Contents
This likelihood method is the same one used in 1D top mass analysis. The fit function consists of a Gamma and two Gaussian probability density function whose parameters are linearly depended on the top width.
These overlayed top mass distributions show that the effect of lepton filter is very small.
Following histograms are the distributions of the top mass at the generatorlevel corresponding to various width. The top mass distribution falls off at 80 GeV/c^2 because the kinematic algoithm requires the invariant top mass to be greater than the sum of the invariant masses of two W bosons and the two b quarks, ensuring the top's decay to real W bosons. Moreover, the mean of the top mass shifts toward lower mass as the width increases due to the parton distribution function of ppbar. Since it is less likely to create partons with such a high energy that the probability of top mass being very large is small. So if there were no cut off at 80 GeV/c^2, the top mass distribution would have a longer tail at the lower energy and shifts the mean toward the lower side as the top width increases. In other words, the higher probability for smaller energy of ppbar results in a higher probability for light top quark production than heavy top quark produciton.
These are the top mass samples that pass the event selection cuts in the massAna fitter.
We use the kinematic chi2 fitter used in the Top Mass Template Method. This template method has been used at the CDF since runI, and it is a well established, standard chi^2 minimalization technique used in the top quark mass measurement. This template method is described in detail in cite{prd}.
In the template method, the four leading jets are assumed to correspond to the four partons from the ttbar decay chain to reconstruct a top mass. In the chi^2 fitter used in the template method, both sets of W decay daughters are constrained to have the invariant mass of the W boson, and both Wb states are constrained to have the same mass. This implies that the W mass have a significant effect on the chi^2 values. The ambiguity arising from the different ways of assigning the jets to the four quarks is resolved by selecting the assignment with the lowest chi^2, taking into account the btagging information. We perform a chi^2 minimization to fit the parton momenta from the ttbar daughters. Furthermore, we constrain m_{t} and m_{tbar} to be the same within the decay width of 1.5 GeV, produing one m_{t}^{reco} for each event.
Furthermore, by applying a chi^2 cut, we can select events with low chi^2 values, and consequently events where the mass of t and tbar are close. However, we lose information of events with large mass difference between ttbar with this chi^2 cut.

On the left is the top mass distributions consisting of signal (yellow) and wbb2p background(blue). The right plots are mean and rms of the distributions as functions of top width. The red lines indicate the values from signal distribution and the blue lines indicate the values from signal and background added.



