Two-loop jet function and jet mass for top quarks

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 and next-to-next-to-leading-log order 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 next-to-next-to-leading-log 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, MS̄, and 1S masses are presented at two-loop order.