Higher-Order Corrections in Threshold Resummation
Moch, S. · Vermaseren, J. A. M. · Vogt, A.
Original · EN
We extend the threshold resummation exponents Gⁿ in Mellin-N space to the fourth logarithmic (N³LL) order collecting the terms alphaₛ² (alphaₛ ln N)ⁿ to all orders in the strong coupling constant as. 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 alphaₛ³, 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.
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