Two-loop Jet-Function and Jet-Mass for Top Quarks

TL;DR

This paper calculates the two-loop heavy quark jet-function and jet-mass for top quarks, enabling precise NNLL predictions of top-jet invariant mass distributions at future colliders.

Contribution

It provides the first two-loop computation of the heavy quark jet-function and introduces a transitive top jet-mass definition with all-order RG evolution.

Findings

Computed the two-loop heavy quark jet-function.

Defined a transitive top jet-mass with RG evolution.

Established relations between jet-mass and other mass schemes.

Abstract

We compute the two-loop heavy quark jet-function in the heavy quark limit. This is one of the key ingredients in next-to-next-to-leading order (NNLO) and next-to-next-to-leading-log order (NNLL) computations of the invariant mass distribution of top-jets at a future e+e- collider. The shape of the top invariant mass distribution is affected by large logs which we compute at NNLL order. Exploiting the non-abelian exponentiation theorem, a definition of the top jet-mass is given which is transitive and whose renormalization group evolution is determined by the cusp-anomalous dimension to all orders in perturbation theory. Relations of the jet-mass to the pole, MSbar, and 1S masses are presented at two-loop order.