A new suite of Lund-tree observables to resolve jets

TL;DR

This paper introduces Lund-Tree Shapes, a new class of jet observables derived from declustering trees, which effectively characterize multi-jet events and are suitable for higher-order QCD calculations and collider phenomenology.

Contribution

The paper presents a novel set of jet observables called Lund-Tree Shapes, with simple all-order structure and no non-global logarithms, applicable to various collider processes and compatible with advanced theoretical calculations.

Findings

Derived NNLL predictions for $e^+e^-$, $pp$, and $ep$ colliders.

Matched NNLO predictions for LHC processes.

Demonstrated the observables' theoretical simplicity and phenomenological utility.

Abstract

We introduce a class of collider observables, named Lund-Tree Shapes (LTS), defined from declustering trees originating from the Lund jet plane representation of the QCD radiation pattern in multi-jet scattering processes. At the differential level, they are continuous global variables akin classical event shapes and $n\to n+1$ jet-resolution parameters, which probe the geometry and hierarchical structure of the radiation in an event. At the integrated, cumulative level, they naturally define $n$ jet rates, providing a jet-multiplicity-based characterisation of multi-jet final states. Their definition applies to scattering processes with any number of resolved jets in the final state, as well as to groomed jets. They are thus usable as resolution variables in the context of higher-order calculations via phase-space slicing, matching fixed-order calculations to parton showers, and testing the logarithmic accuracy of shower algorithms. From a theoretical viewpoint, such observables feature a simple all-order structure and are free of non-global logarithmic corrections. As an initial application, we derive next-to-next-to-leading-logarithmic accurate predictions for processes with two QCD legs at $e e$, $pp$ and $e p$ colliders, and matched predictions to next-to-next-to-leading order for the LHC, discussing aspects of collider phenomenology.