Resummation of electroweak Sudakov logarithms for real radiation

TL;DR

This paper derives analytic expressions for resummed real radiation in electroweak processes, demonstrating that including these corrections significantly impacts predictions at high-energy colliders like the 100 TeV proton-proton collider.

Contribution

It provides the first analytic resummation formulas for real electroweak radiation integrated over phase space, highlighting their importance at multi-TeV energies.

Findings

Resummation of real corrections is as important as virtual corrections.

Resummation effects are sizable at energies above a few TeV.

At 10 TeV and higher, resummation significantly alters cross-section estimates.

Abstract

Using the known resummation of virtual corrections together with knowledge of the leading-log structure of real radiation in a parton shower, we derive analytic expressions for the resummed real radiation after they have been integrated over all of phase space. Performing a numerical analysis for both the 13 TeV LHC and a 100 TeV $pp$ collider, we show that resummation of the real corrections is at least as important as resummation of the virtual corrections, and that this resummation has a sizable effect for partonic center of mass energies exceeding $\sqrt{s} = {\cal O}$(few TeV). For partonic center of mass energies $\sqrt{s} \gtrsim$ 10 TeV, which can be reached at a 100 TeV collider, resummation becomes an O(1) effect and needs to be included even for rough estimates of the cross-sections.