QCD Analysis of the Scale-Invariance of Jets

TL;DR

This paper develops an analytic resummation method for jet substructure observables in QCD, revealing that jets are approximately scale-invariant over a broad range, and compares it with simulations and NLO results.

Contribution

It introduces a global next-to-leading-log resummation of the angular correlation function using soft-collinear effective theory, providing insights into QCD scale invariance in jets.

Findings

Jets are approximately scale-invariant over a wide dynamical range.

Analytic resummation agrees well with Monte Carlo and NLO results.

Deviations from scale invariance trace back to QCD effects.

Abstract

Studying the substructure of jets has become a powerful tool for event discrimination and for studying QCD. Typically, jet substructure studies rely on Monte Carlo simulation for vetting their usefulness; however, when possible, it is also important to compute observables with analytic methods. Here, we present a global next-to-leading-log resummation of the angular correlation function which measures the contribution to the mass of a jet from constituents that are within an angle R with respect to one another. For a scale-invariant jet, the angular correlation function should scale as a power of R. Deviations from this behavior can be traced to the breaking of scale invariance in QCD. To do the resummation, we use soft-collinear effective theory relying on the recent proof of factorization of jet observables at e+ e- colliders. Non-trivial requirements of factorization of the angular correlation function are discussed. The calculation is compared to Monte Carlo parton shower and next-to-leading order results. The different calculations are important in distinct phase space regions and exhibit that jets in QCD are, to very good approximation, scale invariant over a wide dynamical range.