An “all-poles” approximation to collinear resummations in the Regge limit of perturbative QCD

The procedure to improve the convergence in transverse momentum space of the NLL BFKL kernel using a ω-shift is revisited. An accurate approximation to this shift only depending on transverse momenta is presented. This approximation is based on a Bessel function of the first kind with argument depending on the strong coupling and a double logarithm of the ratio of transverse scales. A comparison between different renormalization schemes is also included.