
Search for Electroweak Single TopQuark Production using Neural Networks with 3.2 fb^{1} of CDF II data 
Dominic Hirschbühl, Jan Lück, Thomas Müller, Adonis Papaikonomou, Wolfgang Wagner, Jeannine WagnerKuhr 

KIT, Universität Karlsruhe 



Abstract  
Results  
Event Selection  
Neural Network Input Variables  
Templates for Combined Search  
Templates for Separate Search  
Systematic Uncertainties  
Expected Significance for Combined Search  
Binned Likelihood Fit to Data for Combined Search  
Binned Likelihood Fit to Data for Separate Search  
Observed Significance for Combined Search  
Variables in the 2Jets 1Tag highoutput region of the Combined Search  
To download a plot in .eps format, leftclick on the plot. To view a plot with full resolution in .gif format , rightclick and select "View Image." 
Abstract 
We report on a search for electroweak single topquark production with CDF II data corresponding to 3.2 fb^{1} of integrated luminosity. We apply neural networks to construct discriminants that distinguish between single topquark and background events. Two analyses are performed, assuming a topquark mass of 175 GeV/c^{2}. 
In the first one, we combine s and tchannel events to one single topquark signal under the assumption that the ratio of the two processes is given by the standard model (SM). The expected significance under the assumption of a SM crosssection is determined to be 5.2 σ (pvalue of 0.11 x 10^{6}). A binned likelihood fit to the data measures a single topquark production crosssection of 1.8_{0.6}^{+0.6} pb. The observed pvalue is 240.14 x 10^{6} which corresponds to a significance of 3.5 σ. 
In the second analysis, we separate the two single topquark production modes, namely s and tchannel. A binned likelihood fit done simultanously to twodimensional and onedimensional distributions of neural network outputs yields most probable values for the cross sections of 2.0_{0.6}^{+0.7} pb for the schannel and 0.7_{0.5}^{+0.5} pb for the tchannel production mode. 
Event Selection  
The CDF event selection exploits the kinematic features of the signal final state, which contains a top quark, a bottom quark, and possibly additional light quark jets. To reduce multijet backgrounds, the W boson originating from the top quark is required to decay leptonically. One therefore demands a single highenergetic electron (E_{T}(e) > 20 GeV) or muon (P_{T}(μ) > 20 GeV/c) and large missing transverse energy (MET > 25 GeV) from the undetected neutrino. 

The backgrounds belong to the following categories: Wbb, Wcc, Wc, Wqq (mistagged light quarks misidentified as heavy flavor jets), top pair production tt events (one lepton or two jets are lost due to detector acceptance), QCD (nonW multijet events where a jet is erroneously identified as a lepton), Z+jets and Diboson WW, WZ, and ZZ. We remove a large fraction of the backgrounds by demanding exactly two jets with E_{T }> 20 GeV and η < 2.8 be present in the event. At least one of these two jets has to be tagged as a bquark jet by using displaced vertex information from the silicon vertex detector (SVX). The QCD content of the selected dataset is further reduced by several requirements to MET, MET significance, transverse W boson mass, and several angles between the MET vector, lepton vectors and jet vectors. 
Neural Network Input Variables  
Using neural networks, kinematic or event shape variables are combined to a powerful discriminant. In the combined search we use four different networks in our analysis, one for the 2jet1tag category, one for 2jet2tag events, one for 3jet1tag events, and one for 3jets2tags. We devide each of the four categories into two separate channels, one containing triggered electrons and muons called Triggered Lepton Coverage (TLC), and the other containing muons from an Extended Muon Coverage (EMC) accepted through the MET + 2 jets trigger. For the separate search we include an additional network in the 2jet1tag category to build a 2D discriminant. This improves the apriori sensitivity for schannel of about 15%.  
One of the variables is the output of the KIT flavor separator. The KIT flavor separator gives an additional handle to reduce the large background components where no real b quarks are contained, mistags and charmbackgrounds. Both of them amount to about 50% in the W+2 jets data sample even after imposing the requirement that one jet is identified by the secondary vertex tagger of CDF. The following plots show the 14 variables for the TLC 2jet1tag channel. The plots in the third column show the variables in the 0 Tag sideband sample for modelling validation.

Expected Significance for Combined Search  
To compute the significance of a potentially observed signal, we perform a hypothesis test. Two hypotheses are considered. The first one, H_{0}, assumes that the singletop cross section is zero (β_{1} = 0) and is called the null hypothesis. The second hypothesis, H_{1}, assumes that the singletop production cross section is the one predicted by the standard model (β_{1} = 1). The objective of our analysis is to observe singletop, that means to reject the null hypothesis. The hypothesis test is based on the Qvalue, Q= 2(ln L_{red}(β_{1}=1)  ln L_{red}(β_{1}=0)) , where L_{red}(β_{1}=1) is the value of the reduced likelihood function at the standard model prediction and L_{red}(β_{1}=0) is the value of the reduced likelihood function for a singletop cross section of zero. Using the two ensemble tests the distribution of Qvalues is determined for the case with singletop included at the standard model rate, q_{1}, and for the case of zero singletop cross section, q_{0}. The two Qvalue distributions are shown below. In order to quantify the probability for the null hypothesis to be correct we define the pvalue, often also named 1CL_{b}. To quantify the sensitivity of our analysis we define the expected pvalue p_{exp} = p(Q_{1}^{me}^{d}) where Q_{1}^{me}^{d} is the median of the Qvalue distribution q_{1} for the hypothesis H_{1}. The meaning of p_{exp }is the following: Under the assumption that H_{1} is correct one expects to observe p_{exp} with a probability of 50%. We find p_{exp} = 0.11 x 10^{6}, including all systematic uncertainties. In other words, assuming the predicted singletop cross section, we expect, with a probability of 50%, to see at least that many singletop events that the observed excess over the background corresponds to a 5.2σ background fluctuation. 
Binned Likelihood Fit to Data for Separate Search  
The templates for all channels are fitted simultaneously in all eight channel to the observed distributions using a binned likelihood function. The fit yields a schannel single topquark production cross section of 2.0_{0.6}^{+0.7} pb for the schannel and 0.7_{0.5}^{+0.5} pb for the tchannel production mode. Below you find the resulting likelihood as a function of the s and tchannel cross section.

Observed Significance for Combined Search  
Variables in the 2Jets 1Tag highoutput region of the Combined Search  
By requirering a NN output above 0.8 (see inset of top figure) in the dominating TLC and EMC sample with 2 jets and 1 b tag, about 33 singletop and 32 background events are expected, yielding S/B=1; 49 events are observed. The bottom figures show the corresponding high NN output distributions of reconstructed top quark mass, the KIT flavor separator, and the product of the leptoncharge and the pseudorapidity of the light quark. 

Our single topquark results were approved (blessed) by CDF on Thursday 2/19/2009. 