  We propose a novel strategy for the perturbative resummation of transverse
momentum-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 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 $b$, but in such a way designed to obtain a Gaussian form (in $\ln
b$) for the exponentiated rapidity evolution kernel, guaranteeing convergence
of the $b$ integral. We then apply this scheme to obtain the $q_T$ 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.
