Abstract
We compute the two-loop massless QCD corrections to the four-point amplitude g + g → H + H resulting from effective operator insertions that describe the interaction of a Higgs boson with gluons in the infinite top quark mass limit. This amplitude is an essential ingredient to the third-order QCD corrections to Higgs boson pair production. We have implemented our results in a numerical code that can be used for further phenomenological studies.
Highlights
The two-loop massless corrections to the g + g → H + H amplitude derived above complete the set of purely virtual amplitudes required for the prediction of the N3LO corrections to Higgs boson pair production in gluon fusion, in the infinite top quark mass limit
We deal with two classes of amplitudes separately, named class-A and class-B
The amplitudes of class-A can be related to the gluon form factor which is already known up to three loop order while amplitudes of class-B were known previously up to one loop
Summary
We compute the relevant amplitudes in an effective theory where the top quark degrees of freedom are integrated out. The effective Lagrangian that describes the coupling of one and two Higgs bosons to gluons is given by. Note that we have taken only those terms in the Leff into account that are relevant for the production of two Higgs bosons in a gluongluon initiated process. The constants CH and CHH are the Wilson coefficients [28, 34,35,36,37,38] determined by matching the effective theory to the full theory and they can be expanded in powers of the renormalized strong coupling constant as = gs2(μ2R)/(16π2) = αs(μ2R)/(4π) with μR the renormalisation scale, CH (as).
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