Grooming at the Cusp: All-Orders Predictions for the Transition Region of Jet Groomers

TL;DR

This paper develops an all-orders theoretical framework to accurately describe the behavior of jet observables near the cusp region in groomed jets, improving understanding of the transition region in jet grooming.

Contribution

It introduces a novel factorization theorem for the cusp region in groomed jets, including contributions from collinear modes crossing hemisphere boundaries and explicit subtraction methods.

Findings

Resummation of the cusp region achieved at next-to-leading logarithmic accuracy.

Identification of collinear modes crossing hemisphere boundaries.

Formulation of an all-orders factorization theorem for the cusp region.

Abstract

Jet grooming has emerged as a necessary and vital tool for mitigating contamination radiation in jets. The additional restrictions on emissions imposed by the groomer can result in non-smooth behavior of resulting fixed-order distributions of observables measured on groomed jets. As a concrete example, we study the cusp in the hemisphere mass distribution of $e^+e^-\to$ hadrons events groomed with soft drop. We identify the leading emissions that contribute in the region about the cusp and formulate an all-orders factorization theorem that describes how the cusp is resolved through arbitrary strongly-ordered soft and collinear emissions. The factorization theorem exhibits numerous novel features such as contributions from collinear modes that can cross hemisphere boundaries as well as requiring explicit subtraction of the limit in which resolved emissions become collinear to the hard core. We present resummation of the cusp region through next-to-leading logarithmic accuracy and describe how it can be matched with established factorization theorems that describe other groomed phase space regions.