We investigate some well-known problematic aspects of the single-jet inclusive cross section, specifically its nonunitarity and the possibly related issue of apparent perturbative instability at low orders. We study and clarify their origin by introducing possible alternative weighted definitions of the observable which restore unitarity. We show that the perturbative instability of the standard definition is an accidental artifact of the smallness of the next-to-leading order $K$ factor which only manifests itself for values of the jet radius in the range $R\sim 0.3–0.6$, and that its nonunitarity is necessary in order to ensure cancellation of logs of the momentum cutoff used in the jet definition. We also show that alternative unitary definitions do not have better perturbative properties compared to the conventional nonunitary definition, while suffering from lack of cancellation of large logs.

• Received 11 July 2019

DOI:https://doi.org/10.1103/PhysRevD.100.114015

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

Published by the American Physical Society