First Subleading Power Resummation for Event Shapes

TL;DR

This paper develops a systematic method for resumming logarithms at subleading power in event shape observables, providing analytic results and field theory definitions, with applications to thrust spectrum in gluon jets.

Contribution

It introduces a novel framework for subleading power resummation using RG equations and universal jet and soft functions, extending the understanding of power corrections in collider physics.

Findings

Derived and solved RG equations for subleading power operators

Obtained analytic leading logarithmic results for thrust spectrum in gluon jets

Established the exponentiation of higher order corrections at subleading power

Abstract

We derive and analytically solve renormalization group (RG) equations of gauge invariant non-local Wilson line operators which resum logarithms for event shape observables $\tau$ at subleading power in the $\tau\ll 1$ expansion. These equations involve a class of universal jet and soft functions arising through operator mixing, which we call $\theta$-jet and $\theta$-soft functions. An illustrative example involving these operators is introduced which captures the generic features of subleading power resummation, allowing us to derive the structure of the RG to all orders in $\alpha_s$, and provide field theory definitions of all ingredients. As a simple application, we use this to obtain an analytic leading logarithmic result for the subleading power resummed thrust spectrum for $H\to gg$ in pure glue QCD. This resummation determines the nature of the double logarithmic series at subleading power, which we find is still governed by the cusp anomalous dimension. We check our result by performing an analytic calculation up to ${\cal O}(\alpha_s^3)$. Consistency of the subleading power RG relates subleading power anomalous dimensions, constrains the form of the $\theta$-soft and $\theta$-jet functions, and implies an exponentiation of higher order loop corrections in the subleading power collinear limit. Our results provide a path for carrying out systematic resummation at subleading power for collider observables.