Abstract
We present a procedure to calculate the Sudakov radiator for a generic recursive infrared and collinear (rIRC) safe observable whose distribution is characterised by two widely separated momentum scales. We give closed formulae for the radiator at next-to-next-to-leading-logarithmic (NNLL) accuracy, which completes the general NNLL resummation for this class of observables in the ARES method for processes with two emitters at the Born level. As a byproduct, we define a physical coupling in the soft limit, and we provide an explicit expression for its relation to the overline{mathrm{MS}} coupling up to mathcal{O}left({alpha}_s^3right) . This physical coupling constitutes one of the ingredients for a NNLL accurate parton shower algorithm. As an application we obtain analytic NNLL results, of which several are new, for all angularities τx defined with respect to both the thrust axis and the winner-take-all axis, and for the moments of energy-energy correlation FCx in e+e− annihilation. For the latter observables we find that, for some values of x, an accurate prediction of the peak of the differential distribution requires a simultaneous resummation of the logarithmic terms originating from the two-jet limit and at the Sudakov shoulder.
Highlights
The study of jet observables led to important advances in the understanding of allorder properties of QCD radiation, which lead to the discovery of the so-called non-global logarithms [2,3,4]
We present a new formulation of the NNLL correction δFcorrel introduced in ref. [53], that we redefined in order to make sure that the Sudakov radiator can be computed analytically for an arbitrary recursive infrared and collinear (rIRC) safe jet observable
In this paper we have completed the study of jet observables at NNLL accuracy in e+e− annihilation, that started in refs. [53, 54]
Summary
We summarise the structure of the NNLL resummed cross section for a generic rIRC observable in e+e− annihilation. We first set up the relevant notation and kinematics, and we move on to derive the resummed cross section up to NNLL accuracy
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