M. Buza et al., CHARM ELECTROPRODUCTION VIEWED IN THE VARIABLE-FLAVOR NUMBER SCHEME VERSUS FIXED-ORDER PERTURBATION-THEORY, EUROPEAN PHYSICAL JOURNAL C-PARTICLES AND FIELDS, 1(1-2), 1998, pp. 301-320
Starting from fixed-order perturbation theory (FOPT) we derive express
ions for the heavy-flavour flavour components of the deep-inelastic st
ructure 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 r
elation between the parton densities parametrized at nf and nf fl ligh
t flavours. One of the results is that the heavy quark parton density
does not vanish when the factorization scale becomes equal to m(H) con
trary 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 ob
servation 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 bet
ter than the one given by FOPT. On the other hand in the charm thresho
ld region i.e. x > 0.01 and Q(2) < 20 (GeV/c)(2) it turns out that the
reverse is true.