Abstract
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.
Highlights
The gluon fusion cross section is very well approximated by a Heavy Quark Effective Field Theory (HQEFT), where the Higgs mass is considered very small with respect to the one of the top quark
The matching procedure requires to fix the integral of the Higgs transverse momentum distribution to a constant, which is conventionally set to the value of the fixed order total cross section [56]
The role effectively played by the scale h has some similarities with the one described in section 2.1 for the resummation scale μres: for pH⊥ < h or for pH⊥ < μres the Sudakov suppression yields a regular behavior of the Higgs transverse momentum distribution, whereas for pH⊥ larger than these scales the fixed-order description is recovered, at the level of description given by POWHEG
Summary
The Higgs boson acquires a transverse momentum pH⊥ because of its recoil against QCD radiation. The resummed partonic cross section has a factorized structure given by the product of a universal exponential factor, which accounts for the resummation to all orders of the logarithmically divergent terms, multiplied by a process dependent function, which describes the details of the hard scattering process This factorization requires the introduction of a scale μres, called resummation scale [56]. The matching procedure requires to fix the integral of the Higgs transverse momentum distribution to a constant, which is conventionally set to the value of the fixed order total cross section [56] This constraint holds exactly for any choice of μres, so that any variation of the resummation scale modifies the shape of the distribution but not its integral and yields a correlation between low- and intermediate-pH⊥ regions. The possibility of defining the finite part Rf in an arbitrary way can be exploited to parameterize the uncertainties related to the matching procedure
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