SUSY-Yukawa Sum Rule at the LHC and the ILC

Abstract: In this talk, we discuss the SUSY-Yukawa sum rule, a relation among masses and mixing angles of the third-generation squarks which follows directly from the coupling relation responsible for canceling the quadratic divergence in the Higgs mass. Radiative corrections modify the sum rule, introducing dependence on a variety of SUSY parameters beyond the third-generation squark sector. If some of those parameters are measured experimentally, a sharp prediction for the sum rule is possible. We demonstrate this point with a quantitative study. We also discuss the prospects for measuring the ingredients of the sum rule at the LHC, and argue that a high-energy electron-positron collider such as the ILC would be necessary to test the sum rule.