Vacuum Stability and the Higgs Boson

The discovery of the Higgs boson at the LHC, and especially the determination of its mass around 125 GeV, together with the absence of any trace of new physics make it conceivable that we live in a metastable (but long-lived) electroweak vacuum. I will describe the state-of-the-art calculation that leads to this conclusion, elaborate on possible implications as well as cures of this instability of the Higgs potential and discuss some possible lines of attack for lattice studies of such metastability.Comment: 15 pages. Proceedings of the 31st International Symposium on Lattice Field Theory - LATTICE 201

Electroweak Baryogenesis with Cosmic Strings ?

I report on a critical analysis of the scenario of electroweak baryogenesis mediated by nonsuperconducting cosmic strings. This mechanism relies upon electroweak symmetry restoration in a region around cosmic strings, where sphalerons would be unsuppressed. I discuss the various problems this scenario has to face, presenting a careful computation of the sphaleron rates inside the strings, of the chemical potential for chiral number and of the efficiency of baryogenesis in different regimes of string networks. The conclusion is that the asymmetry in baryon number generated by this scenario is smaller than the observed value by at least 10 orders of magnitude.Comment: 5 pages, uses sprocl.sty. Talk given at SEWM98, Dec.98, Copenhage

A Fresh Look at the Calculation of Tunneling Actions including Gravitational Effects

Recently, the calculation of tunneling actions, that control the exponential suppression of the decay of metastable vacua, has been reformulated as an elementary variational problem in field space. This paper extends this formalism to include the effect of gravity. Considering tunneling potentials $V_t(\phi)$ that go from the false vacuum $\phi_+$ to some $\phi_0$ on the stable basin of the scalar potential $V(\phi)$, the tunneling action is the minimum of the functional $S_E[V_t]=6 \pi^2m_P^4\int_{\phi_+}^{\phi_0}(D+V_t')^2/(V_t^2D)d\phi$, where $D\equiv [(V_t')^2+6(V-V_t)V_t/m_P^2]^{1/2}$, $V_t'=dV_t/d\phi$ and $m_P$ is the reduced Planck mass. This one-line simple result applies equally to AdS, Minkowski or dS vacua decays and reproduces the Hawking-Moss action in the appropriate cases. This formalism provides new handles for the theoretical understanding of different features of vacuum decay in the presence of gravity.Comment: 12 pages in double-column format. 8 figures. Small changes, errata fixe

Resummation of Goldstone Infrared Divergences: A Proof to All Orders

The perturbative effective potential calculated in Landau gauge suffers from infrared problems due to Goldstone boson loops. These divergences are spurious and can be removed by a resummation procedure that amounts to a shift of the mass of soft Goldstones. We prove this to all loops using an effective theory approach, providing a compact recipe for the shift of the Goldstone mass that relies on the use of the method of regions to split soft and hard Goldstone contributions.Comment: 30 pages, 3 figure