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

Starting from fixed-order perturbation theory (FOPT) we derive expressions for the heavy-flavour flavour components of the deep-inelastic structure functions (F-i,(H)(x, Q(2), m(H)(2)), i = 2,w 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 at nf and nf fl light flavours. One of the results is that the heavy quark parton density does not vanish when the factorization scale becomes equal to m(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 for F-2,F-c(x, Q(2), m(c)(2)) when x < 0.01 and Q(2) > 20 (GeV/c)(2). From this observation and an analysis of the size of the higher order corrections we conclude that in this region the VFNS description of F-2,F-c is better than the one given by FOPT. On the other hand in the charm threshold region i.e. x > 0.01 and Q(2) < 20 (GeV/c)(2) it turns out that the reverse is true.