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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 underlyingnew 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 $\barB_s^0\to(\eta,\eta',\phi)\omega$, which receive sizable QCD- andelectroweak-penguin contributions. These decays are not yet observed, and theirrates are estimated to be relatively small in the SM. Taking into account thepertinent constraints, we find that the $Z'$ effects can greatly increase therates of $\bar B_s^0\to(\eta,\phi)\omega$, by as much as two orders ofmagnitude, 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 alsoundergo substantial $Z'$-induced enhancement. These rare modes can thereforeserve as complementary probes of the potential new physics which may beresponsible for the $b\to s\mu^+\mu^-$ anomalies.

Rare nonleptonic $\bar{B}_s^0$ decays as probes of new physics behind $b\to s\mu\bar\mu$ anomalies