  The most precise measurements of the top quark mass are based on the Matrix
Element method. We present a detailed description of this analysis method,
taking the measurements of the top quark mass in final states with one and two
charged leptons as concrete examples. In addition, we show how the Matrix
Element method is suitable to reduce the dominant systematic uncertainties
related to detector effects, by treating the absolute energy scales for b-quark
and light-quark jets independently as free parameters in a simultaneous fit
together with the top quark mass. While the determination of the light-quark
jet energy scale has already been applied in several recent measurements, the
separate determination of the absolute b-quark jet energy scale is a novel
technique with the prospect of reducing the overall uncertainty on the top
quark mass in the final measurements at the Tevatron and in analyses at the LHC
experiments. The procedure is tested on Monte Carlo generated events with a
realistic detector resolution.
