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

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.

16 pages, 4 figures and 1 table; typos in eqs.(6,21,26,36) corrected

Cited by in corpus (3)

• Towards a Fully Automated Differential ${\text{NNLO}}_{\text{EW}}$ Generator for Lepton Colliders
• Fermionic Electroweak Two-Loop Corrections to Drell-Yan and Related Processes
• Recurrence Relations and Dispersive Techniques for Precision Multi-Loop Calculations