We present a comparative and systematic study of the fine tuning in the Higgs sector of three scale-invariant NMSSM models: the first being the standard Z_3-invariant NMSSM; the second is the NMSSM with additional matter filling 3(5+5*) representations of SU(5) and is called the NMSSM+; while the third model comprises 4(5+5*)and is called the NMSSM++. Naively, one would expect the fine tuning in the plus-type models to be smaller than that in the NMSSM, but we find that LHC limits on sparticles, especially the gluino mass, m_Gluino, can play an indirect, but vital, role in controlling the fine tuning. In particular, working in a semi-constrained framework at the GUT scale, we find that the masses of third generation stops are always larger in the plus-type models than in the NMSSM without extra matter. This is an RGE effect which cannot be avoided, and as a consequence the fine tuning in the NMSSM+ is significantly larger than in the NMSSM, with fine tuning in the NMSSM++ being significantly larger than in the NMSSM+.

Naturalness predicts the existence of new physics at the TeV scale. However, given the observed value of the Higgs mass, m_h ~ 126 GeV, and the current limits on superpartners from the LHC, supersymmetric models are in general fine tuned in the percent to permille level depending on the model. The NMSSM is known to be less fine tuned than the MSSM due to the presence of an additional tree-level contribution to the physical Higgs mass --proportional to the singlet-doublet coupling, lambda. However, there is an upper bound on lambda at the low scale (lambda <= 0.7) if one requires perturbativity to the GUT scale. The presence of extra matter between the low and high scales relaxes the perturbativity bound on lambda at low scales, allowing the Higgs mass at tree-level to be increased even more than in the NMSSM. Motivated by this, a number of models have been built since the relaxation effect might indicate that the fine tuning in models with extra matter could be smaller than models without extra matter. In this paper we show that the opposite is true. In models with extra matter, especially colored states, the RGEs of the gauge couplings and gauginos (particularly the strong coupling and the gluino mass parameter) will act in such a way that the stops in the NMSSM+ will always be larger than in the NMSSM, while they will always be larger in the NMSSM++ than in the NMSSM+. After a careful and comprehensive scans of the parameter spaces of all three models, we find that indeed the fine tuning in the NMSSM is always smaller than the models with extra matter that were considered.