1-loop matching and NNLL resummation for all partonic 2 to 2 processes in QCD

TL;DR

This paper computes 1-loop Wilson coefficients and 2-loop anomalous dimensions for all partonic 2-to-2 processes in QCD, enabling precise resummation of dijet observables at NNLL accuracy in SCET.

Contribution

It provides the first complete calculation of Wilson coefficients and anomalous dimensions for all 4-parton operators in QCD matching to SCET, facilitating advanced resummation techniques.

Findings

Wilson coefficients computed at 1-loop for all 4-parton operators

Anomalous dimensions provided at 2-loop order for RG evolution

Framework established for NNLL resummation of dijet observables

Abstract

The Wilson Coefficients for all 4-parton operators which arise in matching QCD to Soft-Collinear Effective Theory (SCET) are computed at 1-loop. Any dijet observable calculated in SCET beyond leading order will require these results. The Wilson coefficients are separated by spin and color, although most applications will involve only the spin-averaged hard functions. The anomalous dimensions for the Wilson coefficients are given to 2-loop order, and the renormalization group equations are solved explicitly. This will allow for analytical resummation of dijet observables to next-to-next-to-leading logarithmic accuracy. For each channel, there is a natural basis in which the evolution is diagonal in color space. The same basis also diagonalizes the color evolution for the soft function. Even though soft functions required for SCET calculations are observable dependent, it is shown that their renormalization group evolution is almost completely determined by a universal structure. With these results, it will be possible to calculate hadronic event shapes or other dijet observables to next-to-leading order with next-to-next-to-leading log resummation.