Abstract
CP non-invariance is strongly limited by present experiments, while extra sources of CP-violation are needed for a successful baryogenesis. Motivated by those observations we consider a model which predicts spontaneous violation of CP at high temperature and restoration of CP at present temperature of the Universe. In addition we propose a dark matter (DM) candidate that meets all known properties of DM. Looking for a minimal model that satisfies the above conditions leads us to extending the Standard Model (SM) of fundamental interactions by adding a complex singlet scalar S. We impose the CP and Z2 symmetries on the scalar potential. With the complex vacuum expectation value of S at the temperature higher than the EW phase transition, the CP symmetry is spontaneously broken and a strong first-order electro-weak phase transition is easily realized. Introducing a dimension-6 effective operator that gives new complex contributions to the top quark mass, we show that it is easy to yield the observed baryon asymmetry in our Universe. On the other hand, the CP and Z2 symmetries are recovered after the EW phase transition so that the present strong constraints on CP violation can be satisfied and the lighter of ℜS or ℑS can be the dark matter candidate. By scanning the parameter space, we find regions where the model can explain the dark matter relic abundance and the baryon asymmetry simultaneously while satisfying all other experimental constraints. Finally, we discuss the explicit CP symmetry breaking in the scalar potential that can help dynamically eliminate the domains producing the negative baryon asymmetry. It is found that this can be achieved by a tiny explicit CP-violating phase of mathcal{O} (10−15).
Highlights
CP non-invariance is strongly limited by present experiments, while extra sources of CP -violation are needed for a successful baryogenesis
The EWPT can be of strongly first order, and, assisted by the effective operator O6, the CP symmetry is spontaneously broken at finite temperatures, both of which are of great importance to the successful EW baryogenesis
After the EWPT, the Z2 and CP symmetries are restored, so that a dark matter (DM) candidate arises as the lighter component of S which is stabilized by the Z2 symmetry, and the severe constraints on CP violations from low-energy electric dipole moment (EDM) measurements can be evaded
Summary
The extended scalar potential at zero temperature can be written as follows: V0(H, S) = λH. The total finite-temperature Lagrangian is Vtot = V0 + VT. It has recently been pointed out in ref. [52] by rewriting the finite-temperature potential as follows: Vtot λhs 4. (2.1) and (2.4) at T = 0, we can read off the critical temperature for the first-order EWPT. The advantage to introduce the critical-temperature Lagrangian in eq (2.4) is that it makes easier the analysis of the first-order EWPT. A further condition in eq (1.2) is needed to ensure the EWPT strong enough in order to suppress baryon number washout effects in the EW broken phase. For the purpose of illustration, we enforce these parameters to be |λ1,2,3, κ1,2| 5 [63]
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