Effect of anomalous $HHH$ coupling on the decay $H\rightarrow Z\,Z^*\rightarrow$ 4 charged leptons

We have computed the electroweak corrections to $H\rightarrow Z\,Z^*\rightarrow$ 4 charged leptons, including the effect of anomalous $HHH$ coupling in the $κ$-framework. The results of this scaling are gauge invariant. We have computed the results for $ H \to e^+ e^- μ^+ μ^-$ and $ H \to e^+ e^- e^+ e^-$ processes. The corrections for the both processes depend on the input parameter scheme. In the $G_F$ scheme, the electroweak corrections are about $1.26\%$ for the $ H \to e^+ e^- μ^+ μ^-$ and about $0.25\%$ for the $ H \to e^+ e^- e^+ e^-$ process. However changing the $κ$ from $4$ to $-4$, the corrections vary from less than $1\%$ to about $-6\%$. We have plotted a number of kinematic distributions. The corrections over most of the phase space regions are similar. These large corrections can be used to put a bound on the $HHH$ coupling. This can help in determining the structure of the Higgs potential.