QCD Corrections to  \(H \rightarrow e^+ e^- \mu ^+ \mu ^- \)

The Higgs discovery in 2012 started a precision era in particle physics. Most future colliders aim for precision measurements in the Higgs sector to probe any signal of new physics. These precision measurements demand more accurate theoretical predictions of Higgs production and decay rates. In this direction, we compute the contribution of two-loop mixed QCD-Electroweak (EW) corrections at \(\mathcal {O}(\alpha \alpha _s)\) to the golden decay channel of Higgs \(H \rightarrow Z Z^* \rightarrow e^+ e^- \mu ^+ \mu ^-\) . I will discuss a numerical approach to compute the non-trivial two-loop amplitude for the process and relevant checks on our calculation. Finally, I will present numerical results for the partial decay width and some kinematic distributions.