Abstract
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.
Highlights
Results from various kinematic regions are combined using conformal mapping and Pade approximation
At next-to-next-to-leading order (NNLO), the effective-theory calculation of the cross section has been performed in refs. [16,17,18] and an expansion for large top quark masses has been performed in ref. [19] in the soft-virtual approximation
Let us mention that recently two building blocks of the next-to-next-to-next-to-leading order (N3LO) effective-theory result have become available: two-loop virtual corrections have been obtained in ref. [24] and the four-loop matching coefficient for the effective coupling of two Higgs bosons and gluons has been computed in [25, 26]
Summary
We compute the cross section by applying the optical theorem to the forward scattering amplitudes g(q1)g(q2) → g(q1)g(q2) , g(q1)q(q2) → g(q1)q(q2) , g(q1)q(q2) → g(q1)q(q2) , q(q1)q(q2) → q(q1)q(q2) ,. Note the at NNLO, the partonic channel which involves different quark flavours in the initial state does not yet contribute. In order to fix the notation and the pre-factors we discuss the LO and NLO cross sections in detail. We write the perturbative expansion of the partonic cross section for Higgs boson pair production as σij→HH+X (s, ρ). To parametrize the dependence of the cross section on the Higgs boson and top quark masses. Note that we do not need to consider ghost-quark scattering, since this only contributes starting from N3LO. The NLO contributions in the above equations have to be replaced by the NNLO n3h amplitudes (see figures 1 (f), (g) and (h)), which we denote by σ(2),n3h. In the subsection we discuss the collinear counterterm σi(j2,)c,onl3hl
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