baryon and $\eta_c$ quarkonium in leading-order approach to parton production. The transverse momentum, rapidity and Feynman-$x_F$ distributions are shown. We consider $c \to D$ and $g \to D$ as well as $c \to \eta_c$ and $g \to \eta_c$ hadronization processes. The resulting rapidity distributions are much narrower than those obtained in the traditional approach with parton-hadron rapidity equivalence. This has consequences both for mid- and forward rapidities and could have consequences for high-energy neutrino production in the Earth's atmosphere. We discuss also $c \to \Lambda_c^+$ and $b \to \Lambda_c^+$ fragmentation and find that the second mechanism could be partly responsible for the enhanced production of $\Lambda_c^{\pm}$ observed recently by the ALICE collaboration.