Renormalization of Dijet Operators at Order $1/Q^2$ in Soft-Collinear Effective Theory

TL;DR

This paper advances the resummation of power-suppressed logarithms in dijet event shapes using a novel SCET formalism that simplifies operator analysis at order 1/Q^2, aiding high-precision QCD fits.

Contribution

It introduces a new SCET formalism that identifies and computes anomalous dimensions of operators at order 1/Q^2 without referencing modes or lambda-scaling, reducing the number of subleading operators needed.

Findings

Computed anomalous dimensions for relevant operators.

Extended overlap subtraction to subleading operators.

Formalism simplifies operator structure at order 1/Q^2.

Abstract

We make progress towards resummation of power-suppressed logarithms in dijet event shapes such as thrust, which have the potential to improve high-precision fits for the value of the strong coupling constant. Using a newly developed formalism for Soft-Collinear Effective Theory (SCET), we identify and compute the anomalous dimensions of all the operators that contribute to event shapes at order $1/Q^2$. These anomalous dimensions are necessary to resum power-suppressed logarithms in dijet event shape distributions, although an additional matching step and running of observable-dependent soft functions will be necessary to complete the resummation. In contrast to standard SCET, the new formalism does not make reference to modes or $\lambda$-scaling. Since the formalism does not distinguish between collinear and ultrasoft degrees of freedom at the matching scale, fewer subleading operators are required when compared to recent similar work. We demonstrate how the overlap subtraction prescription extends to these subleading operators.