Recursive prescription for logarithmic jet rate coefficients

TL;DR

This paper introduces a recursive method to analytically compute leading logarithmic coefficients in gluon cascades, enabling calculations for up to 80 gluons and suggesting applications in jet algorithm analysis.

Contribution

A new recursion relation for leading logarithmic coefficients in gluon cascades, allowing efficient computation for complex jet configurations.

Findings

Derived recursion relation for gluon cascade coefficients

Computed coefficients for up to 80 gluons analytically

Identified simple ratios for resolved coefficients

Abstract

We derive a recursion relation for the analytic leading logarithmic coefficients of a final state gluon cascade. We demonstrate the potential of our method by analytically computing the rate coefficients for the emission of up to 80 gluons in both the exclusive-kT (Durham) and generalized inclusive-kT class of jet algorithms. There is a particularly simple form for the ratios of resolved coefficients. We suggest potential applications including the efficient generation of shower histories.