New phenomena in the standard no-scale supergravity model

We revisit the no-scale mechanism in the context of the simplest no-scale supergravity extension of the Standard Model. This model has the usual five-dimensional parameter space plus an additional parameter $\xi_{3/2}\equiv m_{3/2}/m_{1/2}$. We show how predictions of the model may be extracted over the whole parameter space. A necessary condition for the potential to be stable is ${\rm Str}{\cal M}^4>0$, which is satisfied if $\bf m_{3/2}\lsim2 m_{\tilde q}$. Order of magnitude calculations reveal a no-lose theorem guaranteeing interesting and potentially observable new phenomena in the neutral scalar sector of the theory which would constitute a ``smoking gun'' of the no-scale mechanism. This new phenomenology is model-independent and divides into three scenarios, depending on the ratio of the weak scale to the vev at the minimum of the no-scale direction. We also calculate the residual vacuum energy at the unification scale ($C_0\, m^4_{3/2}$), and find that in typical models one must require $C_0>10$. Such constraints should be important in the search for the correct string no-scale supergravity model. We also show how specific classes of string models fit within this framework.