Large-n behavior of the deep-inelastic structure functions and the renormalization- and factorization-scheme dependences.

Abstract

The problem of singular perturbation coefficients for n-italic..-->..infinity that appear in the second-order QCD calculation of the moment of the deep-inelastic structure function F-italic/sub 2//sup n-italic/ is investigated by applying the optimized perturbation theory (OPT). Special emphasis is paid to the connection with the kinematical analysis based on the resummation of singular terms. The main results of the present paper are as follows. (i) The simultaneous application of the generalized two-scale OPT to the factorization- and renormalization-scheme dependences of F-italic/sub 2//sup n-italic/ not only absorbs the most singular ln/sup 2/n terms in the perturbation coefficients into the effective mass scale with which the coupling constant runs, but also sweeps up the less singular lnn-italic terms to end up with a suppressing ''form factor.'' (ii) Applying the single-scale OPT to the renormalization-scheme dependence of the Q-italic/sup 2/ dependence of the structure function R-italic/sub 2//sup n-italic/--d lnF-italic/sub 2//sup n-italic//d lnQ-italic, all the singular terms are completely absorbed into the effective mass scale, leaving the nonsingular perturbation coefficients. The R-italic/sub 2//sup n-italic/ thus optimized and the R-italic/sub 2//sup n-italic/ obtained from the F-italic/sub 2//sup n-italic/ optimized as in (i) are shown to agree remarkably well more than expected formally and also to agreemore » numerically very well. (iii) Results (i) and (ii) agree up to the most singular terms with those obtained through the kinematical analyses of Brodsky and Lepage and of Amati e-italict-italic a-italicl-italic.« less