Improving the tunings of the MSSM by adding triplets and singlet

We study an extension of the minimal supersymmetric standard model (MSSM) which includes both new SU(2) triplets with hypercharge +/-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 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 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.