Abstract
We consider the NMSSM extended to include one vector-like family of quarks and leptons. If (some of) these vector-like matter particles, as the Higgs doublets, have Yukawa couplings to the singlet S that exceed unity at about the same scale $\Lambda \lesssim 10^3$ TeV, this gives the order 40 % enhancement of the tree level Higgs boson mass required in the MSSM to reach 125 GeV. It is conceivable that the Yukawa couplings to the singlet S, although naively blowing up close to $\Lambda$, will not spoil gauge coupling unification. In such a case the unified coupling $\alpha_X$ could be interestingly led to a value not far from unity, thus providing a possible explanation for the number of generations. The characteristic signal is an enhanced resonant production of neutral spin zero particles at LHC, that could even explain the putative diphoton resonance hinted by the recent LHC data at 750 GeV.
Highlights
In the MSSM the tree-level prediction for the Higgs boson mass is MZ| cos 2β|
We consider the NMSSM extended to include one vector-like family of quarks and leptons. If these vector-like matter particles, as the Higgs doublets, have Yukawa couplings to the singlet S that exceed unity at about the same scale Λ 103 TeV, this gives the order 40% enhancement of the tree level Higgs boson mass required in the MSSM to reach 125 GeV
As we show in detail shortly, mixing with the singlet scalar leads to a physical Higgs mass somewhat less than mh0
Summary
We take the effective theory below Λ to be described by the scale invariant superpotential. The physical Higgs mass, as the entire scalar spectrum, crucially depends as well on the other dimensionless parameter appearing in the superpotential term (κ/3)S3. This same term is what prevents the vev vs of the field S from running to infinity. The renormalization of the S field leads to κ decreasing in the IR more rapidly than λH so that at the TeV scale it is typically smaller As such κ(1 TeV) takes a value that is sensitive to the boundary values and becomes a relevant parameter in the entire Higgs potential and Higgs spectrum. On λH (1 TeV) and κ(1 TeV) are denoted by λH and κ unless differently stated
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