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We propose a novel strategy for the perturbative resummation of transversemomentum-dependent (TMD) observables, using the $q_T$ spectra of gauge bosons($\gamma^*$, Higgs) in $pp$ collisions in the regime of low (but perturbative)transverse momentum $q_T$ as a specific example. First we introduce a scheme tochoose the factorization scale for virtuality in momentum space instead of inimpact 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. Thefactorization scale for rapidity is still chosen as a function of impactparameter $b$, but in such a way designed to obtain a Gaussian form (in $\lnb$) for the exponentiated rapidity evolution kernel, guaranteeing convergenceof the $b$ integral. We then apply this scheme to obtain the $q_T$ spectra forDrell-Yan and Higgs production at NNLL accuracy. In addition, using this schemewe are able to obtain a fast semi-analytic formula for the perturbativeresummed cross sections in momentum space: analytic in its dependence on allphysical variables at each order of logarithmic accuracy, up to a numericalexpansion for the pure mathematical Bessel function in the inverse Fouriertransform that needs to be performed just once for all observables andkinematics, to any desired accuracy.

A fast and accurate method for perturbative resummation of transverse momentum-dependent observables