Energy Spectra and Energy Correlations in the Decay $H\to ZZ\to {\mu }^{+}{\mu }^{-}{\mu }^{+}{\mu }^{-}$

Abstract

It is shown that in the sequential decay $H\to ZZ\to (f_1\overline{f_1})+(f_2\overline{f_2})$, the energy distribution of the final state particles provides a simple and powerful test of the $HZZ$ vertex. For a standard Higgs boson, the energy spectrum of any final fermion, in the rest frame of $H$, is predicted to be $d\Gamma /dx\sim 1+{\beta }^4-2(x-1{)}^2$, with $\beta =\sqrt{1-4m_Z^2/m_H^2}$ and $1-\beta \le x=4E/m_H\le 1+\beta$. By contrast, the spectrum for a pseudoscalar Higgs is $d\Gamma /dx\sim {\beta }^2+(x-1{)}^2$. There are characteristic energy correlations between $f_1$ and $f_2$ and between $f_1$ and $\overline{f_2}$. These considerations are applied to the ``gold--plated'' reaction $H\to ZZ\to {\mu }^{+}{\mu }^{-}{\mu }^{+}{\mu }^{-}$, including possible effects of CP--violation in the $HZZ$ coupling. Our formalism also yields the energy spectra and correlations of leptons in the decay $H\to W^{+}{W}^{-}\to l^{+}{\nu }_l{l}^{-}\overline{{\nu }_l}$.

Comments: 14 pages + 4 figures