  Within QCD factorization approach, we employ the new results of form factors
of $B_s \to \phi$ and calculate the branching fractions, CP asymmetries (CPAs)
and polarization fractions of the decay modes $B_s \to \phi (\rho^0, \omega)$
in both the standard model (SM) and the family non-universal $Z^\prime$ model.
We find that in SM the above observables are relate to two parameters $\rho_H$
and $\phi_H$, which characterize the end-point divergence in the hard
spectator-scattering amplitudes. When setting $\rho_H=0.5$ and $\phi_H\in
[-180,180]^\circ$, the theoretical uncertainties are large. By combining the
experimental data, our results can be used to constrain these two parameters.
Supposing $\rho_H=0$, we study the effects of $Z^\prime$ boson on the concerned
observables. With the available branching fraction of $B_s \to \phi \rho^0$,
the possible ranges of parameter spaces are obtained. Within the allowed
parameter spaces, the branching fraction of $B_s \to \phi \omega$ can be
enlarged remarkably. Furthermore, the new introduced weak phase plays important
roles in significantly affecting the CPAs and polarization fractions, which are
important observables for probing the effects of NP. If these decay modes were
measured in the on-going LHC-b and Belle-II experiments in future, the peculiar
deviation from SM could provide a signal of the family non-universal $Z^\prime$
model, which can also be used to constrain the mass of $Z^\prime$ boson in
turn.
