Relaxion fluctuations (self-stopping relaxion) and overview of relaxion stopping mechanisms

Abstract

In implementations of the electroweak scale cosmological relaxation mechanism proposed so far, the effect of the quantum fluctuations of the homogeneous relaxion field has been ignored. We show that they can grow during the classical cosmological evolution of the relaxion field passing through its many potential barriers. The resulting production of relaxion particles can act as an efficient stopping mechanism for the relaxion. We revisit the original relaxion proposal and determine under which conditions inflation may no longer be needed as a source of friction. We review alternative stopping mechanisms and determine in detail the allowed parameter space for each of them (whether happening before, during and after inflation), also considering and severely constraining the case of friction from electroweak gauge boson production in models with large and Higgs-independent barriers.

The hierarchy problem of the Standard Model and its solutions

“…which can be trivially evaluated by making use of the superalgebra and the Baker- 18) so that the effect of a SUSY transformation on the coordinates is…”

“…Adding this condition to the stability one, one finds * It must and can not be totally independent from the initial conditions, because, as pointed out, the explicit mechanisms for positive and negative M 2 H,0 are completely distinct. A review on many of the CR models with distinct initial conditions for the Higgs mass parameter is given in [18]. out that (φ eq , M 2 H,SM ) must be an attractor point of the system.…”

“…that, while the equilibrium configurationφ eq is classically stable, it may not be so at the quantum level. As a consequence, the field φ can spread throughout many different minima of the potential and would thus create distinct vacua configurations in the universe [17,18]. But again, it is difficult to make precise statements, because tunnelling effects depend on numerous factors, e.g.…”

“…Having explored the general properties of CR models from the EFT point of view, we now proceed to study a particular realisation of it, the L + N relaxion model [17,18]. It will first be shown how to implement this model in terms of our previous discussion.…”

“…In the upcoming chapters four types of solutions to this problem are studied, of which three, Supersymmetry [11,12], Composite Higgs Models [13,14] and Twin Higgs models [15,16], are more traditional solutions based on the introduction of new symmetries. The fourth type of solution, named Cosmological Relaxation models [17,18], is much more recent and raises many questions regarding the nature of the Hierarchy Problem. The discussion of each of these solutions include: their motivations, the development of the theoretical framework with emphasis on how they solve the problem, implementation of their minimal realisation, and a brief analysis of the most relevant phenomenology and present experimental bounds.…”