  The recently identified possibility of ground-state cooling of a mechanical
oscillator in the unresolved sideband regime by combination of the dissipative
and dispersive optomechanical coupling under the red sideband excitation [Phys.
Rev. A 88, 023850 (2013)], is currently viewed as a remarkable finding. We
present a comprehensive analysis of this protocol, which reveals its very high
sensitivity to small imperfections such as an additional dissipation, the
inaccuracy of the optimized experimental settings, and the inaccuracy of the
theoretical framework adopted. The impact of these imperfections on the cooling
limit is quantitatively assessed. A very strong effect on the cooling limit is
found from the internal cavity decay rate which even being small compared with
the detection rate may drastically push that limit up, questioning the
possibility of the ground state cooling. Specifically, the internal loss can
only be neglected if the ratio of the internal decay rate to the detection rate
is much smaller than the ratio of the cooling limit predicted by the protocol
to the common dispersive-coupling assisted sideband cooling limit. More over,
we establish that the condition of applicability of theory of that protocol is
the requirement that the latter ratio is much smaller than one. A detailed
comparison of the cooling protocol in question with the
dispersive-coupling-assisted protocols which use the red sideband excitation or
feedback is presented.
