On the Forward-Backward Asymmetry of Leptonic Decays of $tbar{t}$ at the Fermilab Tevatron

We report on a study of the measurement techniques used to determine the leptonic forward-backward asymmetry of top anti-top quark pairs in Tevatron experiments with a proton anti-proton initial state. Recently it was shown that a fit of the differential asymmetry as a function of $q_{l}eta_{l}$ (where $q_{l}$ is the charge of the lepton from the cascade decay of the top quarks and $eta_{l}$ is the final pseudorapidity of the lepton in the detector frame) to a hyperbolic tangent function can be used to extrapolate to the full leptonic asymmetry. We find this empirical method to well reproduce the results from current experiments, and present arguments as to why this is the case. We also introduce two more models, based on Gaussian functions, that better model the $q_{l}eta_{l}$ distribution. With our better understanding, we find that the asymmetry is mainly determined by the shift of the mean of the $q_{l}eta_{l}$ distribution, the main contribution to the inclusive asymmetry comes from the region around $|q_{l}eta_{l}| = 1$, and the extrapolation from the detector-covered region to the inclusive asymmetry is stable via a multiplicative scale factor, giving us confidence in the previously reported experimental results.