Abstract
We propose a group theoretic condition which may be applied to extensions of the Standard Model in order to locate regions of parameter space in which the electroweak phase transition is strongly first order, such that electroweak baryogenesis may be a viable mechanism for generating the baryon asymmetry of the universe. Specifically, we demonstrate that the viable corners of parameter space may be identified by their proximity to an enhanced discrete symmetry point. At this point, the global symmetry group of the theory is extended by a discrete group under which the scalar sector is non-trivially charged, and the discrete symmetry is spontaneously broken such that the discrete symmetry relates degenerate electroweak preserving and breaking vacua. This idea is used to investigate several specific models of the electroweak symmetry breaking sector. The phase transitions identified through this method suggest implications for other relics such as dark matter and gravitational waves.
Highlights
Standard Model PT analyses rely on an intensive numerical parameter scan to search for SFOPT
We propose a group theoretic guideline which will aid the search for SFOPT in a large parameter space and help to identify why certain parametric limits are favored over others
We show U (φ), such as to make the discrete symmetry evident at the enhanced discrete symmetry point (EDSP)
Summary
Suppose that a given theory is exactly invariant under an internal discrete symmetry group G. There is no electroweak symmetry in this toy model, there is still a first order phase transition, and we can investigate the parametric dependence of its order parameter v(Tc)/Tc. Since v(Tc) = 2E/λ is independent of M 2, the order parameter can be maximized by varying M 2 to minimize Tc. Even though the high-temperature expansion breaks down when T drops below the mass of the fermion, the formal limit Tc → 0 can be taken assuming that the fermions are massless. Our group theoretic guideline leads us to identify the parametric region in the vicinity of the EDSP 1−α = 0 as favorable for SFOPT For this region to be truly viable, it must be the case that the rate at which bubbles of the broken phase nucleate is sufficiently large that the phase transition completes.
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