Abstract
We perform the all orders resummation of threshold enhanced contributions for the Higgs boson pair production cross section via gluon fusion, including finite top quark mass (Mt) effects. We present results for the total cross section and Higgs pair invariant mass (Mhh) distribution. We obtain results at next-to-leading logarithmic accuracy (NLL) which retain the full Mt dependence, and are matched to the full next-to-leading order (NLO) prediction. Our NLL+NLO results represent the most advanced prediction with full Mt dependence for this process, and produce an increase of about 4% in the total cross section with respect to the NLO result for LHC energies, and for a central scale μ0 = Mhh/2. We also consistently combine the full NLL with the next-to-next-to-leading logarithmically (NNLL) accurate resummation computed in the Born-improved large-Mt limit, and match it to the next-to-next-to-leading order approximation of ref. [1], so called NNLOFTa. We find that the resummation effects are very small at NNLL for μ0 = Mhh/2, in particular below 1% at 13 TeV, indicating that the perturbative expansion is under control. In all cases the resummation effects are found to be substantially larger for the central scale μ0 = Mhh, resulting in a more stable cross section with respect to scale variations than the fixed order calculation.
Highlights
Besides the previously described fixed-order calculations, the all-orders resummation of soft gluon emissions has been performed –again within the HTL– at next-to-next-toleading logarithmic accuracy (NNLL) in refs. [20, 21]
We find that the resummation effects are very small at next-to-leading logarithmically (NNLL) for μ0 = Mhh/2, in particular below 1% at 13 TeV, indicating that the perturbative expansion is under control
We have found that these two approaches agree in the μ0 = Mhh/2 central prediction for the total cross section at the sub-per mille level for all the energies under consideration, being the only noticeable difference the shape of the upper uncertainty band, this one being slightly larger for the prediction defined by eq (3.2), which we choose in the following in order to be more conservative
Summary
We consider the hadronic production of Higgs boson pairs via gluon fusion. The hadronic cross section for a collider center-of-mass energy sH , differential in the Higgs pair system invariant mass Mhh, can be expressed in the following way. The soft-gluon contributions in the large-N limit can be organized in the following all-order resummation formula for the partonic coefficient function in Mellin space, G(grge,sN) (αS, Mh2h/μ2R; Mh2h/μ2F ) = Cgg(αS, Mh2h/μ2R; Mh2h/μ2F ) · ∆N (αS, Mh2h/μ2R; Mh2h/μ2F ) + O(1/N ). All the contributions that are constant in the large-N limit are contained in the function Cgg(αS) They originate in non-logarithmic soft contributions and hard virtual corrections, and can be expanded in powers of the strong coupling: Cgg(αS, Mh2h/μ2R; Mh2h/μ2F ) = 1 +. This coefficient can be obtained from the NiLO fixed order computation; even more, given that the soft gluon contributions in Cg(ig) are universal, the only process dependence enters via the virtual corrections.
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