The Higgs boson decay into ZZ decaying to identical fermion pairs

In order to investigate various decay channels of the Higgs boson $h$ or the hypothetical dilaton, we consider a neutral particle $X$ with zero spin and arbitrary $CP$ parity. This particle can decay into two off-mass-shell $Z$ bosons ($Z_1^{\ast }$ and $Z_2^{\ast }$) decaying to identical fermion-antifermion pairs ($f\bar{f}$): $X\to Z_1^{\ast }{Z}_2^{\ast }\to f\bar{f}f\bar{f}$. We derive analytical formulas for the fully differential width of this decay and for the fully differential width of $h\to Z_1^{\ast }{Z}_2^{\ast }\to 4\mathrm{\ell }$ ($4\mathrm{\ell }$ stands for $4e$, $4\mu$, or $2e2\mu$). Integration of these formulas yields some Standard Model histogram distributions of the decay $h \to Z_1^* Z_2^* \to 4 \ell$, which are compared with corresponding Monte Carlo simulated distributions obtained by ATLAS and with ATLAS experimental data.