  The anomalous results of recent measurements on various $b\to s\mu^+\mu^-$
processes could be initial evidence of physics beyond the standard model (SM).
Assuming this to be the case, we entertain the possibility that the underlying
new physics also affects the rare nonleptonic decays of the $\bar B_s^0$ meson.
We consider in particular new physics arising from the interactions of a heavy
$Z'$ boson and investigate their influence on the decay modes $\bar
B_s^0\to(\eta,\eta',\phi)\omega$, which receive sizable QCD- and
electroweak-penguin contributions. These decays are not yet observed, and their
rates are estimated to be relatively small in the SM. Taking into account the
pertinent constraints, we find that the $Z'$ effects can greatly increase the
rates of $\bar B_s^0\to(\eta,\phi)\omega$, by as much as two orders of
magnitude, with respect to the SM expectations. We have previously shown that
$\bar B_s^0\to(\eta,\phi)\pi^0$, with similarly suppressed SM rates, could also
undergo substantial $Z'$-induced enhancement. These rare modes can therefore
serve as complementary probes of the potential new physics which may be
responsible for the $b\to s\mu^+\mu^-$ anomalies.

High Energy Physics - Phenomenology;High Energy Physics - Experiment