Naturalness Re-examined: Implications for Supersymmetry Searches

We discuss the origin of "focus points" in the scalar mass RGEs of the MSSM and their implications for collider searches. We present a new exact analytic solution to the homogeneous system of scalar mass RGEs in the MSSM for general $\tan\beta$. This is then used to prove that the focus point for $m^2_{H_u}$ depends only on the value of the top Yukawa coupling at the {\em weak} scale (not its value at the GUT scale) and is independent of the bottom Yukawa coupling.