Higgs sector CP violation in the Minimal Supersymmetric Model

We study the possibility that CP is spontaneously broken in the Minimal Supersymmetric Model when radiative corrections to the Higgs potential are included. We show that this can only occur if a light Higgs boson exists. Considering the recent ALEPH Higgs search, we exclude most of the parameter space of the model. The possibility of explicit CP violation in the model is also briefly discussed. It has been known for a long time that when supersymmetry (SUSY) is imposed on the two Higgs doublet model (THDM), tree-level flavor changing neutral currents and CP violation are simultaneously avoided in the Higgs sector [1] . Nevertheless, since SUSY must be softly broken, new terms in the Higgs potential can be induced by radiative corrections and CP non-conserving effects could show up in the Higgs sector. CP may be broken in two different ways: explicitly and spontaneously. In the first case, CP violation derives from complex scalar self-couplings induced by radiative corrections by sectors of the theory which violate CP. In the second case, a relative phase between the vacuum expectation values (VEVs) of the two Higgs doublets arises which spontaneously breaks the CP symmetry [2] . The purpose of this paper is to study the possibility that CP violation appears in one of these ways in the Higgs sector of the minimal supersymmetric model (MSSM). In such a case the CP-even and CP-odd neutral scalars would mix with each other giving rise to important phenomenological consequences [3] . It was recently pointed out [4] that spontaneous CP violation (SCPV) in the MSSM can occur. However, it is known that in order that radiative corrections can cause a spontaneous broken vacuum, a light scalar is required [5,6] . Therefore, an analysis of the physical spectrum, not carried out in ref. [4], is necessary in order to determine the viability of this model. Let Φ1 and Φ2 denote two Higgs doublets with hypercharges Y = 1. The most general renormalizable SU(2)L × U(1)Y gauge invariant two Higgs doublet potential is given by V (Φ1,Φ2) = m 2 1Φ † 1Φ1 +m 2 2Φ † 2Φ2 − (m 2 12Φ † 1Φ2 + h.c.) + λ1(Φ † 1Φ1) 2 + λ2(Φ † 2Φ2) 2 + λ3(Φ † 1Φ1)(Φ † 2Φ2) + λ4(Φ † 1Φ2)(Φ † 2Φ1) + 2 [ λ5(Φ † 1Φ2) 2 + h.c. ] + 1 2 [ Φ1Φ2{λ6(Φ † 1Φ1) + λ7(Φ † 2Φ2)}+ h.c. ] , (1) where by hermiticity only m12, λ5, λ6 and λ7 can be complex. Let us first consider the case where these parameters are real, ie. CP is not explicitly violated. After spontaneous symmetry breaking, the VEVs of the neutral components of the Higgs