  We consider Higgs production in gluon fusion and in particular the prediction
of the Higgs transverse momentum distribution. We discuss the ambiguities
affecting the matching procedure between fixed order matrix elements and the
resummation to all orders of the terms enhanced by $\log(p_T^H/m_H)$ factors.
Following a recent proposal (Grazzini et al., hep-ph/1306.4581), we argue that
the gluon fusion process, computed considering two active quark flavors, is a
multiscale problem from the point of view of the resummation of the collinear
singular terms. We perform an analysis at parton level of the collinear
behavior of the $\mathcal{O}(\alpha_s)$ real emission amplitudes; relying on
the collinear singularities structure of the latter, we derive an upper limit
to the range of transverse momenta where the collinear approximation is valid.
This scale is then used as the value of the resummation scale in the analytic
resummation framework or as the value of the $h$ parameter in the POWHEG-BOX
code. A variation of this scale can be used to generate an uncertainty band
associated to the matching procedure. Finally, we provide a phenomenological
analysis in the Standard Model, in the Two Higgs Doublet Model and in the
Minimal Supersymmetric Standard Model. In the two latter cases, we provide an
ansatz for the central value of the matching parameters not only for a Standard
Model-like Higgs boson, but also for heavy scalars and in scenarios where the
bottom quark may play the dominant role.
