An improved description of charm fragmentation data

Abstract We consider the fragmentation of heavy quarks into heavy-flavoured hadrons, specifically the production of charmed mesons in $$e^+e^-$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mi>e</mml:mi> <mml:mo>+</mml:mo> </mml:msup> <mml:msup> <mml:mi>e</mml:mi> <mml:mo>-</mml:mo> </mml:msup> </mml:mrow> </mml:math> collisions, at different centre-of-mass energies. We focus our attention on the ratio of moments of the $$D^{*+}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mi>D</mml:mi> <mml:mrow/> <mml:mrow> <mml:mrow/> <mml:mo>∗</mml:mo> <mml:mo>+</mml:mo> </mml:mrow> </mml:mmultiscripts> </mml:math> energy spectrum measured by ALEPH and CLEO. This ratio is believed to provide us with a direct test of perturbative QCD evolution because hadronisation effects should cancel between the numerator and denominator. However, state-of-the-art calculations based on standard (final-state) collinear factorisation fail to describe the experimental data. We show that this discrepancy is considerably reduced if heavy-quark threshold effects are accounted for not only in DGLAP evolution, as it is usually done, but also in the resummed coefficient functions.