Next-to-leading non-global logarithms in QCD

Non-global logarithms arise from the sensitivity of collider observables to soft radiation in limited angular regions of phase space. Their resummation to next-to-leading logarithmic (NLL) order has been a long standing problem and its solution is relevant in the context of precision all-order calculations in a wide variety of collider processes and observables. In this article, we consider observables sensitive only to soft radiation, characterised by the absence of Sudakov double logarithms, and we derive a set of integro-differential equations that describes the resummation of NLL soft corrections in the planar, large-N-c limit. The resulting set of evolution equations is derived in dimensional regularisation and we additionally provide a formulation that is manifestly finite in four space-time dimensions. The latter is suitable for a numerical integration and can be generalised to treat other infrared-safe observables sensitive solely to soft wide-angle radiation. We use the developed formalism to carry out a fixed-order calculation to O(alpha(2)(s)) in full colour for both the transverse energy and energy distribution in the interjet region between two cone jets in e(+)e(-) collisions. We find that the expansion of the resummed cross section correctly reproduces the logarithmic structure of the full QCD result.

Automated summary

In this article, the resummation of NLL soft corrections for observables sensitive only to soft radiation is considered, and a set of integro-differential equations that describe the evolution of the corrections is derived. The formulation provided is finite in four space-time dimensions and can be generalized to treat other infrared-safe observables sensitive solely to soft wide-angle radiation.