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We have computed the fourth-order n 2 f contributions to all three non-singlet quark-quark splitting functions and their four n 3 f flavour-singlet counterparts for the evolution of the parton distributions of hadrons in perturbative QCD with n f effectively massless quark flavours. The analytic form of these functions is presented in both Mellin N-space and momentum-fraction x-space; the large-x and small-x limits are discussed. Our results agree with all available predictions derived from lower-order information. The large-x limit of the quark-quark cases provides the complete n 2 f part of the four-loop cusp anomalous dimension which agrees with two recent partial computations.

We compute the NLO virtual corrections to the partonic cross section of gg → HH, in the high energy limit. Finite Higgs boson mass effects are taken into account via an expansion which is shown to converge quickly. We obtain analytic results for the next-to-leading order form factors which can be used to compute the cross section. The method used for the calculation of the (non-planar) master integrals is described in detail and explicit results are presented.

Abstract:We consider the virtual corrections to the process gg → HH at NLO in the high energy limit and compute the corresponding planar master integrals in an expansion for small top quark mass. We provide details on the evaluation of the boundary conditions and present analytic results expressed in terms of harmonic polylogarithms.

We consider the next-to-leading order QCD corrections to Higgs boson pair production, using our recent calculation of the form factors in the high-energy limit. We compute the virtual corrections to the partonic cross section, applying Padé approximations to extend the range of validity of the high-energy expansion. This enables us to compare to the exact numerical calculation in a significant part of the phase space and allows us to extend the virtual matrix element grid, based on the exact numerical calculation, to larger values of the (partonic) transverse momentum of the Higgs boson, which is important for boosted Higgs studies. Improved predictions for hadron colliders with centre-of-mass energies of 14 TeV and 100 TeV are presented. The updated grid is made publicly available.

We compute the next-to-leading order virtual corrections to the partonic cross-section of the process gg → ZH, in the high-energy and large-mt limits. We use Padé approximants to increase the radius of convergence of the high-energy expansion in $$ {m}_t^2/s $$ m t 2 / s , $$ {m}_t^2/t $$ m t 2 / t and $$ {m}_t^2/u $$ m t 2 / u and show that precise results can be obtained down to energies which are fairly close to the top quark pair threshold. We present results both for the form factors and the next-to-leading order virtual cross-section.

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