Top Quark Mass Measurement from Dilepton Events at CDF II with the Matrix-Element Method
The CDF Collaboration
We describe a measurement of the top quark mass using events with two charged leptons collected by the CDF II detector from $p\overline{p}$ collisions with $\sqrt s = 1.96$ TeV at the Fermilab Tevatron. The likelihood in top quark mass is calculated for each event by convoluting the leading order matrix element describing $q\overline{q} \to t\overline{t} \to b\ell\nu_{\ell}\overline{b}\ell'\nu_{\ell'}$ with detector resolution functions. The presence of background events in the data sample is modeled using similar calculations involving the matrix elements for major background processes. In a data sample with integrated luminosity of 340 pb$^{-1}$, we observe 33 candidate events and measure $M_{top} = 165.2 \pm 6.1(stat.) \pm 3.4(syst.) \mathrm{~GeV}/c^2.$ This measurement represents the first application of this method to events with two charged leptons and is the most precise single measurement of the top quark mass in this channel. %%\input Author_List_Feb_2005.include % input author list
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\begin{document}

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\title{Top Quark Mass Measurement from Dilepton Events at CDF II with the Matrix-Element Method}

\input January_2006_Authors.include

%\author{The CDF Collaboration}
%\affiliation{URL: http://www-cdf.fnal.gov}


\begin{abstract}
We describe a measurement of the top quark mass using events with two charged leptons collected by the CDF II detector from $p\overline{p}$ collisions with $\sqrt s = 1.96$ TeV at the Fermilab Tevatron.  The likelihood in top quark mass is calculated for each event by convoluting the leading order matrix element describing $q\overline{q} \to t\overline{t} \to b\ell\nu_{\ell}\overline{b}\ell'\nu_{\ell'}$ with detector resolution functions.  The presence of background events in the data sample is modeled using similar calculations involving the matrix elements for major background processes. In a data sample with integrated luminosity of 340 pb$^{-1}$, we observe 33 candidate events and measure $M_{top} = 165.2 \pm 6.1(\textrm{stat.}) \pm 3.4(\textrm{syst.}) \mathrm{~GeV}/c^2.$  This measurement represents the first application of this method to events with two charged leptons and is the most precise single measurement of the top quark mass in this channel.
%%\input Author_List_Feb_2005.include  % input author list


\end{abstract}
\pacs{14.65.Ha, 13.85.Ni, 13.85.Qk, 12.15.Ff}
\maketitle 

\section{Introduction}
\input{intro.include}

\section{The CDF Detector}
\input{detector.include}

\section{Data Sample}
\label{sec:datasample}
\input{datasample.include}

\section{Analysis Overview}
\label{sec:method}
\input{method.include}

\section{Transfer Functions}
\label{sec:tfs}
\input{transferfuncs.include}

\section{Signal Likelihood}
\label{sec:signal}
\input{signallhood.include}

\section{Background Likelihoods}
\label{sec:bkgd}
\input{bglhood.include}

\section{Top Quark Mass Reconstruction}
\label{sec:massxtract}
\input{massextraction.include}


\section{Systematic Uncertainties}
\label{sec:syst}
\input{systematics.include}

\section{Measurement}
\label{sec:result}
\input{measurement.include}

\section{Conclusion}

We report the first application of a matrix-element based method to the measurement of the top quark mass in $t\overline{t}$ events containing two leptons.  We measure

\[ M_t = 165.2 \pm 6.1(\textrm{stat.}) \pm 3.4(\textrm{syst.}) \textrm{ GeV}/c^2,  \]

\noindent
which is the most precise determination to date of the top quark mass in dilepton events. This result is consistent with recent measurements of the mass in this channel at CDF using template methods,

\[ M_t = 170.1 \pm 6.0(\textrm{stat.}) \pm 4.1(\textrm{syst.}) \textrm{ GeV}/c^2 \textrm{~\cite{cdf2dilepprd}}, \]

\noindent with measurements in run I from CDF,

\[ M_t = 167.4 \pm 10.3(\textrm{stat.}) \pm 4.8(\textrm{syst.}) \textrm{ GeV}/c^2 \textrm{~\cite{cdfdilep}}, \]

\noindent and D\O,
\[ M_t = 168.4 \pm 12.3(\textrm{stat.}) \pm 3.6(\textrm{syst.}) \textrm{ GeV}/c^2 \textrm{~\cite{d0dilep}}. \]

This measured value is smaller than the current precision measurements of the mass in single lepton events,

\[ M_t = 173.5^{+3.7}_{-3.6} (\textrm{stat.}) \pm 1.3(\textrm{syst.}) \textrm{ GeV}/c^2 \textrm{~\cite{ljetsprl}}. \]

\noindent
A global combination of the most precise measurements~\cite{worldave}, however, suggests that current discrepancies are consistent with statistical fluctuations.

Extrapolating the use of the method to a future top quark dilepton data sample from the Tevatron corresponding to an integrated luminosity of $\int L dt = 4$ fb$^{-1}$, the expected statistical uncertainty of this technique in Monte Carlo experiments is 2.5 GeV$/c^2$, for $M_t = 178$ GeV$/c^2$. In this regime, uncertainty in the jet energy scale would be the dominant source of uncertainty.

\subsection*{Acknowledgments}

We thank the Fermilab staff and the technical staffs of the participating institutions for their vital contributions. This work was supported by the U.S. Department of Energy and National Science Foundation; the Italian Istituto Nazionale di Fisica Nucleare; the Ministry of Education, Culture, Sports, Science and Technology of Japan; the Natural Sciences and Engineering Research Council of Canada; the National Science Council of the Republic of China; the Swiss National Science Foundation; the A.P. Sloan Foundation; the Bundesministerium f\"ur Bildung und Forschung, Germany; the Korean Science and Engineering Foundation and the Korean Research Foundation; the Particle Physics and Astronomy Research Council and the Royal Society, UK; the Russian Foundation for Basic Research; the Comisi\'on Interministerial de Ciencia y Tecnolog\'{\i}a, Spain; in part by the European Community's Human Potential Programme under contract HPRN-CT-2002-00292; and the Academy of Finland.

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