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We analyze the constraints imposed by Higgs vacuum stability on models withnew fermions beyond the Standard Model. We focus on the phenomenology of Higgscouplings accessible at the Large Hadron Collider. New fermions that affectHiggs couplings lead to vacuum instability of the Higgs potential. Above thescale of vacuum instability, bosonic states must stabilize the potential,implying a cut-off to the pure fermion model. Conservatively tuning the modelsto produce the maximal cut-off for a given Higgs coupling effect, we show thatobserving a deviation in the $Htt$, $H$-diphoton, or $H$-digluon coupling,larger than 20$%$, would require that new bosons exist in order to stabilizethe Higgs potential below about 100 TeV. For generic parameter configurations,and unless the new fermions are made as light as they can possibly be givencurrent experimental constraints, observing a 10$%$ deviation in any of thesecouplings would suggest an instability cut-off below 10-100 TeV. Similarly, ifnew bosons are absent up to a high scale, then a deviation in the $Hbb$ or$H\tau\tau$ coupling, larger than about 20$%$, should be accompanied by asizable deviation in the $Zbb$ or $Z\tau\tau$ couplings that can beconclusively tested with electroweak precision measurements at planned leptoncolliders.

Vacuum stability bounds on Higgs coupling deviations