Paper
A fast and accurate method for perturbative resummation of transverse momentum-dependent observables
Authors
Abstract
We propose a novel strategy for the perturbative resummation of transverse momentum-dependent (TMD) observables, using the spectra of gauge bosons (, Higgs) in collisions in the regime of low (but perturbative) transverse momentum as a specific example. First we introduce a scheme to choose the factorization scale for virtuality in momentum space instead of in impact parameter space, allowing us to avoid integrating over (or cutting off) a Landau pole in the inverse Fourier transform of the latter to the former. The factorization scale for rapidity is still chosen as a function of impact parameter , but in such a way designed to obtain a Gaussian form (in ) for the exponentiated rapidity evolution kernel, guaranteeing convergence of the integral. We then apply this scheme to obtain the spectra for Drell-Yan and Higgs production at NNLL accuracy. In addition, using this scheme we are able to obtain a fast semi-analytic formula for the perturbative resummed cross sections in momentum space: analytic in its dependence on all physical variables at each order of logarithmic accuracy, up to a numerical expansion for the pure mathematical Bessel function in the inverse Fourier transform that needs to be performed just once for all observables and kinematics, to any desired accuracy.