  The recent LHC indications of a SM-like Higgs boson near 125 GeV are
consistent not only with the Standard Model (SM) but also with Supersymmetry
(SUSY). However naturalness arguments disfavour the Minimal Supersymmetric
Standard Model (MSSM). We consider the Next-to-Minimal Supersymmetric Standard
Model (NMSSM) with a SM-like Higgs boson near 125 GeV involving relatively
light stops and gluinos below 1 TeV in order to satisfy naturalness
requirements. We are careful to ensure that the chosen values of couplings do
not become non perturbative below the grand unification (GUT) scale, although
we also examine how these limits may be extended by the addition of extra
matter to the NMSSM at the two-loop level. We then propose four sets of
benchmark points corresponding to the SM-like Higgs boson being the lightest or
the second lightest Higgs state in the NMSSM or the NMSSM-with-extra-matter.
With the aid of these benchmark points we discuss how the NMSSM Higgs boson
near 125 GeV may be distinguished from the SM Higgs boson in future LHC
searches.
