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Lepton-mass effects in the decays $H \to Z Z^{} \to ℓ^{+} ℓ^{-} τ^{+} τ^{-}$ and $H \to W W^{} \to ℓ ν τ ν_{τ}$

S. Berge¹, S. Groote^2,3, J. G. Körner³, and L. Kaldamäe²

¹Institut für Theoretische Physik, RWTH Aachen University, 52056 Aachen, Germany
²Loodus- ja Tehnoloogiateaduskond, Füüsika Instituut, Tartu Ülikool, Tähe 4, 51010 Tartu, Estonia
³PRISMA Cluster of Excellence, Institut für Physik, Johannes-Gutenberg-Universität, Staudinger Weg 7, 55099 Mainz, Germany

Phys. Rev. D 92, 033001 – Published 3 August, 2015

DOI: https://doi.org/10.1103/PhysRevD.92.033001

Abstract

We consider $τ$ -lepton mass effects in the cascade decays $H \to Z (\to ℓ^{+} ℓ^{-}) + Z^{*} (\to τ^{+} τ^{-})$ and $H \to W^{-} (\to ℓ^{-} {\bar{ν}}_{ℓ}) + W^{+ *} (\to τ^{+} ν_{τ})$ . Since the scale of the problem is set by the off-shellness $q^{2}$ of the respective gauge bosons in the limits $(m_{ℓ} + m_{ℓ^{'}})^{2} \leq q^{2} \leq (m_{H} - m_{W, Z})^{2}$ and not by $m_{W, Z}^{2}$ , lepton-mass effects are non-negligible for the $τ$ modes in particular close to the threshold of the off-shell decays. Lepton-mass effects show up in the rate and 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 $H \to Z (\to ℓ ℓ) Z^{*} (\to τ τ)$ mode which, in part, is due to the fact that the ratio of lepton helicity-flip/nonflip contributions in the decay $Z^{*} \to ℓ^{+} ℓ^{-}$ is four times larger than in the decay $W^{+ *} \to ℓ^{+} ν$ . Overall the inclusion of $τ$ mass effects leads to a 3.97% reduction in the leptonic $H \to Z Z^{*}$ rate. Lepton mass effects are quite pronounced for $q^{2}$ values from threshold up to $\sim 200 {GeV}^{2}$ . For example, at $q^{2} = 50 {GeV}^{2}$ the transverse–longitudinal–scalar helicity composition of the off-shell $Z$ –boson changes from $0.06 : 0.94 : 0$ to $0.04 : 0.65 : 0.31$ for the $τ$ lepton. This has observational consequences for the angular decay distributions of the final-state leptons. We also briefly consider the corresponding off-shell–off-shell decays $H \to Z^{*} (\to ℓ^{+} ℓ^{-}) + Z^{*} (\to τ^{+} τ^{-})$ and $H \to W^{- *} (\to ℓ^{-} {\bar{ν}}_{ℓ}) + W^{+ *} (\to τ^{+} ν_{τ})$ .

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Lepton-mass effects in the decays $H \to Z Z^{} \to ℓ^{+} ℓ^{-} τ^{+} τ^{-}$ and $H \to W W^{} \to ℓ ν τ ν_{τ}$

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Lepton-mass effects in the decays H→ZZ*→ℓ+ℓ−τ+τ− and H→WW*→ℓντντ

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Lepton-mass effects in the decays $H \to Z Z^{} \to ℓ^{+} ℓ^{-} τ^{+} τ^{-}$ and $H \to W W^{} \to ℓ ν τ ν_{τ}$