Lepton-mass effects in the decays $H\to Z{Z}^{\ast }\to {\ell }^{+}{\ell }^{-}{\tau }^{+}{\tau }^{-}$ and $H\to W{W}^{\ast }\to \ell \nu \tau {\nu }_{\tau }$

Abstract

We consider lepton-mass effects in the cascade decays $H\to Z(\to {\ell }^{+}{\ell }^{-})+Z^{\ast }(\to {\tau }^{+}{\tau }^{-})$ and $H\to W^{-}(\to {\ell }^{-}{\bar{\nu }}_{\ell })+W^{+\ast }(\to {\tau }^{+}{\nu }_{\tau })$. Since the scale of the problem is set by the off-shellness $q^2$ of the respective gauge bosons in the limits $(m_{\ell }+m_{{\ell }^{\prime }}{)}^2\le q^2\le (m_H-m_{W,Z}{)}^2$ and not by $m_{W,Z}^2$, lepton-mass effects are non-negligible for the $\tau$ modes in particular close to the threshold of the off-shell decays. Lepton-mass effects show up e.g.\ in the three-fold joint angular decay distribution for the decays. Nonzero lepton masses lead to leptonic helicity-flip contributions which in turn can generate novel angular dependencies in the respective three-fold angular decay distributions. Lepton-mass effects are more pronounced in the $H\to Z(\to \ell \ell )Z^{\ast }(\to \tau \tau )$ mode which, in part, is due to the fact that the ratio of lepton helicity flip/nonflip contributions in the decay $Z^{\ast }\to {\ell }^{+}{\ell }^{-}$ is four times larger than in the decay $W^{+\ast }\to {\ell }^{+}\nu$. We also briefly consider the corresponding off-shell -- off-shell decays $H\to Z^{\ast }(\to {\ell }^{+}{\ell }^{-})+Z^{\ast }(\to {\tau }^{+}{\tau }^{-})$ and $H\to W^{-\ast }(\to {\ell }^{-}{\bar{\nu }}_{\ell })+W^{+\ast }(\to {\tau }^{+}{\nu }_{\tau })$.

45 pages, 9 figures and 6 tables, published version

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