Papers › The Sudakov radiator for jet observables and the soft physical coupling
The Sudakov radiator for jet observables and the soft physical coupling
Andrea Banfi, Basem Kamal El-Menoufi, Pier Francesco Monni
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We present a procedure to calculate the Sudakov radiator for a generic recursive infrared and collinear (rIRC) safe observable in two-scale problems. 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 {\tt 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 MS coupling up to O(αₛ³). 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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