Probing the top squark sector of the MSSM with the Higgs boson at the CERN LHC

We propose using the lightest $CP$-even Higgs boson in the minimal supersymmetric standard model to probe the stop sector. Unlike measuring stop masses in production/decay processes which requires knowledge of masses and mixing angles of other superparticles, our strategy depends little on supersymmetric parameters other than those in the stop sector in a large region of the parameter space. We show that measurements of the Higgs mass and the production rate in the gluon fusion channel, the dominant channel at the CERN LHC, allow for determination of two parameters in the stop mass-squared matrix, including the off-diagonal mixing term. This proposal is very effective when stops are light and their mixing is large, which coincides with the region where the electroweak symmetry breaking is minimally fine-tuned. We also argue that a lightest $CP$-even Higgs mass in the upper range of allowed values and a production rate significantly smaller than the rate predicted in the standard model would be difficult to reconcile within the minimal supersymmetric standard model, except in extreme corners of the parameter space.