Effect of anomalous $HHH$ coupling on the decay $H\to Z{Z}^{\ast }\to$ 4 charged leptons

We have computed the electroweak corrections to $H\to Z{Z}^{\ast }\to$ 4 charged leptons, including the effect of anomalous $HHH$ coupling in the $\kappa$-framework. The results of this scaling are gauge invariant. We have computed the results for $H\to e^{+}{e}^{-}{\mu }^{+}{\mu }^{-}$ 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 $1.26\mathrm{\%}$ for the $H\to e^{+}{e}^{-}{\mu }^{+}{\mu }^{-}$ and about $0.25\mathrm{\%}$ for the $H\to e^{+}{e}^{-}{e}^{+}{e}^{-}$ process. However changing the $\kappa$ from $4$ to $-4$, the corrections vary from less than $1\mathrm{\%}$ to about $-6\mathrm{\%}$. 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.