Vacuum Instabilities with a Wrong-Sign Higgs-Gluon-Gluon Amplitude

The recently discovered 125 GeV boson appears very similar to a Standard Model Higgs, but with data favoring an enhanced h to gamma gamma rate. A number of groups have found that fits would allow (or, less so after the latest updates, prefer) that the h-t-tbar coupling have the opposite sign. This can be given meaning in the context of an electroweak chiral Lagrangian, but it might also be interpreted to mean that a new colored and charged particle runs in loops and produces the opposite-sign hGG amplitude to that generated by integrating out the top, as well as a contribution reinforcing the W-loop contribution to hFF. In order to not suppress the rate of h to WW and h to ZZ, which appear to be approximately Standard Model-like, one would need the loop to "overshoot," not only canceling the top contribution but producing an opposite-sign hGG vertex of about the same magnitude as that in the SM. We argue that most such explanations have severe problems with fine-tuning and, more importantly, vacuum stability. In particular, the case of stop loops producing an opposite-sign hGG vertex of the same size as the Standard Model one is ruled out by a combination of vacuum decay bounds and LEP constraints. We also show that scenarios with a sign flip from loops of color octet charged scalars or new fermionic states are highly constrained.