TOP PAIR PRODUCTION CROSS-SECTION MEASUREMENT IN THE ALL-HADRONIC CHANNEL AT CDF AND D\O
\footnotesize DANIEL WICKE
Measurements of the {$t\bar t$} production cross-section at $\sqrt{s} = 1.96$~TeV in proton-antiproton collisions were performed by the CDF and D\O\ collaborations using $t\bar t$ final states where both $W$'s decay hadronically. Each experiment uses luminosity of about 160~pb$^{-1}$ of data collected during Run II of the Fermilab Tevatron collider. Beside kinematical observables both experiments take advantage of identifying $b$~jets based on lifetime tagging. While CDF counts the number of $b$-tags over background after a cut based analysis, D\O\ counts the excess of events after a neural network based kinematical selection and requiring a $b$-tagged jet. CDF obtains $\sigma_{t\bar t}=7.8\pm2.5_\mathrm{stat}~^{+4.7}_{-2.3} \,_\mathrm{syst}$; ~~D\O\, $\sigma_{t\bar t}=7.7~^{+3.4}_{-3.3}\,_\mathrm{stat}~^{+4.7}_{-3.8} \,_\mathrm{syst}\pm0.5 \,_\mathrm{lumi}$. \keywords{top; cross-section; Tevatron.}
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\begin{document}

\markboth{Daniel Wicke}
{Top Pair Production Cross-Section in the All-Hadronic Channel}

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\title{TOP PAIR PRODUCTION CROSS-SECTION MEASUREMENT IN THE ALL-HADRONIC CHANNEL AT CDF AND D\O}

\author{\footnotesize DANIEL WICKE}


\address{Fermilab, P.O. Box 500\\
Batavia, Illinois 60510,
USA\footnote{on leave of absence from Bergische Universit\"at Wuppertal}\\[1.4mm]
\em on behalf of the CDF and the D\O\ Collaborations
}

\maketitle

\pub{%$Revision: 1.13.2.1 $ 
~}{~}

\begin{abstract}
Measurements of the {$t\bar t$} production cross-section at 
$\sqrt{s} = 1.96$~TeV in proton-antiproton collisions were performed by the CDF and
D\O\ collaborations using $t\bar t$ final states where both $W$'s decay
hadronically. Each experiment uses luminosity of about 160~pb$^{-1}$ of data
collected during Run II of the Fermilab Tevatron collider. Beside kinematical
observables both experiments take advantage of identifying $b$~jets based on
lifetime tagging. While CDF counts the number of $b$-tags over background
after a cut based analysis, D\O\ counts the excess of events after a neural
network based kinematical selection and requiring a $b$-tagged jet.

CDF obtains
$\sigma_{t\bar t}=7.8\pm2.5_\mathrm{stat}~^{+4.7}_{-2.3} \,_\mathrm{syst}$;
~~D\O\,
$\sigma_{t\bar t}=7.7~^{+3.4}_{-3.3}\,_\mathrm{stat}~^{+4.7}_{-3.8} \,_\mathrm{syst}\pm0.5 \,_\mathrm{lumi}$.
\keywords{top; cross-section; Tevatron.}
\end{abstract}

\section{Introduction}
The  measurement of the $t\bar t$  cross-section is an important cross check of our
understanding of the top-production mechanism and of the completeness of its
decay modes. Such measurements are performed  in the ``dilepton'', the
``lepton+jets'' and the ``all hadronic'' decay channel, which are named after 
the decays of the $W$'s, because in the Standard Model the top almost always decays to a
$b$ and a $W$. 

This note summarises the measurements done in the ``all hadronic'' channel 
by CDF\cite{cdfnote7075} and D\O\cite{d0note4428} 
in $p\bar p$-collisions at $\sqrt{s}=1.96\TeV$.
This channel has the highest branching ratio
of $44\%$, however, it suffers from an
overwhelming background from light quark pair-production which has many orders
of magnitude higher cross-section. The additional jets faking the hadronically
decaying $W$'s stem from hard gluon radiation and splitting.

Following the pieces of the master formula for cross-section measurements
\begin{equation}
\sigma_{t\bar t}=\frac{N-B}{\varepsilon  {\cal L}\cdot\mathrm{BR}}
\label{eq:xsec_master}
\end{equation}
first the selection of signal events in this environment,
then the background and the efficiency determination are discussed.
The branching ratio, BR, is taken from standard model predictions\cite{Berger:1997gz,Bonciani:1998vc,Kidonakis:2003qe}.
Luminosity measurements for CDF and D\O\ are discussed elsewhere\cite{Acosta:2001zu,d0lumi}.

