Resummation of Super-Leading Logarithms

Thomas Becher,Ding Yu Shao,Matthias Neubert

doi:10.1103/physrevlett.127.212002

Abstract

Jet cross sections at high-energy colliders exhibit intricate patterns of logarithmically enhanced higher-order corrections. In particular, so-called nonglobal logarithms emerge from soft radiation emitted off energetic partons inside jets. While this is a single-logarithmic effect at lepton colliders, at hadron colliders phase factors in the amplitudes lead to double-logarithmic corrections starting at four-loop order. Thiseffect was discovered a long time ago, but not much is known about the higher-order behavior of these terms and their process dependence. We derive, for the first time, the all-order structure of these "super-leading logarithms" for generic 2→l scattering processes at hadron colliders and resum them in closed form.

Highlights

While this is a single-logarithmic effect at lepton colliders, at hadron colliders phase factors in the amplitudes lead to double-logarithmic corrections starting at four-loop order
If the radiation in a high-energy scattering process is restricted by experimental cuts, higher-order terms in the perturbative series are enhanced by large logarithms associated with soft and collinear emissions
The effect is absent in the large-Nc limit and not captured by any of the existing parton showers, which do not account for the leading-logarithmic corrections to nonglobal observables at hadron colliders

Summary

Published by the American Physical Society

We compute the cross section in Eq (1) using the lowest-order expression for Wm at the low scale μs ∼ Q0 At this order the soft Wilson lines are trivial and the collinear matrix elements reduce to the usual parton distribution functions, i.e., Wmðfng; Q0; x1; x2; μsÞ 1⁄4 fa ðx1Þfa ðx2Þ1: ð4Þ where Etot and p⃗ tot are the total energy and momentum of the final-state particles in the partonic center-of-mass frame. The low-energy matrix elements Wm consist of squared matrix elements of m soft Wilson lines for the incoming and outgoing partons together with two collinear fields for the incoming particles. The second part, ΓS, contains soft as well as soft þ collinear terms This part is absent for inclusive cross sections, but present in our case because of the restrictions on hard radiation in the veto region.

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