Employing Helicity Amplitudes for Resummation
Ian Moult, Iain W. Stewart, Frank J. Tackmann, Wouter J. Waalewijn
TL;DR
This work develops a helicity-based SCET framework that directly ties hard SCET Wilson coefficients to color-ordered QCD helicity amplitudes, enabling straightforward resummation combined with fixed-order results for high-multiplicity jet processes. By constructing a helicity operator basis and a complete color basis, the authors derive explicit matching coefficients for Higgs and vector-boson production with up to three jets, illustrating crossing symmetry and scheme conversions. They also derive the all-orders RG evolution structure, including one-loop anomalous dimensions and explicit color-mspace mixing matrices, and discuss soft-function evolution within nonorthogonal color bases. The approach simplifies the integration of analytic resummation into fixed-order amplitude calculations and provides a versatile, crossing-symmetric toolkit applicable to a wide range of collider processes. Collectively, this framework facilitates precision predictions for exclusive jet observables at the LHC by uniting helicity amplitudes with SCET factorization and RG evolution.
Abstract
Many state-of-the-art QCD calculations for multileg processes use helicity amplitudes as their fundamental ingredients. We construct a simple and easy-to-use helicity operator basis in soft-collinear effective theory (SCET), for which the hard Wilson coefficients from matching QCD onto SCET are directly given in terms of color-ordered helicity amplitudes. Using this basis allows one to seamlessly combine fixed-order helicity amplitudes at any order they are known with a resummation of higher-order logarithmic corrections. In particular, the virtual loop amplitudes can be employed in factorization theorems to make predictions for exclusive jet cross sections without the use of numerical subtraction schemes to handle real-virtual infrared cancellations. We also discuss matching onto SCET in renormalization schemes with helicities in $4$- and $d$-dimensions. To demonstrate that our helicity operator basis is easy to use, we provide an explicit construction of the operator basis, as well as results for the hard matching coefficients, for $pp\to H + 0,1,2$ jets, $pp\to W/Z/γ+ 0,1,2$ jets, and $pp\to 2,3$ jets. These operator bases are completely crossing symmetric, so the results can easily be applied to processes with $e^+e^-$ and $e^-p$ collisions.