Naturalness of scale-invariant NMSSMs with and without extra matter

Abstract

We present a comparative and systematic study of the fine-tuning in Higgs sectors in three scale-invariant next-to-minimal supersymmetric standard model (NMSSM) models: the first is the standard Z3-invariant NMSSM; the second is the NMSSM plus additional matter filling 3(5+5¯) representations of SU(5) and is called the NMSSM+; while the third model comprises 4(5+5¯) and is called the NMSSM++. Naively, one would expect the fine-tuning in the plus-type models to be smaller than that in the NMSSM since the presence of extra matter relaxes the perturbativity bound on λ at the low scale. This, in turn, allows larger tree-level Higgs mass and smaller loop contribution from the top squarks. However we find that LHC limits on the masses of sparticles, especially the gluino mass, can play an indirect, but vital, role in controlling the fine-tuning. In particular, working in a semiconstrained framework at the grand unified theory scale, we find that the masses of third generation top squarks are always larger in the plus-type models than in the NMSSM without extra matter. This is a renormalization group equation effect which cannot be avoided, and as a consequence the fine-tuning in the NMSSM+ (Δ∼200) is significantly larger than in the NMSSM (Δ∼100), with fine-tuning in the NMSSM++ (Δ∼600) being significantly larger than in the NMSSM+.