Jet Shapes and Jet Algorithms in SCET

TL;DR

This paper develops a theoretical framework using Soft-Collinear Effective Theory to predict jet shape distributions in e+e- collisions, enabling detailed analysis of jet internal structure and partonic origin with resummation techniques.

Contribution

It proves a factorization theorem for jet shape distributions with multiple jets and calculates jet and soft functions at one-loop order, including resummation for NLL accuracy.

Findings

Predictions match Monte Carlo simulations for jet shape distributions.

Resummation improves accuracy of jet shape predictions.

Framework applies to various jet algorithms and configurations.

Abstract

Jet shapes are weighted sums over the four-momenta of the constituents of a jet and reveal details of its internal structure, potentially allowing discrimination of its partonic origin. In this work we make predictions for quark and gluon jet shape distributions in N-jet final states in e+e- collisions, defined with a cone or recombination algorithm, where we measure some jet shape observable on a subset of these jets. Using the framework of Soft-Collinear Effective Theory, we prove a factorization theorem for jet shape distributions and demonstrate the consistent renormalization-group running of the functions in the factorization theorem for any number of measured and unmeasured jets, any number of quark and gluon jets, and any angular size R of the jets, as long as R is much smaller than the angular separation between jets. We calculate the jet and soft functions for angularity jet shapes \tau_a to one-loop order (O(alpha_s)) and resum a subset of the large logarithms of \tau_a needed for next-to-leading logarithmic (NLL) accuracy for both cone and kT-type jets. We compare our predictions for the resummed \tau_a distribution of a quark or a gluon jet produced in a 3-jet final state in e+e- annihilation to the output of a Monte Carlo event generator and find that the dependence on a and R is very similar.