Perturbative QCD Fragmentation Functions as a Model for Heavy-Quark Fragmentation

TL;DR

The paper develops a HQET-based, perturbative QCD framework to describe heavy-quark fragmentation into heavy-light mesons, deriving leading and 1/m_Q corrections for D_{Q→P} and D_{Q→V} and confirming heavy-quark spin symmetry. It then promotes the PQCD fragmentation functions as a phenomenological model with a small set of scaling parameters, providing explicit z- and k_T-dependent predictions and a gauge-invariant comparison to other models. A key application is the vector-to-pseudoscalar ratio P_V, whose z- and k_T-dependence are predicted and used to extract the light-quark mass parameter r from D-D^* data, with consistent scaling to B mesons. Overall, the PQCD-based approach yields robust, spin-sensitive predictions for heavy-quark fragmentation that align with heavy-quark symmetry and offer practical, testable guidance for experiments.

Abstract

The perturbative QCD fragmentation functions for a heavy quark to fragment into heavy-light mesons are studied in the heavy-quark limit. The fragmentation functions for S-wave pseudoscalar and vector mesons are calculated to next-to-leading order in the heavy-quark mass expansion using the methods of heavy-quark effective theory. The results agree with the $m_b\to \infty$ limit of the perturbative QCD fragmentation functions for $\bar b$ into $B_c$ and $B_c^*$. We discuss the application of the perturbative QCD fragmentation functions as a model for the fragmentation of heavy quarks into heavy-light mesons. Using this model, we predict the fraction $P_{V}$ of heavy-light mesons that are produced in the vector meson state as functions of the longitudinal momentum fraction $z$ and the transverse momentum relative to the jet axis. The fraction $P_V$ is predicted to vary from about 1/2 at small $z$ to almost 3/4 near $z=1$.