Jet Function with a Jet Algorithm in SCET

TL;DR

This paper derives the jet function within Soft-Collinear Effective Theory (SCET) for $e^+e^-$ dijet production, incorporating a generic jet algorithm at one-loop order, and explores its properties and dependencies.

Contribution

It provides a detailed calculation of the jet function with a generic jet algorithm in SCET at $ ext{O}(\alpha_s)$, including its independence from certain soft radiation parameters.

Findings

Jet function is independent of the soft radiation energy fraction $eta$.

Anomalous dimension remains consistent with and without the cone half-angle $ heta$.

Finite part of the jet function depends on the cone angle $ heta$.

Abstract

The jet function for the factorized cross section $e^+e^-$ into dijets is given as a function of the jet invariant mass s and with a generic jet algorithm at $\mathcal{O}(\alpha_s)$. We demonstrate the results using the Sterman-Weinberg algorithm and show that the jet function is independent of the energy fraction $\beta$ of the soft radiation. The anomalous dimension has the same form with and without the cone half-angle $\delta$. The dependence of the finite part of the jet function on the cone angle is given.