Quantum-chromodynamic higher-order contributions to deep-inelastic scaling violations

Nonleading higher-order contributions to the ($x, Q^2$) dependence of scaling violations of nonsinglet as well as singlet structure functions are studied for different renormalization schemes and for various input parton distributions, and are compared with standard leading-order (leading-logarithm) results. Higher-order corrections turn out to be small in the experimentally accessible range of $x$ and $Q^2$; since their theoretical uncertainties are of about the same magnitude as the experimental ones, modifications due to second-order contributions are unlikely to be distinguished from standard leading-logarithm results by present experiments. In addition, we represent the nonleading two-loop nonsinglet as well as singlet splitting functions by simple analytic expressions which will facilitate future detailed ($x, Q^2$) analyses of structure functions.