Subleading Corrections To Thrust Using Effective Field Theory
Simon M. Freedman
TL;DR
The paper tackles subleading corrections to the thrust rate within Soft-Collinear Effective Theory (SCET) by systematically matching QCD currents and thrust measurement operators onto SCET dijet and measurement operators, ensuring explicit decoupling of the n-collinear, \bar{n}-collinear, and soft sectors. The authors show how the O(α_s τ) rate can be factorized into a hard function times convolutions of jet and soft operator matrix elements, employing a hierarchy of subleading dijet and measurement operators and a consistent λ-power expansion. They reproduce the known perturbative QCD results at O(α_s τ) and provide a framework to extend the approach to other jet shapes, with explicit operator bases and matching coefficients laid out. The methodology enables separate renormalization of jet and soft sectors and generalizes beyond thrust to a range of jet observables, paving the way for higher-order subleading corrections.
Abstract
We calculate the subleading corrections to the thrust rate using Soft-Collinear Effective Theory to factorize the rate and match onto jet and soft operators that describe the degrees of freedom of the relevant scales. We work in the perturbative regime where all the scales are well above Λ_QCD. The thrust rate involves an incomplete sum over final states that is enforced by a measurement operator. Subleading corrections require matching onto not only the higher dimensional dijet operators, but also matching onto subleading measurement operators in the effective theory. We explicitly show how to factorize the O(α_s τ) thrust rate into a hard function multiplied by the convolution of the vacuum expectation value of jet and soft operators. Our approach can be generalized to other jet shapes and rates.