Next-to-minimal supersymmetric model close to theR-symmetry limit and naturalness inh→aadecays forma<2mb

Abstract

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 $\mathrm{Br}(h\ensuremath{\rightarrow}aa)>.7$ and ${m}_{a}<2{m}_{b}$ (so that $a\ensuremath{\rightarrow}{\ensuremath{\tau}}^{+}{\ensuremath{\tau}}^{\ensuremath{-}}$ or light quarks and gluons). The mass of the lightest $CP$-odd Higgs boson is controlled by the soft-trilinear couplings, ${A}_{\ensuremath{\lambda}}({m}_{Z})$ and ${A}_{\ensuremath{\kappa}}({m}_{Z})$. 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 ${m}_{a}<2{m}_{b}$ with ${A}_{\ensuremath{\lambda}}({m}_{Z})$, ${A}_{\ensuremath{\kappa}}({m}_{Z})$ 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, $\mathrm{Br}(h\ensuremath{\rightarrow}aa)$ is typically above 70% in this region of parameter space and thus an appropriately large value requires no additional tuning.