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.
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