The top quark mass, systematic limitations, and my tracker-driven measurements

Top quark mass measurements have achieved an unexpected level of accuracy in the last several years. This accuracy is only possible because of a new procedure that calibrates away the dominant jet energy uncertainty of past measurements. In this thesis I will give an overview of how these measurements are performed, and I will present some studies illustrating my suspicions that the calibration procedure is leading us to claim overly optimistic results. Additionally, I present my three measurements of the top quark mass that will be almost entirely independent of jet energies, and will thus serve as important cross checks of the standard measurements once enough statistics have been collected.;I perform my measurements of the top quark mass in the lepton plus jets channel with approximately 1.9 fb-1 of integrated luminosity collected with the CDF II detector using quantities with minimal dependence on the jet energies. One measurement exploits the transverse decay length of b-tagged jets to determine a top quark mass of 166.9+9.5-8.5 (stat) +/- 2.9 (syst) GeV/c2, and another the transverse momentum of electrons and muons from W decays to determine a top quark mass of 173.5+8.8-8.9 (stat) +/- 3.8 (syst) GeV/c2. I combine these quantities in a third, simultaneous mass measurement to determine a top quark mass of 170.7 +/- 6.3 (stat) +/- 2.6 (syst) GeV/ c2.