  We consider the Higgs boson mass in a class of the UMSSM models in which the
MSSM gauge group is extended by an additional U(1)' group. Implementing the
universal boundary conditions at the GUT scale we target phenomenologically
interesting regions of UMSSM where the necessary radiative contributions to the
lightest CP-even Higgs boson mass are significantly small and LSP is always the
lightest neutralino. We find that the smallest amount of radiative
contributions is about 50 GeV in UMSSM, this result is much lower than that
obtained in MSSM, which is around 90 GeV. Additionally, we examine the Higgs
boson properties in these models to check if it can behave similar to the SM
Higgs boson under the current experimental constraints. We find that
enforcement of smaller radiative contribution mostly restricts the U(1)'
breaking scale as v_S <~ 10 TeV. Besides, such low contributions demand h_S ~
0.2 - 0.45. Because of the model dependency in realizing these radiative
contributions theta_E_6 < 0 are more favored, if one seeks for the solutions
consistent with the current dark matter constraints. As to the mass spectrum,
we find that stop and stau can be degenerate with the LSP neutralino in the
range from 300 GeV to 700 GeV; however, the dark matter constraints restrict
this scale as m_stop, m_stau >~ 500$ GeV. Such degenerate solutions also
predict stop-neutralino and stau-neutralino coannihilation channels, which are
effective to reduce the relic abundance of neutralino down to the ranges
consistent with the current dark matter observations. Finally, we discuss the
effects of heavy M_Z' in the fine-tuning. Even though the radiative
contributions are significantly low, the required fine-tuning can still be
large. We comment about reinterpretation of the fine-tuning measure in the
UMSSM framework, which can yield efficiently low results for the fine-tuning at
the electroweak scale.
