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

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\%.