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already in the MSSM from top-stop loop but here we consider more general ϵ$_{3}$ which is not directly related to the stop mass. ϵ$_{3}$ can arise in the BMSSM if there is an extra U(1) and only H$_{u}$ is charged under the extra U(1). We do not discuss the detailed BMSSM model beyond TeV. Instead we will focus on the effective operators. ϵ$_{1}$ affects both the diagonal elements and the off-diagonal elements. ϵ$_{2}$ enters only in the diagonal entries. ϵ$_{4}$ affects only the off-diagonal elements. The dependence of CP even Higgs mass on BMSSM parameters can be read off from the two by two matrix. The one in the diagonal elements can increase the eigenvalues if it is positive. On the other hand the cancelation in the off- diagonal elements can reduce the level repulsion such that the lightest eigenvalue can be larger than before. Thus as long as the light CP even Higgs mass is concerned, the role of ϵ$_{2}$ and ϵ$_{4}$ are almost the same. 

Tree level mass of Charged Higgs is given by 

<img src='content_image/359955.jpg'>

ϵ$_{1}$ and ϵ$_{3}$ does not affect the relation between m$_{A}$ and m$_{H}$ ± . Sizable corrections to the MSSM relation between m$_{A}$ and m$_{H}$ ± are expected if ϵ$_{2}$ and/or ϵ$_{4}$ are sizable. As charged Higgs mass bound is stiff at around m$_{W}$ , i.e., it can not be much lighter than W boson mass, ϵ$_{2}$ and ϵ$_{4}$ are expected to be positive if sizable. In the following discussion, we mainly focus on the effects of ϵ$_{1}$ and ϵ$_{2}$ . The role of ϵ$_{4}$ is very similar to ϵ$_{2}$ as long as light CP even Higgs mass and charged Higgs mass are concerned. Only the impact on heavy CP even Higgs mass will be different and the phenomenological distinction is less clear. ϵ$_{3}$ is taken to be -0.1 in the following discussion. It can be achieved for very light stop or can be obtained with BMSSM operators. The origin of the operator is not the main concern of this paper. 

Higgs spectrum is shown in Fig. 1. In the plots, the CP odd Higgs mass is chosen to be 7 GeV. A few GeV difference in m$_{A}$ makes a little difference in CP even and charged Higgs mass spectrum. Two representative values of tan β (1.04 and 2) are chosen. When tan β is chosen to 1.04 (close to 1) (Fig. 1 (a)(b)(c)), the mass matrix of CP even Higgs has a special structure such that one of the eigenvalue is nearly constant ( M$_{Z}$ ). The transition point appears when the off-diagonal element is almost canceled by ϵ$_{1}$ . In the following discussion, we are interested in the region in which the off-diagonal element is positive after all. ( ϵ$_{1}$ > 0 . 04 in the plots.) Thus to reduce the light CP even mass to 80 GeV, we choose 

