Test of Analysis Method for Top-Antitop Production and Decay Events

We have carried out Monte Carlo calculations on two sets of randomly generated QCD events due to $p\bar{p} \to t \bar{t}$ with top mass $m_t = 170$ GeV, one set leading to $e^+e^-$ or $e^{\pm}\mu^{\mp}$ or $\mu^+\mu^-$ 2jets (dilepton) and the other leading to $e^{\pm}$ or $\mu^{\pm}$ 4jets (unilepton) configurations, in order to test the likelihood methods we have proposed for determining the top mass by analyses of these two sets of configurations. For the set of unilepton events, our method gives a very efficient and quite sharp measure of the top mass lying several GeV below the input mass. For the dilepton set, our method gives a much broader and markedly asymmetric distribution for the top mass estimates, 75% of them lying below 170 GeV, but the dilepton data will have much lower background than unilepton data. We then illustrate these methods by applying them to the data available from CDF in 1995 and discuss the results obtained in relation to the results for the sets of Monte Carlo events. The dilepton events yield masses spread widely, over 140 to 180 GeV, generally lower than the unilepton events, which cluster around $175\pm 8$ GeV. In an appendix, we discuss the nature of the additional ``slow'' $\mu^{+}$ observed in one CDF dilepton event, concluding that it is most probably a ``tertiary lepton'' resulting from the decay sequence $b\to c + hadrons$, followed by $c\to s \mu^{+} \nu$.