Dynamical mechanism for ultra-light scalar Dark Matter

Assuming a double-well bare potential for a self-interacting scalar field, with the Higgs vacuum expectation value, it is shown that non-perturbative quantum corrections naturally lead to ultra-light particles of mass $\simeq10^{-23}$eV, if these non-perturbative effects occur at a time consistent with the Electroweak phase transition. This mechanism could be relevant in the context of Bose Einstein Condensate studies for the description of cold Dark Matter. Given the numerical consistency with the Electroweak transition, an interaction potential for Higgs and Dark Matter fields is proposed, where spontaneous symmetry breaking for the Higgs field leads to the generation of ultra-light particles, in addition to the usual Higgs mechanism. This model also naturally leads to extremely weak interactions between the Higgs and Dark Matter particles.Comment: 12 pages, includes the derivation of the effective potential suppressed by the volum

From N=1 to N=2 supersymmetries in 2+1 dimensions

Starting from N=1 scalar and vector supermultiplets in 2+1 dimensions, we construct superfields which constitute Lagrangians invariant under N=2 supersymmetries. We first recover the N=2 supersymmetric Abelian-Higgs model and then the N=2 pure super Yang-Mills model. The conditions for this elevation are consistent with previous results found by other authors.Comment: Reference adde

Concepts of Renormalization in Physics

A non technical introduction to the concept of renormalization is given, with an emphasis on the energy scale dependence in the description of a physical system. We first describe the idea of scale dependence in the study of a ferromagnetic phase transition, and then show how similar ideas appear in Particle Physics. This short review is written for non-particle physicists and/or students aiming at studying Particle Physics.Comment: 13 pages, qualitative introductio

Convexity at finite temperature and non-extensive thermodynamics

Assuming that tunnel effect between two degenerate bare minima occurs, in a scalar field theory at finite volume, this article studies the consequences for the effective potential, to all loop orders. Convexity is achieved only if the two bare minima are taken into account in the path integral, and a new derivation of the effective potential is given, in the large volume limit. The effective potential has then has a universal form, it is suppressed by the space time volume, and does not feature spontaneous symmetry breaking as long as the volume is finite. The finite temperature analysis leads to surprising thermal properties, following from the non-extensive expression for the free energy. Although the physical relevance of these results is not clear, the potential application to ultra-light scalar particles is discussed.Comment: 17 page

Inflaton in R-dependent potential

We consider a non-minimally coupled inflaton, in a higher order curvature background, leading to a potential which evolves with the curvature scalar of the Universe, and which describes two regimes. The first one is a de Sitter phase, where the potential is static, and an exact exponential solution is found for the inflaton. The second regime, triggered by the inflaton reaching a threshold, leads to a power-law expansion, during which the potential becomes flat, quickly enough for the inflaton never to reach the minimum of the initial symmetry breaking potential. This scenario is an alternative to the inflaton oscillating about a minimum of the potential, and where preheating is a consequence of the flattening of the potential during the power-law expanding phase