Go Mishima

In this contribution we consider NNLO real radiation corrections to the total cross section for Higgs boson pair production in gluon fusion. Special emphasis is put on the cross check of the asymptotic expansion in the inverse top quark mass.

In this contribution we consider NNLO real radiation corrections to the total cross section for Higgs boson pair production in gluon fusion. Special emphasis is put on the cross check of the asymptotic expansion in the inverse top quark mass.

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 real-radiation corrections, i.e. the virtual corrections to the single real emission of a parton, to Higgs boson pair production at next-to-next-to-leading order in QCD, in an expansion for large top quark mass. We concentrate on the radiative corrections to the interference contribution from the next-to-leading order one-particle reducible and the leading order amplitudes. This is a well defined and gauge invariant subset of the full real-virtual corrections to the inclusive cross section. We obtain analytic results for all phase-space master integrals both as an expansion around the threshold and in an exact manner in terms of Goncharov polylogarithms. We demonstrate that for many applications it is sufficient to use the expanded expressions.

We apply the method of regions to the massive two-loop integrals appearing in the Higgs pair production cross section at the next-to-leading order, in the high energy limit. For the non-planar integrals, a subtle problem arises because of the indefinite sign of the second Symanzik polynomial. We solve this problem by performing an analytic continuation of the Mandelstam variables such that the second Symanzik polynomial has a definite sign. Furthermore, we formulate the procedure of applying the method of regions systematically. As a by-product of the analytic continuation of the Mandelstam variables, we obtain crossing relations between integrals in a simple and systematic way. In our formulation, a concept of "template integral" is introduced, which represents and controls the contribution of each region. All of the template integrals needed in the computation of the Higgs pair production at the next-to-leading order are given explicitly. We also develop techniques to solve Mellin-Barnes integrals, and show them in detail. Although most of the calculation is shown for the concrete example of the Higgs pair production process, the application to other similar processes is straightforward, and we anticipate that our method can be useful also for other cases.

We apply the method of regions to the massive two-loop integrals appearing in the Higgs pair production cross section at the next-to-leading order, in the high energy limit. For the non-planar integrals, a subtle problem arises because of the indefinite sign of the second Symanzik polynomial. We solve this problem by performing an analytic continuation of the Mandelstam variables such that the second Symanzik polynomial has a definite sign. Furthermore, we formulate the procedure of applying the method of regions systematically. As a by-product of the analytic continuation of the Mandelstam variables, we obtain crossing relations between integrals in a simple and systematic way. In our formulation, a concept of “template integral” is introduced, which represents and controls the contribution of each region. All of the template integrals needed in the computation of the Higgs pair production at the next-to-leading order are given explicitly. We also develop techniques to solve Mellin-Barnes integrals, and show them in detail. Although most of the calculation is shown for the concrete example of the Higgs pair production process, the application to other similar processes is straightforward, and we anticipate that our method can be useful also for other cases.

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.

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.