The PDG is listing values of "$Z$ couplings to neutral leptons" as
$$ \begin{eqnarray} g^{\nu_{\ell}} & = & 0.5008 \, \pm \, 0.0008 \\ g^{\nu_{e}} & = & 0.53 \, \pm \, 0.09 \\ g^{\nu_{\mu}} & = & 0.502 \, \pm \, 0.017 \end{eqnarray} $$
where $\nu_e$ and $\nu_{\mu}$ denote neutrino species or neutrino fields "participating in the weak interaction", appearing (presumably) explicitly for instance in the decays
$$ W^+ \rightarrow e^+ \, \nu_e $$ and $$ W^+ \rightarrow \mu^+ \, \nu_{\mu},$$
and $\nu_{\ell}$ refers to an "average of neutrino species" which involves species $\nu_{\tau}$ as well.
Also, the value of the "invisible" relative branching fraction of $Z$ is given as
$$\Gamma( Z \rightarrow \text{invisible} ) / \Gamma^Z_{total} := \Gamma_6 / \Gamma^Z_{total} = (2.000 \, \pm \, 0.006) \times 10^{-1} .$$
Assuming that all "invisible" decays of the $Z$ boson proceed to the final state $\nu \, \overline{\nu}$ ("neutral lepton and anti-lepton") which all contribute to the "average of neutrino species, $\nu_{\ell}$", is it possible to calculate (or at least to express in terms of suitable parameters)
(1) the relative branching fraction of $Z$ e.g. to final state $\nu_e \, \overline{\nu_e}$,
(2) the relative branching fraction of $Z$ to any final state $\nu_{final} \, \overline{\nu_{final}}$ which is completely devoid of any $\nu_e$ or $\overline{\nu_e}$ contribution, i.e. such that
$$ \langle \nu_{final} \, \overline{\nu_{final}} | \nu_e \, \overline{\nu_e} \rangle = 0,$$
(3) the relative branching fraction of $Z$ e.g. to final state $\nu_3 \, \overline{\nu_3}$, i.e. to a pair of "neutral lepton and anti-lepton" of one particular neutrino mass eigenstate, $\nu_3$ (and where the "suitable parameters" may involve coefficients of the PMNS matrix), and
(4) the relative branching fraction of $Z$ to any final state $\nu_{final} \, \overline{\nu_{final}}$ which is completely devoid of any $\nu_3$ or $\overline{\nu_3}$ contribution, i.e. such that
$$ \langle \nu_{final} \, \overline{\nu_{final}} | \nu_3 \, \overline{\nu_3} \rangle = 0,$$
please ?
