Next-to-next-to-leading logarithmic threshold resummation for deep-inelastic scattering and the Drell–Yan process

The soft-gluon resummation exponents GN in moment space are investigated for the quark coefficient functions in deep-inelastic structure functions and the quark–antiquark contribution to the Drell–Yan cross section dσ/dM. Employing results from two- and three-loop calculations we obtain the next-to-next-to-leading logarithmic terms αs(αs lnN)n of GN to all orders in the strong coupling constant αs. These new contributions facilitate a reliable assessment of the numerical effect and the stability of the large-N expansion.