Perturbative QCD fragmentation functions as a model for heavy-quark fragmentation

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 ${\mathit{m}}_{\mathit{b}}$→∞ limit of the perturbative QCD fragmentation functions for b¯ into ${\mathit{B}}_{\mathit{c}}$ and ${\mathit{B}}_{\mathit{c}}^{\mathrm{*}}$. 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 ${\mathit{P}}_{\mathit{V}}$ 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 ${\mathit{P}}_{\mathit{V}}$ is predicted to vary from about 1/2 at small z to almost 3/4 near z=1.