D^0, D^+, D_s^+, and Lambda_c^+ Fragmentation Functions from CERN LEP1
Bernd A. Kniehl, Gustav Kramer
TL;DR
The paper derives nonperturbative fragmentation functions for D^0, D^+, D_s^+, and Λ_c^+ by fitting OPAL LEP1 e^+e^− data within a nf=5 MSbar massless framework at LO and NLO, using a Peterson form for charm FFs and a flexible bottom FF. It demonstrates DGLAP-driven scaling violations and tests the universality of these FFs by comparing to lower-energy e^+e^− data, finding reasonable agreement overall, though the Λ_c^+ spectrum is challenging at NLO. The study highlights the scheme dependence of the charm ε parameter and the limitations of the massless approximation at small x (x ≈ 0.1), suggesting that a GM-VFN global analysis including finite-mass effects would be a valuable future direction. Overall, the work provides a set of heavy-flavor fragmentation inputs consistent with multiple experiments and scalable to other high-energy processes.
Abstract
We present new sets of nonperturbative fragmentation functions for D^0, D^+, and D_s^+ mesons as well as for Lambda_c^+ baryons, both at leading and next-to-leading order in the MSbar factorization scheme with five massless quark flavors. They are determined by fitting data of e^+e^- annihilation taken by the OPAL Collaboration at CERN LEP1. We take the charm-quark fragmentation function to be of the form proposed by Peterson et al. and thus obtain new values of the epsilon_c parameter, which are specific for our choice of factorization scheme.