The Minimal Scale Invariant Extension of the Standard Model

Abstract: We perform a systematic analysis of an extension of the Standard Model that includes a complex singlet scalar field and is scale invariant at the tree level. We call such a model the Minimal Scale Invariant extension of the Standard Model (MSISM). The tree-level scale invariance of the model is explicitly broken by quantum corrections, which can trigger electroweak symmetry breaking and potentially provide a mechanism for solving the gauge hierarchy problem. Even though the scale invariant Standard Model is not a realistic scenario, the addition of a complex singlet scalar field may result in a perturbative and phenomenologically viable theory. We present a complete classification of the flat directions which may occur in the classical scalar potential of the MSISM. After calculating the one-loop effective potential of the MSISM, we investigate a number of representative scenarios and determine their scalar boson mass spectra, as well as their perturbatively allowed parameter space compatible with electroweak precision data. We discuss the phenomenological implications of these scenarios, in particular, whether they realize explicit or spontaneous CP violation, neutrino masses or provide dark matter candidates. In particular, we find a new minimal scale-invariant model of maximal spontaneous CP violation which can stay perturbative up to Planck-mass energy scales, without introducing an unnaturally large hierarchy in the scalar-potential couplings.