  Using newly available form factors obtained from light cone QCD sum rules in
full theory, we study the flavor changing neutral current transition of
$\Sigma_b \rar \Sigma \mu^+ \mu^-$ decay in the family non-universal $Z^\prime$
model. In particular, we evaluate the differential branching ratio,
forward-backward asymmetry as well as some related asymmetry parameters and
polarizations. We compare the obtained results with the predictions of the
standard model and discuss the sensitivity of the observables under
consideration to family non-universal $Z^\prime$ gauge boson. The order of
differential branching ratio shows that this decay mode can be checked at LHC
in near future.
