Charm and strange meson fragmentation functions

TL;DR

This paper develops a comprehensive model for quark fragmentation functions, including light and heavy mesons, using covariant wave functions and coupled jet equations, providing a unified description of the hadronization process.

Contribution

It introduces a novel set of coupled jet equations derived from covariant Bethe-Salpeter wave functions to compute fragmentation functions for multiple meson types.

Findings

Consistent fragmentation functions for pions, kaons, D, and D_s mesons.

Unified description across light and heavy meson sectors.

Solution of twenty-five coupled jet equations.

Abstract

Quark fragmentation functions describe the hadronization process of a quark where any of the final-state hadrons carries a fraction of its initial momentum. We compute these fragmentation functions for a cascade that includes pions, kaons, and the charmed $D$ and $D_s$ mesons, starting from the elementary quark-to-meson fragmentation process. The latter is obtained from the relevant cut diagram, and employs Poincar\'e covariant Bethe-Salpeter wave functions and quark propagators. We derive a set of twenty-five coupled jet equations that describe the cascade of emitted mesons in the fragmentation process. Their solutions yield full fragmentation functions that offer a consistent picture of the quark fragmentations across the light and heavy sectors.