Next-to-minimal supersymmetric model close to the R-symmetry limit and naturalness in h → aa decays for ma < 2mb

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 Br(h -> aa)>.7 and m(a)< 2m(b) (so that a ->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, Br(h -> aa) is typically above 70% in this region of parameter space and thus an appropriately large value requires no additional tuning.