CP Violating Bubble Wall Profiles

Abstract

We solve the equations of motion for a CP violating phase between the two Higgs doublets at the bubble wall of the MSSM electroweak phase transition. Contrary to earlier suggestions, we do not find indications of spontaneous ``transitional'' CP violation in the MSSM. On the other hand, in case there is explicit CP violation in the stop and chargino/neutralino sectors, the relative phase between the Higgses does become space dependent, but only mildly even in the maximal case. We also demonstrate that spontaneous CP violation within the bubble wall could occur, e.g., if the Higgs sector of the MSSM were supplemented by a singlet. Finally we point out some implications for baryogenesis computations.

Figures (3)

• Figure 1: The average value of $m_3^2$ versus $\mu$ and $A_t$. We observe that small values of $m_3^2$ are not typical in any part of the plane but are on the average more likely for small $\mu,A_t$, and that the distribution is wider (and thus more favourable) for like signs of $\mu,A_t$, as shown by the noisy contours obtained with a finite amount of statistics.
• Figure 2: The phase $\theta$ and its derivative $\theta'$ in the case of large explicit phases (see the text) for three sets of $m_A,\tan\!\beta$: $m_A=80$ GeV, $\tan\!\beta=2.0$ (solid); $m_A=120$ GeV, $\tan\!\beta=2.0$ (dashed); $m_A=120$ GeV, $\tan\!\beta=3.0$ (dot-dashed). We have $m_U =0$ GeV, $T_c\approx 100$ GeV.
• Figure 3: Spontaneous transitional CP violation in the bubble wall. A full solution with 5 fields is shown. The phase $\theta$ varies from a finite value in the symmetric phase to zero in the broken phase.