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. 
C.P. Burgess, V. Di Clemente and J.R. Espinosa