On the Spontaneous CP Breaking at Finite Temperature in a Nonminimal Supersymmetric Standard Model

TL;DR

The paper investigates spontaneous CP breaking (SCPB) at finite temperature in the NMSSM with a gauge singlet, focusing on whether SCPB during the electroweak phase transition can generate the baryon asymmetry, while avoiding large neutron EDM constraints. The authors compute the one-loop finite-temperature effective potential including Standard Model particles, stops, charginos, neutralinos, and charged and neutral Higgs bosons, with plasma effects and Debye (Daisy) resummation for bosons. Renormalization of the tree-level NMSSM potential shows that SCPB at $T=0$ requires specific conditions, but at finite temperature the dominant positive zero-temperature effect from the top/stop sector is countered by sizable negative Higgs-sector contributions, typically preventing SCPB inside the bubble; nevertheless within the bubble wall region at the tunneling temperature $T^*$ maximal SCPB can occur. The analysis finds that SCPB in the bubble wall can occur in parameter regions that satisfy experimental LEP bounds and EDM constraints at $T=0$, and only very tiny explicit CP-violating phases of order $10^{-6}$--$10^{-5}$ are needed to bias baryon-number production, while producing negligible neutron EDM. Thus, in the NMSSM, finite-temperature SCPB localized in the bubble wall offers a viable mechanism for electroweak baryogenesis without excessive fine-tuning.

Abstract

We study the spontaneous CP breaking at finite temperature in the Higgs sector in the Minimal Supersymmetric Standard Model with a gauge singlet. We consider the contribution of the standard model particles and that of stops, charginos, neutralinos, charged and neutral Higgs boson to the one-loop effective potential. Plasma effects for all bosons are also included. Assuming CP conservation at zero temperature, so that experimental constraints coming from, {\it e.g.}, the electric dipole moment of the neutron are avoided, and the electroweak phase transition to be of the first order and proceeding via bubble nucleation, we show that spontaneous CP breaking cannot occur inside the bubble mainly due to large effects coming from the Higgs sector. However, spontaneous CP breaking can be present in the region of interest for the generation of the baryon asymmetry, namely inside the bubble wall. The important presence of very tiny explicit CP violating phases is also commented.