Sparticle spectroscopy

We propose a program where measurements of sparticle masses at future accelerators such as the Large Hadron Collider and the Superconducting Super Collider determine $tan\beta$, the universal soft supersymmetry-breaking gaugino mass $m_{\frac{1}{2}}$, and the universal soft supersymmetry-breaking scalar mass $m_0$. This could be accomplished with the knowledge of three sparticle masses. If additional sparticle masses are not consistent with the derived values of $tan\beta$, $m_{\frac{1}{2}}$, and $m_0$, this could signal a gauge group with rank greater than that of the standard model. We explain how measurements of additional sparticle masses discriminate between different extensions of the standard-model gauge group. Other exotic physics such as additional Yukawa couplings, extra generation-dependent heavy gauge bosons, and nonuniversal supersymmetry breaking also leave imprints on the sparticle spectrum. We briefly address fine points in calculating sparticle masses and experimental prospects for determining sparticle masses.