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We present an approach to the momentum-space resummation of global, recursiveinfrared and collinear safe observables featuring kinematic zeros away from theSudakov limit. In the hadro-production of a generic colour singlet, we considerthe family of inclusive observables which do not depend on the rapidity of theradiation, prime examples being the transverse momentum of the singlet, and$\phi^*$ in Drell-Yan pair production. We derive a resummation formula valid upto next-to-next-to-next-to-leading-logaritmic accuracy for the consideredobservables. This formula reduces exactly to the customary resummationperformed in impact-parameter space in the known cases, and it also predictsthe correct power-behaved scaling of the cross section in the limit of smallvalue of the observable. We show how this formalism is efficiently implementedby means of Monte Carlo techniques in a fully exclusive generator that allowsone to apply arbitrary cuts on the Born variables for any colour singlet, aswell as to automatically match the resummed results to fixed-ordercalculations. As a phenomenological application, we present state-of-the-artpredictions for the Higgs-boson transverse-momentum spectrum at the LHC atnext-to-next-to-next-to-leading-logarithmic accuracy matched to fixednext-to-next-to-leading order.

Momentum-space resummation for transverse observables and the Higgs $p_\perp$ at N$^3$LL+NNLO