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 $M_Z$.