Saddle-point method for resummed form factors in QCD

We consider the form factor appearing in QCD resummation formalism for event-shape distributions in the two-jet (or back-to-back) region.We present an analytic formula for the inverse transform of the form factor, namely from the conjugate moment space to the (physical) momentum space, based on the saddle-point method. The saddlepoint itself is determined by means of an analytic recursion method as well as by standard numerical methods.The results we have found are in very good agreement with the exact (numerical) evaluation of the inverse transform, while they significantly differ from classical analytic formulations of resummation in momentum space. The latter are based on a Taylor expansion of the form factor around the free-theory (αS = 0) saddle point, while our method involves an expansion of the form factor around the interacting-theory saddle point (αS ≠ 0).