Higher-order corrections in threshold resummation

Abstract

We extend the threshold resummation exponents G N in Mellin-N space to the fourth logarithmic (N 3 LL) order collecting the terms α 2 s (α s ln N) n to all orders in the strong coupling constant α s . Comparing the results to our previous three-loop calculations for deep-inelastic scattering (DIS), we derive the universal coefficients B q and B g governing the final-state jet functions to order α 3 s , 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 N 3 LL corrections using both the fully exponentiated form and the expansion of the coefficient function in towers of logarithms.

Refining threshold resummations

“…In fact, the only missing contribution in order to resum exactly to that accuracy is the four-loop cusp anomalous dimension γ (4) K , which in principle lies close the current boundaries of computability. In any case it can be convincingly shown [26] that γ (4) K makes a numerically negligible contribution to the cross section. Having at our disposal, with a good approximation, four towers of logarithms for both DIS and EW annihilation, we can stringently test the level of convergence of the perturbative expansion, both with and without resummation.…”

On higher-order flavour-singlet splitting and coefficient functions at large x

“…For DIS structure functions (and some other semi-leptonic processes) this resummation is known at the next-to-next-to-nextto-leading logarithmic accuracy, i.e., the highest six logs are completely known to all orders [16]. No resummation has been derived so far for the off-diagonal (flavour-singlet) coefficient functions such as C 2,g and C φ,q which are of the form…”

Third-order QCD corrections to the charged-current structure function

“…For the same reason we use the same quark distribution at all orders of Eq. An estimate of the large-x fourth-order coefficient function by the seven +-distributions fixed the next-to-next-to-next-to-leading logarithmic soft-gluon (threshold) resummation [57] strongly suggests that this trend will continue at even higher orders. As shown in the right part of Fig.…”