Factorization Constraints on Jet Substructure

TL;DR

This paper derives theoretical constraints on jet substructure algorithms at the LHC from factorization principles, identifying which methods can be modified to ensure factorization and improve predictive power.

Contribution

It introduces a power counting analysis to constrain jet substructure methods based on factorization, and proposes modifications for non-factorizing algorithms.

Findings

Factorization constrains parameter scaling in jet algorithms.

Generic declustering techniques do not naturally factorize.

Simple modifications can enable factorization in certain algorithms.

Abstract

Factorization underpins our ability to make predictions at the LHC, both in Monte Carlo simulations and direct calculations. An improved theoretical understanding of jet substructure can lead to calculations that can confront data and validate the Monte Carlo description of jets. We derive constraints on jet substructure algorithms from factorization, focusing on the broad class of jet observables where the soft and collinear dynamics of QCD dominate. A necessary condition for factorization is that the phase space constraints on soft and collinear dynamics for a given observable are independent of each other. This condition allows us to use a simple power counting analysis to place strong constraints on the form of jet substructure methods that can factorize. We illustrate this approach by considering four substructure algorithms, the mass-drop filter Higgs tagger, pruning, trimming, and N-subjettiness. We find that factorization constrains the scaling of parameters in all of the substructure algorithms, and that the generic declustering and filtering techniques do not factorize. However, we determine simple modifications that can be made to allow for factorization.