Improving the tunings of the MSSM by adding triplets and singlet

Abstract

We study an extension of the minimal supersymmetric standard model (MSSM) which includes both new $SU(2)$ triplets with hypercharge $\ifmmode\pm\else\textpm\fi{}1$ and a standard model gauge singlet (\`a la the next-to-minimal supersymmetric standard model [NMSSM]) which are coupled to each other. We are motivated by the little hierarchy problem, as well as by the $\ensuremath{\mu}$ problem of the MSSM. We show that the NMSSM and the triplet-extended MSSM can successfully solve problems of one another: while triplets are responsible for large correction to the lightest physical Higgs mass, the singlet's vacuum expectation value (VEV) explains why the $\ensuremath{\mu}$ terms (for the Higgs doublets and the new triplets) are naturally of order the electroweak (EW) scale. We also show that singlet-triplet coupling significantly changes the renormalization group evolution of the singlet mass squared, helping to render this mass squared negative, as required for the singlet to acquire a VEV. We analyze constraints on this scenario from EW precision measurements and find that a relatively large region of the parameter space of this model is viable, especially with the triplet fermions (including doubly charged) being light.