Assuming that the particle with mass ∼ 126 GeV discovered at LHC is the Standard Model Higgs boson, we find that the stability of the EW vacuum strongly depends on new physics interaction at the Planck scale MP , despite of the fact that they are higher-dimensional interactions, apparently suppressed by inverse powers of MP . In particular, for the present experimental values of the top and Higgs masses, if τ is the lifetime of the EW vacuum, new physics can turn τ from τ >> TU to τ << TU , where TU is the age of the Universe, thus weakening the conclusions of the so called meta-stability scenario.Introduction.-When the particle with mass ∼ 126 GeV discovered at LHC [1, 2] is identified with the Standard Model (SM) Higgs boson, serious and challenging questions arise. Among them, the vacuum stability issue. The Higgs effective potential V ef f (φ) bends down for values of φ larger the EW minimum, an instability due to top loop-corrections. By requiring stability, lower bounds on the Higgs mass M H were found [3][4][5][6][7][8][9].A variation on this picture is the so called metastability scenario [4,[10][11][12]. For φ much larger than v (location of the EW minimum), V ef f (φ) develops a new minimum at φ

If the Standard Model (SM) is valid up to extremely high energy scales, then the Higgs potential becomes unstable at approximately 10 11 GeV. However, calculations of the lifetime of the SM vacuum have shown that it vastly exceeds the age of the Universe. It was pointed out by two of us (VB,EM) that these calculations are extremely sensitive to effects from Planck scale higher-dimensional operators and, without knowledge of these operators, firm conclusions about the lifetime of the SM vacuum cannot be drawn. The previous paper used analytical approximations to the potential and, except for Higgs contributions, ignored loop corrections to the bounce action. In this work, we do not rely on any analytical approximations and consider all contributions to the bounce action, confirming the earlier result. It is surprising that the Planck scale operators can have such a large effect when the instability is at 10 11 GeV. There are two reasons for the size of this effect. In typical tunneling calculations, the value of the field at the center of the critical bubble is much larger than the point of the instability; in the SM case, this turns out to be numerically within an order of magnitude of the Planck scale. In addition, tunneling is an inherently non-perturbative phenomenon, and may not be as strongly suppressed by inverse powers of the Planck scale. We include effective Φ 6 and Φ 8 Planck-scale operators and show that they can have an enormous effect on the tunneling rate.

The possibility that new physics beyond the Standard Model (SM) appears only at the Planck scale M P is often considered. However, it is usually assumed that new physics interactions at M P do not affect the electroweak vacuum lifetime, so the latter is obtained neglecting these terms. According to the resulting stability phase diagram, for the current experimental values of the top and Higgs masses, our universe lives in a metastable state (with very long lifetime), near the edge of stability. However, we show that the stability phase diagram strongly depends on new physics and that, despite claims to the contrary, a more precise determination of the top (as well as of the Higgs) mass will not allow to discriminate between stability, metastability or criticality of the electroweak vacuum. At the same time, we show that the conditions needed for the realization of Higgs inflation scenarios (all obtained neglecting new physics) are too sensitive to the presence of new interactions at M P . Therefore, Higgs inflation scenarios require very severe fine tunings that cast serious doubts on these models.