\section{Signal Selection}
\subsection{Trigger and Preselection}
At $p\bar p$ colliders signal selection begins with the trigger. 
To select all hadronic $t\bar t$ events CDF and D\O\ require 4 clusters
with a transverse energy above $15\GeV$ and $12\GeV$, respectively. 
CDF in addition requires a minimal
value for the scalar sum of all transverse momenta $H_T\ge125\GeV$, while D\O\
asks the two hardest jets to have $p_T>25\GeV$ and the third jet 
$p_T>15\GeV$.
%*very similar*

Both experiments confirm their trigger selection with offline objects and 
veto on isolated high $p_T$ leptons to keep the analyses orthogonal to
their measurements in the other channels.
While D\O\ continues with 6 or more jet
events CDF keeps the 4 jet events for calibration in the background
determination.

Both experiments work with an integrated luminosity of around $160\ipb$.

\subsection{Final Signal Selection}
General kinematic observables can distinguish between $t\bar t$-signal
and multi-jet background. Top events are expected on average to
have a larger overall energy scale and harder sub-leading jets. Their shape is
expected to be more spherical and less planar. Their rapidity
distribution is more central than that of light quark production.

\subsubsection{Kinematic Observables}
To select signal events CDF uses 
the sum of all transverse momenta, $H_T$, the sum of the transverse momenta
without the two leading jets, $H_T^{\mathrm{3j}}$, Aplanarity and Centrality
for the signal selection. 

D\O\ uses in addition  $\sqrt{s}$, the geometric
mean of the 5th and 6th jets $E_T$, $E_{T_{5,6}}$, the $E_T$ weighted number
of jets, $N^A_{\mathrm{jets}}$,
Sphericity and a momentum weighted rapidity moment, $\left<\eta^2\right>$.
D\O\ also exploits observables obtained from assuming a $t\bar t$-event and
reconstructing the decay chain. The consistency of the reconstructed $W$-
and $t$-masses with the known values, the invariant $t \bar t$-mass, the
invariant $WW$-mass as well as the highest and the second highest dijet-mass 
are considered.

\subsubsection{$B$-Tagging}
Besides the kinematic properties the presence of $b$-jets in $t\bar t$-events 
is an important feature that is used in the signal selection.
%
Both CDF and D\O\ are equipped with silicon vertex detectors which are used to 
reconstruct displaced secondary vertices stemming from $B$-decays. 
Such secondary vertices are reconstructed using tracks belonging to a jet of
interest. The significance of the displacement of the secondary vertex
from the primary vertex is used to decide whether the jet originates from a $b$-quark.
CDF requires a significance of 3, D\O\ one of 7 to call a jets \em $b$-tagged\em.

\subsubsection{Cut Procedures}
To have optimal cuts in the presence of correlated observables D\O\ uses a
series of neural networks (NN) for the selection. A first neural net (NN0) uses a subset of
kinematic information to perform a final step of loose preselection.
Then one $b$-tag is required. The next NN combines all kinematic observables 
into a single number which is then fed into the final neural net (NN2) which includes the
reconstructed top-properties. After cutting on the output of NN2 D\O\
\em selects 220 events\em.

CDF uses straight cuts in which a linear combination of Aplanarity and
$H_T^{\mathrm{3j}}$  is used to find an optimal cut for these correlated
observables. After the kinematic cuts CDF \em counts 326 $b$-tags \em.


\section{Background Estimation}
Both experiments estimate their background contribution directly from data
by removing the actual $b$-tag and instead weighting the events with the probability
of a random event to be $b$-tagged, the so called Tag Rate Function (TRF).
To provide a background estimate, the TRFs must be measured on background samples.

CDF uses the 4-jet events after the preselection to measure their TRF
as function of $p_T$, $\eta$, number of tracks at the primary vertex, total
number of tracks and Aplanarity.
%
D\O\ uses all preselected events (after NN0) and parametrises the TRF as
function of $p_T$ and $\eta$ in 4 bins of $H_T$.

The validity of the TRFs is checked by comparing distributions obtained by
applying the TRF on the data with those obtained using the actual $b$-tag.

