Investigation of the structure of the Standard Model effective potential at very large field strengths opens a window towards new phenomena and can reveal properties of the UV completion of the SM. The map of the lifetimes of the vacua of the SM enhanced by nonrenormalizable scalar couplings has been compiled to show how new interactions modify stability of the electroweak vacuum. Whereas it is possible to stabilize the SM by adding Planck scale suppressed interactions and taking into account running of the new couplings, the generic effect is shortening the lifetime and hence further destabilisation of the SM electroweak vacuum. These findings have been illustrated with phase diagrams of modified SM-like models. It has been demonstrated that stabilisation can be achieved by lowering the suppression scale of higher order operators while picking up such combinations of new couplings, which do not deepen the new minima of the potential. Our results show the dependence of the lifetime of the electroweak minimum on the magnitude of the new couplings, including cases with very small couplings (which means very large effective suppression scale) and couplings vastly different in magnitude (which corresponds to two different suppression scales).

Spontaneous breaking of quantum scale invariance may provide a solution to the hierarchy and cosmological constant problems. In a scale-invariant regularization, we compute the two-loop potential of a higgs-like scalar φ in theories in which scale symmetry is broken only spontaneously by the dilaton (σ). Its vev σ generates the DR subtraction scale (µ ∼ σ ), which avoids the explicit scale symmetry breaking by traditional regularizations (where µ=fixed scale). The two-loop potential contains effective operators of non-polynomial nature as well as new corrections, beyond those obtained with explicit breaking (µ=fixed scale). These operators have the form: φ 6 /σ 2 , φ 8 /σ 4 , etc, which generate an infinite series of higher dimensional polynomial operators upon expansion about σ ≫ φ , where such hierarchy is arranged by one initial, classical tuning. These operators emerge at the quantum level from evanescent interactions (∝ ǫ) between σ and φ that vanish in d = 4 but are demanded by classical scale invariance in d = 4 − 2ǫ. The Callan-Symanzik equation of the two-loop potential is respected and the two-loop beta functions of the couplings differ from those of the same theory regularized with µ =fixed scale. Therefore the running of the couplings enables one to distinguish between spontaneous and explicit scale symmetry breaking. *

We study domain walls which can be created in the Standard Model under the assumption that it is valid up to very high energy scales. We focus on domain walls interpolating between the physical electroweak vacuum and the global minimum appearing at very high field strengths. The creation of the network which ends up in the electroweak vacuum percolating through the Universe is not as difficult to obtain as one may expect, although it requires certain tuning of initial conditions. Our numerical simulations confirm that such domain walls would swiftly decay and thus cannot dominate the Universe. We discuss the possibility of detection of gravitational waves produced in this scenario. We have found that for the standard cosmology the energy density of these gravitational waves is too small to be observed in present and planned detectors. *

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