Single-jet inclusive cross section and its definition

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 similar to 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.