Dominant decay of a SM-like Higgs boson into particles beyond those contained in the minimal supersymmetric standard model has been identified as a natural scenario to avoid fine-tuning in electroweak symmetry breaking while satisfying all LEP limits. In the simplest of such an extension, the next-to-minimal supersymmetric model, the lightest $CP$-even Higgs boson can decay into two pseudoscalars. In the scenario with the least fine-tuning the lightest $CP$-even Higgs boson has a mass of order 100 GeV. In order to escape LEP limits it must decay to a pair of the lightest $CP$-odd Higgs bosons with $\mathrm{Br}(h\to aa)>.7$ and $m_a<2m_b$ (so that $a\to {\tau }^{+}{\tau }^{-}$ or light quarks and gluons). The mass of the lightest $CP$-odd Higgs boson is controlled by the soft-trilinear couplings, $A_{\lambda }(m_Z)$ and $A_{\kappa }(m_Z)$. We identify the region of parameter space where this situation occurs and discuss how natural this scenario is. It turns out that in order to achieve $m_a<2m_b$ with $A_{\lambda }(m_Z)$, $A_{\kappa }(m_Z)$ of order the typical radiative corrections, the required tuning of trilinear couplings needs not be larger than 5%–10%. Further, the necessity for this tuning can be eliminated in specific SUSY-breaking scenarios. Quite interestingly, $\mathrm{Br}(h\to aa)$ is typically above 70% in this region of parameter space and thus an appropriately large value requires no additional tuning.

• Received 5 January 2007

DOI:https://doi.org/10.1103/PhysRevD.75.075019