On the evaluation of two-loop electroweak box diagrams for $e^+e^- \to HZ$ production

TL;DR

This paper introduces a numerical method for efficiently computing complex two-loop electroweak box diagrams crucial for precise $e^+e^- o HZ$ production predictions at future colliders, achieving high accuracy within minutes.

Contribution

It presents a novel numerical technique transforming one sub-loop with Feynman parameters and dispersion relations, enabling fast and precise evaluation of challenging two-loop diagrams.

Findings

Numerical integrals evaluated in minutes on a single CPU core.

Achieved about 0.1% relative precision in calculations.

Method applicable to tensor integrals and complex topologies.

Abstract

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, $e^+e^- \to HZ$, 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.