Musings on cosmological relaxation and the hierarchy problem - Jaeckel, Joerg; Mehta, Viraf M.; Witkowski, Lukas T. (Physical review, 2016)
Recently Graham, Kaplan and Rajendran proposed cosmological relaxation as a mechanism for generating a hierarchically small Higgs vacuum expectation value. Inspired by this we collect some thoughts on steps towards a solution to the electroweak hierarchy problem and apply them to the original model of cosmological relaxation [Phys. Rev. Lett. 115, 221801 (2015)]. To do so, we study the dynamics of the model and determine the relation between the fundamental input parameters and the electroweak vacuum expectation value. Depending on the input parameters the model exhibits three qualitatively different regimes, two of which allow for hierarchically small Higgs vacuum expectation values. One leads to standard electroweak symmetry breaking whereas in the other regime electroweak symmetry is mainly broken by a Higgs source term. While the latter is not acceptable in a model based on the QCD axion, in non-QCD models this may lead to new and interesting signatures in Higgs observables. Overall, we confirm that cosmological relaxation can successfully give rise to a hierarchically small Higgs vacuum expectation value if (at least) one model parameter is chosen sufficiently small. However, we find that the required level of tuning for achieving this hierarchy in relaxation models can be much more severe than in the Standard Model.