Factorization and momentum-space resummation in deep-inelastic scattering

Renormalization-group methods in soft-collinear effective theory are used toperform the resummation of large perturbative logarithms for deep-inelasticscattering in the threshold region x->1. The factorization theorem for thestructure function F_2(x,Q^2) for x->1 is rederived in the effective theory,whereby contributions from the hard scale Q^2 and the jet scale Q^2(1-x) areencoded in Wilson coefficients of effective-theory operators. Resummation isachieved by solving the evolution equations for these operators. Simpleanalytic results for the resummed expressions are obtained directly in momentumspace, and are free of the Landau-pole singularities inherent to thetraditional moment-space results. We show analytically that the two methods arenonetheless equivalent order by order in the perturbative expansion, andperform a numerical comparison up to next-to-next-to-leading order inrenormalization-group improved perturbation theory.Comment: 39 pages, 9 figure