Two-Loop Electroweak Corrections with Fermion Loops to $e^+ e^- \to ZH$

TL;DR

This paper computes precise two-loop electroweak corrections involving fermion loops for the process e+ e- to ZH, enhancing the accuracy of theoretical predictions at future colliders.

Contribution

It introduces a semi-numerical method for calculating two-loop diagrams with fermion loops, providing the first complete NNLO electroweak correction for this process.

Findings

NNLO corrections increase the cross-section by 0.7%.

The method handles UV divergences effectively.

Numerical results are provided at 240 GeV.

Abstract

We present a complete calculation of the next-to-next-to-leading (NNLO) electroweak corrections involving closed fermion loops to the $e^+ e^- \to ZH$ process. This has been achieved by using a semi-numerical technique for the two-loop vertex and box diagrams, which is based on Feynman parameters and dispersion relations for one of the two sub-loops. UV divergences are treated with suitable subtraction terms. Numerical results for the unpolarized differential and integrated cross-section at center-of-mass energy $\sqrt{s}=240~\text{GeV}$ are provided. Combining the NNLO contributions with one and two closed fermions loops, they are found to increase the NLO cross-section by 0.7\%.