TOP MASS MEASUREMENT IN THE ALL HADRONIC CHANNEL WITH THE TEMPLATE METHOD
---- with Neural Net Selection ----
***** 1020 pb-1 *****

Authors (cdf-allhad6@fnal.gov)
A. Castro, F. Margaroli (Univ. of Bologna)


Dataset
    We are using for the data the multi-jet sample (1020pb-1). For the signal we are using mainly Monte Carlo tt events generated with Herwig and with the top mass between 150 and 200 GeV/c2. Other Monte Carlo samples generated with Pythia and Herwig under different conditions are used to study the systematic uncertainties on the mass measurement.


Pre-requisites (learn more from XSEC web page)
    For a minimal clean-up of the samples, we apply the follow pre-requisites:
    A) number of tight lepton = 0 (to guarantee the orthogonality with lepton+jets analysis);
    B) |Zjvert| < 60 cm;
    C) |Zjvert - Zpvert| < 5 cm;
    D) N(vert_class12) >= 1
    E) MET_significance < 3 (to guarantee the orthogonality with tau+jets analysis).


Topology (learn more from XSEC web page)
    F) 6 <= Njet <= 8;
    G) DeltaRmin >=0.5;

Neural Net Kinematical selection (learn more from XSEC web page)
11 Input variables+ 2 hidden nodes (20 and 10 nodes):
    1) SumEt; 2) SumEt3; 3) Aplanarity 4) Centrality; 5) M2jMin; 6) M2jMax; 7) M3jMin; 8) M3jMax; 9) Et1Star(=Et*sin^2\theta^*); 10) Et2Star; 11) <EtStar>3N(geometric average over the 3rd-4th...Nth jets);


Kinematic fitter
    For events with 6-to-8 jets we consider the 6 leading jets (highest in Et) and define a chi2 containing 2 dijet masses (set to be equal to the W mass), 2 triplet masses (set to be equal one to the other) and 6 terms representing the jet energy resolution. For each event with at least one b-tagged jet we consider all possible combinations where the tagged jets are assigned to b partons and keep the mass corresponding to the combination with the smallest chi2. Multiple masses are obtained for events with multiple tags because we consider only one tagged jet at a time to be assigned to the b partons. This is the case both for signal and background events since the data-driven background provides an inclusive (in terms o tags) estimate.


Data-driven background with a 3-dim Matrix (learn more from XSEC web page)
    This matrix is made starting from a sample with only 4 jets and using:
    1) 6 bins in Number of primary vertices
    2) 13 bins in Number of good tracks inside jets (with silicon hits)
    3) 5 bins in Et
    This matrix is used to obtain a prediction of the invariant mass distribution for background events, by weighting each event with the total tagging probability.
Invariant mass for different NN regions (eps)
Chi2 for different NN regions (eps)


Neural net selection and chi2 cut optimization
    We search the NNout cut and the chi2 cut which provide the smallest expected statistical uncertainty on the top mass: Stat uncertainty vs chi2 cut (after NNout>=0.91 cut) (eps)
The smallest uncertainty is reached for NNout>=0.91 and chi2<=16.

Template parametrization
The background template is parametrized with one gaussian and two gamma functions whose parameters depend linearly on the top mass. The expected contibution from tt events is removed.
    The signal templates are parametrized with two gaussian and a gamma functions whose parameters depend linearly on the top mass.
Signal templates (eps)
Background template (eps)

Likelihood fit
The expected uncertainty on the top mass depends slightly on the mass itself:
    We define a likelihood function which depends on the number of signal and background masses (one mass per tag) and on the corresponding probability density functions (templates) We then find the input top mass which maximizes the likelihood.Before applying this to the data we test the performance on a set of pseudo-experiments where we sum background and signal masses (for different input top masses) in the expected proportion. We study the linearity of the values returned by the fit with respect to the input values, the residuals and pulls of these values and see no bias in the measurement.
Linearity plot (eps)
Pull mean vs input mass (eps)
Residuals (Mfit-Min) vs input mass (eps)
Pull width vs input mass (eps)
Expected statistical uncertainty (eps)


The 1.02 fb-1 top mass measurement measurement
    The 1.02 fb-1 top mass measured in the all hadronic channel is:
    mt = 174.0 +- 2.2 (stat) +- 4.8 (syst) Gev/c2


Invariant mass for data, signal and background
Tags vs NNout (eps)
Expected and observed statistical uncertainties (eps)


Systematic uncertainties
Table 1
Source Systematics (GeV/c2)
Jet energy scale 4.5
generator 1.0
b-jet energy scale 0.5
PDF's 0.5
Background shape 0.5
background fraction 0.5
ISR 0.5
FSR 0.5
b-tag 0.5
MC statistics 0.1
Template parametrization 0.1
Total 4.8
Note: some of the uncertainties are very small so we quote the uncertainty on their values to be conservative.