The Sudakov radiator for jet observables and the soft physical coupling

Understand

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 $\overline{\rm MS}$ coupling up to ${\cal O}(\alpha_s^3)$.
• This physical coupling constitutes one of the ingredients for a NNLL accurate parton shower algorithm.