have masses of order $\tilde{m}$. These states make a significant contribution to gauge coupling unification, and the color triplet states in $H, \bar{H}$ yield an interesting proton decay signal.

The $H \Sigma \bar{H}$ coupling is of order $\tilde{m}/\Lambda$, and hence leads to a negligible contribution to the Higgs quartic, which is dominated by the electroweak gauge contribution: $\lambda(\tilde{m}) 
\simeq 0.03\, (\tan^2\!\beta -1)^2$ for $|\tan^2\!\beta - 1| \ll 1$, where $\lambda$ is normalized such that $V(h) \supset (\lambda/2) 
(h^\dagger h)^2$, and the angle $\beta$ defines the combination of Higgs doublets that is fine-tuned light to become the SM Higgs. A value of $\tan^2\!\beta$ in the range of about $0.5$ to $2$ is sufficient to understand a small value of $\lambda(\tilde{m})$; however, in the limit that the Higgs mixing parameter (the Higgsino mass) $\mu$ becomes larger than $\tilde{m}$, $\tan^2\!\beta - 1 \sim O(\tilde{m}^2/\mu^2)$, so that $\lambda(\tilde{m})$ rapidly drops below $0.01$.[^1]

The organization of the rest of the paper is as follows. In Section \[sec:ISS\] we closely examine the running of the Higgs quartic coupling in the SM, and with the addition of a TeV-scale wino, to determine the range of $\mu_c$. In Section \[sec:model\] we introduce and study a specific simple $SU(5)$ 