From these studies CDF expects $264.7\pm17.2$ background \em tags \em
thus claiming 61 surplus $b$-tags.
D\O\ expects $186\pm14.8$ background events, i.e. sees an excess of 34 events.
The uncertainties are obtained by repeating the analysis with TRFs obtained
from samples with varied selection cuts.

\section{Efficiency Determination}
The efficiency for the $t\bar t$ signal to survive the applied cuts is obtained from
$t\bar t$ simulation. The obtained total efficiencies are $ 0.047\pm0.010$ and
$0.058\pm0.001_\mathrm{stat}\pm 0.018_\mathrm{syst}$ for CDF and D\O,
respectively.
The CDF efficiency includes a factor of two needed to account for the expected
two $b$-tags in an ideal experiment when applying \eq{eq:xsec_master}.
CDF also neglected their trigger efficiency, which is believed 
to be above $95\%$.

The two  experiments investigated several systematic uncertainties. In both
cases the by far dominating systematic uncertainty comes from the jet energy
scale resolution. It accounts for $28\%$ uncertainty on the efficiency.
Other uncertainties investigated are below $10\%$.
%
\section{Summary and Results}
CDF and D\O\ preformed  a measurement of the $t\bar t$ cross-section in the
all-hadronic channel.
Combining the described background estimates from data 
and efficiencies obtained from simulation 
with the luminosity of each experiment the following results are obtained:
\beq
\mbox{CDF:}\;\sigma_{t\bar t}=7.8\pm2.5_\mathrm{stat}~^{+4.7}_{-2.3} \,_\mathrm{syst}\quad
\mbox{D\O:}\;\sigma_{t\bar t}=7.7~^{+3.4}_{-3.3}\,_\mathrm{stat}~^{+4.7}_{-3.8} \,_\mathrm{syst}\pm0.5 \,_\mathrm{lumi}
\eeq
The dominating systematic uncertainties in the final result are the jet energy
scale uncertainty of the selection efficiency and the uncertainty of the
TRF-based background prediction, which gets inflated due to the subtraction 
in  \eq{eq:xsec_master}.
\begin{figure}[b]
  \centering
\epsfig{file=figs/Tag_78.eps,height=.45\textwidth}
\hfill \epsfig{file=figs/nn2_log.eps,height=.45\textwidth}
\caption{\label{fig:results}%
CDF (left): Number of $b$-tags vs. number of jets per event. Signal is at 6 and above.
D\O (right): The final neural network (NN2) output (required to be above 0.75 for signal).
Background estimates and a Standard Model expectation are
shown by both experiments.}
\end{figure}
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\end{document}



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Proceedings.bbl
\begin{thebibliography}{1}

\bibitem{cdfnote7075}
{\em The~CDF Collaboration}.
\newblock Measurement of the $t\bar t$ production cross section in the
  all-hadronic channel.
\newblock CDF note 7075, August 2004.

\bibitem{d0note4428}
{\em The~D\O\ Collaboration}.
\newblock Measurement of the $t\bar t$ cross section in the all-jets channel.
\newblock D\O\ note 4428, April 2004.

\bibitem{Berger:1997gz}
{\em Edmond~L. Berger and Harry Contopanagos}.
\newblock Threshold resummation of the total cross section for heavy quark
  production in hadronic collisions.
\newblock {\em Phys. Rev.} {\bf D57}(1998)  253--264.

\bibitem{Bonciani:1998vc}
{\em Roberto Bonciani et~al.}
\newblock {NLL} resummation of the heavy-quark hadroproduction cross- section.
\newblock {\em Nucl. Phys.} {\bf B529}(1998)  424--450.

\bibitem{Kidonakis:2003qe}
{\em Nikolaos Kidonakis and Ramona Vogt}.
\newblock Next-to-next-to-leading order soft-gluon corrections in top quark
  hadroproduction.
\newblock {\em Phys. Rev.} {\bf D68}(2003)  114014.

\bibitem{Acosta:2001zu}
CDF Collaboration, {\em D.~Acosta et~al.}
\newblock The {CDF} {C}herenkov luminosity monitor.
\newblock {\em Nucl. Instrum. Meth.} {\bf A461}(2001)  540--544.

\bibitem{d0lumi}
{\em T.~Edwards et~al.}
\newblock Determination of the effective inelastic {$p\bar p$} cross-section
  for the {D\O} {R}un {II} luminosity measurement.
\newblock FERMILAB-TM-2278-E, 2004.

\end{thebibliography}
