Effective operators and vacuum instability as heralds of new physics

For a light enough Higgs boson, the effective potential of the Standard Model develops a dangerous instability at some high energy scale, Lambda, signalling the need for new physics below that scale. On the other hand, a typical low-energy remnant of new physics at some heavy scale, M, is the presence of effective non-renormalizable operators (NROs), suppressed by powers of 1/M. It has been claimed that such operators may modify the behaviour of the effective potential, in such a way as to significantly lower the instability scale. We critically reanalyze the interplay between non-renormalizable operators and vacuum instabilities and find that, contrary to these claims, the effect of NROs on instability bounds is generically small whenever it can be reliably computed.