Detailed Study of Gluino Decay into Third Generation Squarks at the CERN LHC

In supersymmetric models a gluino can decay into $tb\tilde{\chi}^{\pm}_1$ through a stop or a sbottom. The decay chain produces an edge structure in the $m_{tb}$ distribution. Monte Carlo simulation studies show that the end point and the edge height would be measured at the CERN LHC by using a sideband subtraction technique. The stop and sbottom masses as well as their decay branching ratios are constrained by the measurement. We study interpretations of the measurement in the minimal supergravity model. We also study the gluino decay into $tb\tilde{\chi}^{\pm}_2$ as well as the influence of the stop left-right mixing on the $m_{bb}$ distribution of the tagged $tb$ events.