Evidence for Production of Single Top Quarks
using Bayesian Neural Networks

The DØ Collaboration

December 2006

Abstract

Using 0.9 fb^-1 of data collected from DØ, we apply Bayesian neural networks to separate single top quark signals from the background. We use the resulting discriminant outputs to measure the cross sections for single top quark production for the first time. The results are:

σ(p pbar -> tb + X) = 3.8 + 1.5 -1.5 pb
σ(p pbar -> tqb + X) = 3.7 + 2.0 -1.8 pb
σ(p pbar -> tb + X, tqb + X) = 5.0 + 1.9 -1.9 pb

Analysis Description

Bayesian Neural Networks

Neural networks (NN) are parameterized nonlinear functions for regression or classification modeling and is a familar technique in high energy physics. Neural networks, however, run into problems of overtraining which Bayesian neural networks do not. In the Bayesian approach one determines the posterior probability for every possible set of parameter values using Bayes' theorem. In classifying an event one then performs an average over all points weighted by this probability. We use the Flexible Bayesian Modeling (FBM) package, by Radford Neal.

The FBM package uses the Markov Chain Monte Carlo (MCMC) method to compute the posterior density. Using MCMC methods, a sample is generated where one steps through a parameter space in such a way that points are visited with a probability propertional to the density one needs to sample. Points where the posterior density is larage will be visited more often than points where this posterior density is small. The problem of moving through the network parameter space is re-cast as a problem of statistical mechanics, specifically, of a single particle moving through a potential.

Training

After dividing our dataset by lepton type (eletron or muon), our dataset was divided into one and two b-tagged jet events which were further separated into samples with two, three and four exclusive jets. 25 sensitive variables related to individual object kinematics, global kinematics, and variables based on angular correlations were used to train the network. The variable list was not optimized. The signal and background files were split into two different streams of samples. One was used for training the network and the other was used for measurement of yields. We trained on tb and tqb combined as our signal files and all other backgrounds (ttbar, W+jets, QCD) combined, according to their weights, as our background files for the twelve separate channels. The resulting filter functions, trained on tb and tqb combined, were used to discriminate against all single top (tb+tqb), the s-channel (tb), and the t-channel (tqb). We used 40 hidden nodes and ran on 250 Markov chain iterations. The final filter functions are extracted by averaging over the last 50 iterations.

Results

From 1D BNN output histograms, we calculate binned likelihood posterior densities for the single top production cross section for tb+tqb combined and for tb and tqb separately. Using the remaining samples, we get the following cross section measurements:

and posterior density distributions for tb, tqb, and tb+tqb:

We then use our data and make the following cross section measurements:

and posterior density distributions for tb, tqb, and tb+tqb:

Material for Talks

Electron	Filter Function	Efficiency	BNN Output	Muon	Filter Function	Efficiency	BNN Output
Electron One b-tag Two jets	jpg eps	jpg eps	jpg eps	Muon One b-tag Two jets	jpg eps	jpg eps	jpg eps
Electron One b-tag Three jets	jpg eps	jpg eps	jpg eps	Muon One b-tag Three jets	jpg eps	jpg eps	jpg eps
Electron One b-tag Four jets	jpg eps	jpg eps	jpg eps	Muon One b-tag Four jets	jpg eps	jpg eps	jpg eps
Electron Two b-tags Two jets	jpg eps	jpg eps	jpg eps	Muon Two b-tags Two jets	jpg eps	jpg eps	jpg eps
Electron Two b-tags Three jets	jpg eps	jpg eps	jpg eps	Muon Two b-tags Three jets	jpg eps	jpg eps	jpg eps
Electron Two b-tags Four jets	jpg eps	jpg eps	jpg eps	Muon Two b-tags Four jets	jpg eps	jpg eps	jpg eps

Variables

eps jpg

Expected Cross Sections

jpg eps

Measured Cross Sections