Abstract
We consider the production of the Standard Model Higgs boson through the gluon fusion mechanism in hadron collisions. We present the next-to-next-to-leading order (NNLO) QCD result of the hard-collinear coefficient function for the all-order resummation of logarithmically enhanced contributions at small transverse momentum. The coefficient function controls NNLO contributions in resummed calculations at full next-to-next-to-leading logarithmic accuracy. The same coefficient function is used in applications of the subtraction method to perform fully exclusive perturbative calculations up to NNLO.
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Notes
These analogies may hide important physical, conceptual and technical differences, which are discussed in the literature on transverse-momentum resummation.
In this introductory part we are using a shorthand notation, since the symbol \({\mathcal{H}}^{(2)}\) actually refers to a set of several coefficient functions.
To be precise, the logarithms are combined with corresponding ‘contact’ terms, which are proportional to \(\delta(q_{T}^{2})\). These combinations define regularized (integrable) ‘plus distributions’ \([\frac{1}{q_{T}^{2}}\ln^{m} (M^{2}/q_{T}^{2}) ]_{+}\) with respect to \(q_{T}^{2}\). The cumulative cross section in Eq. (2) is insensitive to the precise mathematical definition of these ‘plus distributions’.
This is the region where the size of the momenta of the virtual loops is of the order of M.
The reader who is not interested in issues related to the specification of a resummation scheme can simply assume that \(H_{g}^{H}(\alpha _{\mathrm {S}}) \equiv1\) throughout this paper.
The coupling \(\alpha _{\mathrm {S}}(b_{0}^{2}/b^{2})\) can be expressed in terms of α S(M 2) and \(\ln(b^{2}M^{2}/b_{0}^{2})\) by using the renormalization-group equation for the perturbative μ 2-evolution of the running coupling α S(μ 2).
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Acknowledgement
This work was supported in part by the Research Executive Agency (REA) of the European Union under the Grant Agreement number PITN-GA-2010-264564 (LHCPhenoNet, Initial Training Network).
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M. Grazzini is on leave of absence from INFN, Sezione di Firenze, Sesto Fiorentino, Florence, Italy.
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Catani, S., Grazzini, M. Higgs boson production at hadron colliders: hard-collinear coefficients at the NNLO. Eur. Phys. J. C 72, 2013 (2012). https://doi.org/10.1140/epjc/s10052-012-2013-2
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DOI: https://doi.org/10.1140/epjc/s10052-012-2013-2