On the evaluation of two-loop electroweak box diagrams for e+e- → HZ production

Precision studies of the Higgs boson at future e(+)e(-) colliders can help to shed light on fundamental questions related to electroweak symmetry breaking, baryogenesis, the hierarchy problem, and dark matter. The main production process, e(+)e(-)-> HZ, will need to be controlled with sub-percent precision, which requires the inclusion of next-to-next-to-leading order (NNLO) electroweak corrections. The most challenging class of diagrams are planar and non-planar double-box topologies with multiple massive propagators in the loops. This article proposes a technique for computing these diagrams numerically, by transforming one of the sub-loops through the use of Feynman parameters and a dispersion relation, while standard one-loop formulae can be used for the other sub-loop. This approach can be extended to deal with tensor integrals. The resulting numerical integrals can be evaluated in minutes on a single CPU core, to achieve about 0.1% relative precision.

Automated summary

A technique for computing diagrams involving multiple massive propagators in loops is proposed, using Feynman parameters and a dispersion relation. The approach allows for sub-percent precision control of the main production process of the Higgs boson at future e(+)e(-) colliders, with the ability to evaluate numerical integrals in minutes on a single CPU core. This method can be extended to handle tensor integrals as well.