Recent analysis shows that if the 125-126 GeV LHC resonance turns out to be the Standard Model Higgs boson, the electroweak vacuum would be a metastable state at 98% C.L. In this paper we argue that, during inflation, the electroweak vacuum can actually be very short-lived, contrary to the conclusion that follows from the flat spacetime analysis. Namely, in the case of a pure Higgs potential the electroweak vacuum decays via the Hawking-Moss transition, which has no flat spacetime analogue. As a result, the Higgs vacuum is unstable, unless the rate of inflation is low enough: H inf 10 9 −10 12 GeV. Models of inflation with such a low rate typically predict negligible tensor perturbations in the cosmic microwave background radiation (CMBR). This is also true for models in which the perturbations are produced by a curvaton field. We also find that if the effective curvature of the Higgs potential at a local maximum (which may be induced by inflaton-Higgs interactions) is large enough, then the decay of the electroweak vacuum is dominated by the Coleman-de Luccia transition. The electroweak vacuum is also short-lived in this case, due to a negative effective self-interaction coupling. Based on our analysis of Higgs vacuum stability during inflation, we conclude that the observation of tensor perturbations by the Planck satellite would provide strong indirect evidence for new physics beyond the Standard Model responsible for stabilisation of the electroweak vacuum.

The phonon Hall effect has been observed in the paramagnetic insulator, Tb3Gd5O12. A magnetic field applied perpendicularly to a heat current induces a temperature gradient that is perpendicular to both the field and the current. We show that this effect is due to resonant skew scattering of phonons from the crystal field states of superstoichiometric Tb 3+ ions. This scattering originates from the coupling between the quadrupole moment of Tb 3+ ions and the lattice strain. The estimated magnitude of the effect is consistent with experimental observations at T ∼ 5 K, and can be significantly enhanced by increasing temperature.PACS numbers: 72.20.Pa, 72.15.Gd When a linear magnetic field is applied perpendicularly to a heat current in a sample of terbium gallium garnet (TGG), Tb 3 Ga 5 O 12 , a transverse temperature gradient is induced in the third perpendicular direction 1,2 . This is the "phonon Hall effect (PHE)". The effect was observed in this insulator at low temperature (T ∼ 5 K), a situation in which there are no mobile charges such as electrons or holes 3 . The Neel temperature of TGG is 0.24 K 4 , so it is a paramagnet at T ∼ 5 K. Hence magnons do not contribute to the heat current and one does not expect a contribution from the magnon Hall effect 5-8 . Phonons are not charged and hence cannot be affected by the Lorentz force which gives rise to the usual classical Hall effect. Therefore the mechanism for the PHE must be related to the spin-orbit interaction. However, the spin-orbit interaction for phonons is not at all obvious, unlike in the anomalous Hall effect and spin Hall effect for electrons [9][10][11] . Thus, an understanding of the origin of the observed PHE is a fundamental problem.So far, there have been a few theoretical attempts to explain the PHE 12-15 . Refs. 12 and 13 assumed a Ramantype interaction between the spin of stoichiometric Tb 3+ ions and the phonon. This interaction results in "elliptically polarized" phonons. According to 12,13, the "elliptic polarization", in combination with scattering from impurities, leads to the PHE. In this scenario the type of impurity is unimportant and hence phonon -impurity scattering is considered in the leading Born approximation. This is an intrinsic-extrinsic scenario, i.e., the "elliptic polarization" is an intrinsic effect and the scattering from impurities is an extrinsic effect. The major problem with this scenario was realized in Ref. 14 -in spite of the "elliptic polarization" the Born approximation does not result in the PHE. Ref. 14 attempted to go beyond the leading Born approximation in impurity scattering. However, the problem has not been resolved yet. An intrinsic mechanism for the PHE, based on the Berry curvature of phonon bands, was suggested in Ref. 15. This is similar to the Berry curvature mechanism in the Hall effect for light 16 . The Berry curvature mechanism is certainly valid for materials with specially structured phonon bands, however, it is hard to see how the mechanism can be realized in TGG which has the simple...

The Standard Model electroweak vacuum has been found to be metastable, with the true stable vacuum given by a large, phenomenologically unacceptable vacuum expectation value ≈ M P . Moreover, it may be unstable in an inflationary universe. Motivated by the necessity of physics beyond the Standard Model and to accommodate non-zero neutrino masses, we investigate vacuum stability within type-II seesaw and left-right symmetric models. Our analysis is performed by solving the renormalisation group equations, carefully taking into account the relevant threshold corrections. We demonstrate that a phenomenologically viable left-right symmetric model can be constructed by matching it with the SM at one-loop. In both models we demonstrate the existence of a large area of parameter space where the Higgs vacuum is absolutely stable. arXiv:1305.7283v1 [hep-ph] 31 May 2013The presence of new physics modifies the Higgs potential at higher energies by changing the β-functions for the couplings, since we now include new particles running in loops when calculating radiative corrections. New bosonic particles provide a positive contribution to the running of the Higgs quartic coupling, whist new fermionic particles contribute negatively. Examples of this effect, as applied to the Higgs potential, were given in [6,7] where the presence of an additional scalar singlet, introduced below µ I , was found to preserve positivity of the quartic coupling up to the Planck scale.Whilst one can construct many different ad hoc new physics models to resolve the vacuum stability problem [8][9][10][11][12][13][14], we believe that models addressing other SM problems deserve primary consideration. In fact, empirically, we have firmly established evidence for physics beyond the SM: neutrino oscillations (and hence neutrino masses), dark matter and matter-antimatter asymmetry. Additional theoretical considerations based on the naturalness principle, such as the strong CP problem and the gauge hierarchy problem, also provide a hint of new physics beyond the SM. Amongst this evidence, neutrino mass is perhaps the most compelling, from a purely phenomenological point of view. Therefore, in this paper we analyse the effect of some models of neutrino mass generation upon stability of the Higgs vacuum.The rest of the paper is organised as follows. In the next section we briefly discuss the running of the Higgs quartic coupling in the SM and possible new physics which may affect this running at high energies. In Sec. 3 and 4 we present a thorough study of vacuum stability in the type-II seesaw and left-right symmetric models. Finally, in Sec. 5 the reader can find our conclusions. In Appendix A we provide details of the matching between MS and pole masses for the Higgs boson and top quark and values of the gauge couplings at the electroweak scale, while the relevant RGEs and β-functions are collected in Appendices B, C and D.