Eur. Phys. J. C (1998) 1: 301-320
https://doi.org/10.1007/BF01245820

Charm electroproduction viewed in the variable-flavour number scheme versus fixed-order perturbation theory

¹ NIKHEF/UVA, POB 41882, NL-1009, DB Amsterdam, The Netherlands
² Institute for Theoretical Physics, State University of New York at Stony Brook, 11794-3840, New York, USA
³ Deutsches Electronen-Synchrotron DESY Notkestrasse 85, D-22603, Hamburg, Germany
⁴ Instituut-Lorentz, University of Leiden, PO Box 9506, NL-2300, RA Leiden, The Netherlands

Received: 9 April 1997
Published online: 27 February 2005

Abstract

Starting from fixed-order perturbation theory (FOPT) we derive expressions for the heavy-flavour components of the deep-inelastic structure functions (F _i,H (x, Q ², m_H ²),i = 2, L; H = c, b, t) in the variable-flavour number scheme (VFNS). These expressions are valid in all orders of perturbation theory. This derivation establishes a relation between the parton densities parametrized atn _f andn _f + 1 light flavours. One of the results is that the heavy quark parton density does not vanish when the factorization scale becomes equal tom _H contrary to what is assumed in the literature. Further we observe that in charm electroproduction the exact and asymptotic expressions for the heavy-quark coefficient functions yield identical results forF _2,c(ξ, Q², m_c ²) whenx < 0.01 andQ ² > 20 (GeV/c)². From this observation an analysis of the size of the higher order corrections we conclude that in this region the VFNS description and ofF _2,c is better than the one given by FOPT. On the other hand in the charm threshold region i.e.x > 0.01 andQ ² < 20 (GeV/c)² it turns out that the reverse is true.