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Perturbative and non-perturbative QCD effects in transverse momentum distributions

The recent formulation of the factorization theorem for transverse momentum spectra in terms of well-defined transverse momentum dependent distributions (TMDs), allows for a better understanding of the role of the perturbative and non-perturbative QCD contributions and their interplay. In particular, non-perturbative effects are often included both in the evolution of the TMDs and in the modeling of their scale-independent part. Using the available Drell-Yan and $Z$-production data at low and high energy we show that, for the currently available dilepton invariant mass values, the TMD evolution is driven mainly by its perturbative contribution, while the needed non-perturbative correction is scale independent. We then detail the difference between the scale dependences in the high and low boson transverse momentum regime and discuss the related theoretical errors.