Constraints on Trilinear Coupling Constant A_0 in minimal Supergravity Model

Constraints on the common trilinear coupling constant $A_0$ are obtained in the minimal supergravity model. $A_0$ is usually given at GUT scale $M_X$ by-hand, and has been regarded as one of the five arbitrary parameters in this model. However, $B(M_Z)$ as the common bilinear coupling constant $B$ at the electroweak scale $M_Z\simeq 91$(GeV) is fixed by the shape of the Higgs potential. With the renormalization group equations, this $B(M_Z)$ is evolved to $B_0$ at $M_X$ where a well-known relation exists between the evolved $B_0$ and $A_0$ as $B_0=(A_0-1)m_0$. Therefore, $A_0$ is fixed as a function of the other arbitrary parameters. In other words, the number of arbitrary parameters are reduced by this method. Additionally, large $\tan \beta >40$ is forbidden by the conditions at $M_Z$.