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

## TL;DR

This paper critically examines how quark and antiquark fragmentation into massive particles occurs in proton-proton collisions, comparing different definitions of the fragmentation variable and their effects at various energies, especially at the LHC.

## Contribution

It introduces a comprehensive comparison of various fragmentation schemes and their impact on D-meson production, highlighting the conditions under which these schemes converge or differ.

## Key findings

- All schemes agree for D-meson transverse momenta above 2 GeV at LHC energies.
- Emission direction relative to the parent quark affects D-meson rapidity distributions.
- Different prescriptions significantly impact low-energy fixed target experiment results.

## Abstract

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).