Higher-order corrections in threshold resummation

We extend the threshold resummation exponents GN in Mellin-N space to the fourth logarithmic (N3LL) order collecting the terms αs2(αslnN)n to all orders in the strong coupling constant αs. Comparing the results to our previous three-loop calculations for deep-inelastic scattering (DIS), we derive the universal coefficients Bq and Bg governing the final-state jet functions to order αs3, extending the previous quark and gluon results by one and two orders. A curious relation is found at second order between these quantities, the splitting functions and the large-angle soft emissions in Drell-Yan type processes. We study the numerical effect of the N3LL corrections using both the fully exponentiated form and the expansion of the coefficient function in towers of logarithms.