Implications of a Light Stop for the Spontanous CP Breaking at Finite Temperature in a Nonminimal Supersymmetric Model

We study the implications of a light stop for the spontaneous CP breaking at finite temperature in the Higgs sector of the Minimal Supersymmetric Standard Model with a gauge singlet. Assuming CP conservation at zero temperature, we show that the presence of a large mixing between the leftand the right-handed stops can trigger easily the spontaneous breaking of CP inside the bubbles nucleated during the electroweak phase transition. This allows to avoid the fine-tuning among the vacuum expectation values in the region of interest for the generation of the baryon asymmetry, namely the bubble walls, which has been recently analized. Email: [email protected] 2 Email:[email protected] On leave of absence from International School for Advanced Studies (ISAS), Trieste, Italy; Email:[email protected] The generation of the baryon asymmetry in the Universe (BAU) requires three basic ingredients [1]: baryonic violating interactions, departure from thermal equilibrium and C and CP violation. Anomalous electroweak processes are known to provide the source of B violation [2], whereas the departure from thermal equilibrium can occur if the electroweak phase transition (EWPT) is of the first order and proceeds via bubble nucleation. These considerations make the possibility of generating the BAU during the electroweak phase transition very appealing [3]. As far as the CP violation is concerned, it is still an open question if the necessary amount of CP violation to produce enough baryon asymmetry is present in the standard model [4]. In the minimal supersymmetric extension of the standard model (MSSM) [5] the requirement that explicit CP violating phases provide the necessary amount of CP violation necessary for the generation of the BAU gives rise to additional strong constraints on the parameter space of the model [6]. Spontaneous CP breaking (SCPB) in the Higgs sector can be triggered by radiative corrections [7] at zero temperature. Nevertheless, as predicted by Georgi and Pais [8], it requires the existence of a pseudoscalar Higgs boson with a mass of a few GeV [9], which has been ruled out by LEP [10]. When finite temperature effects are considered, even if SCPB in the MSSM during the EWPT can occur in a wide region of the parameter space [11, 12] it requires as a general tendency small values of the mass of the pseudoscalar Higgs boson, whereas recent results on the phase transition in the MSSM [13] seem to point towards the opposite direction in order not to wash out the generated baryon asymmetry. Very recently, the question of SCPB at finite temperature in the MSSM with a gauge singlet, the so-called next-to-minimal supersymmetric standard model (NMSSM) [14], has been addressed [15] in the case of negligible left-right mixing in the stop sector. Assuming CP conservation at zero temperature and including the contributions to the one-loop effective potential both of the standard model particles and of the supersymmetric ones, it has been shown that SCPB in the broken phase (i.e. inside the bubbles nucleated during the EWPT) is prevented by two main reasons: large plasma effects in the Higgs sector and the great reduction at finite temperature of the large one-loop corrections coming from the top-stop sector at zero temperature when both the stops present in the spectrum are nearly degenerate (i.e. negligible left-right mixing) and with a mass of order of the critical