% TeX'ing this file requires that you have AMS-LaTeX 2.0 installed
% as well as the rest of the prerequisites for REVTeX 4.0

\documentclass[prd,amsmath,amssymb]{revtex4}
% use this for PRL/PRD
%\documentclass[prd,twocolumn,showpcs,amsmath,amssymb]{revtex4}

\usepackage{graphicx}% Include figure files
\usepackage{dcolumn}% Align table columns on decimal point
\usepackage{bm}% bold math

\begin{document}
\input{definitions}

% remove the following for PRL/PRD
\begin{figure}
\leftline{\includegraphics[scale=0.5]{d0logo_conf}\hfill D\O Note
XXXX - v1.33 - CONF}
\end{figure}

\vspace*{1.5cm}

\title{Evidence for $Z\rightarrow b\overline{b}$ Decays at D\O \\ \vspace*{2.0cm}}

% throughout the internal review, the note will be authored by individuals
% who contributed to the paper
\author{Amber Jenkins, Per Jonsson, Gavin Davies, and Andrew Haas \vspace*{0.5cm} }
\noaffiliation

% once the note is approved for conferences, the following author will be used
%\author{The D\O\ Collaboration}
%\affiliation{
%URL: http://www-d0.fnal.gov \\
%Contact Person for This Analysis: Per Jonsson (jonsson@fnal.gov) and Andrew Haas (haas@fnal.gov) \\
%}

\date{\today}

\begin{abstract}
\vspace*{3.0cm}

A search for $Z\rightarrow b\overline{b}$ production and decay has
been performed at D\O\ using the initial 300 pb$^{-1}$ of Run II
data. Candidate events are selected by triggering on muons coming
from the semileptonic decay of the $b$-jets. Two slightly different
methods of estimating the background from data have been explored.
In both approaches, a significant excess of events is observed after
background subtraction. The first yields an excess of 1353 $\pm$ 151
{\tiny(stat.)} $\pm$ 306 {\tiny(syst.)} events, which corresponds to
a $Z\rightarrow b\overline{b}$ signal of 4.0$\sigma$ and a
cross-section for \ppbar\rarrow Z of 1.XX $\pm$ XX {\tiny(stat.)}
$\pm$ XX {\tiny(syst.)} nb. The second method reveals an excess of
810 $\pm$ 230 {\tiny(stat.)} events, using different event criteria.
Both results are in good agreement with Monte Carlo predictions of
the Standard Model.

% remove this for PRL/PRD
\vspace*{5.0cm} \centerline{\em Preliminary Results for Winter 2006
Conferences}

\end{abstract}

\maketitle
\newpage


%=====================================================================================
\section{Motivation} \label{sec.intro}
%=====================================================================================

The measurement of $Z\rightarrow b\overline{b}$ is an important part
of the Run II physics programme at D\O. $Z\rightarrow b\overline{b}$
is an essential tool in the calibration of $b$-jets, which affects
much of the high $p_{T}$ physics studied at the Tevatron. The
current uncertainty on the $b$-jet energy scale - of the order of
3\% - dominates the uncertainty on the mass of the top quark. In
addition, $Z\rightarrow b\overline{b}$ can be used to better
understand the $b$-jet energy resolution. $Z\rightarrow
b\overline{b}$ also serves as an important benchmark signal for
Higgs physics, since it is the closest observable process to the
dominant decay of a light Higgs to $b\overline{b}$.

The upgraded tracking system, improved muon triggering, and the
possibility of online $b$-jet tagging make the accumulation of a
significant $Z\rightarrow b\overline{b}$ signal possible during Run
II. The main challenge is to sufficiently reduce the QCD backgrounds
such that $b\overline{b}$ events from the $Z$ can be observed. To
this end, careful analysis techniques are critical and effective
triggers must be employed. This paper describes the first search for
$Z\rightarrow b\overline{b}$ at D\O\ in Run II of the Tevatron
collider.

%=====================================================================================
\section{Event Samples} \label{sec.samples}
%=====================================================================================

The data used in the analysis come from the ``BID'' skim, processed
and fixed with the p14 versions of the reconstruction software.
(Background subtraction method 1 uses PASS2 corrections, whereas
method 2 is based on the older PASS1 corrections.) The skim has the
following properties:

\begin{itemize}

\item A ``loose'' offline reconstructed muon in each event, with $p_T>4$ GeV/c,
matched within $\Delta R<$0.7 to a Run II cone jet \cite{RunIIcone}
of radius 0.5. This requirement enhances the fraction of
heavy-flavor events due to the decays of $b\rightarrow \mu$ and
$b\rightarrow c\rightarrow \mu$; \footnote{The BID skim was the best
data-set available at the time of this analysis. A new
skim,``2JET'', has been proposed for future use, which would require
exactly two 0.5 cone jets with $p_T>15$ GeV/c but not demand any
muons. Initial studies indicate that the total efficiency for signal
events would increase by 50--100\% using this new skim.}

\item The skim contains about 90 million events and corresponds to an
integrated luminosity of about 300 pb$^{-1}$ for pre-v13 triggers used.

\end{itemize}

The following run selection is imposed to ensure data quality:

\begin{itemize}
\item Events are required to be in good luminosity blocks;
\item Good calorimeter and jet/Missing $E_{T}$ runs are selected;
\item Bad muon runs are removed;
\item Runs with bad central tracking system information (SMT and CFT) are excluded.
\end{itemize}

In addition, a range of Monte Carlo (MC) samples are used, as listed
in Table~\ref{table:MCsamples}. Each MC sample is generated with
Pythia, overlaid with an average of 0.8 minimum bias events, passed
through a full GEANT simulation of the detector, and processed with
version p14 of the reconstruction software.

\begin{table}[ht]
\begin{center}
\begin{tabular}{|c|c|c|}
\hline
\textbf{Monte Carlo Sample}  & \boldmath{$p_{T}$} \textbf{Cut Applied at Parton Level, GeV/c} & \textbf{Number of Events} \\
\hline \multicolumn{3}{|c|}{\textit{Signal}} \\ \cline{2-3} \hline
$Z\rightarrow b\overline{b}$ & None     & 100--200,000 \\
\hline \multicolumn{3}{|c|}{\textit{Heavy-flavor QCD Backgrounds}}
\\ \cline{2-3} \hline
$b\overline{b}$              & 5--20    & 200,000      \\
\hline
$b\overline{b}$              & 20--40   & 125,000      \\
\hline
$b\overline{b}$              & 40--80   & 150,000      \\
\hline
$b\overline{b}$              & 80--160  & 100,000      \\
\hline
$b\overline{b}$              & 160--320 & 25,000       \\
\hline
$b\overline{b}$              & $>$ 40   & 200,000      \\
\hline \multicolumn{3}{|c|}{\textit{Light-quark (u,d,s) QCD
Backgrounds}} \\ \cline{1-3} \hline
$q\overline{q}$              & 5--20    & 200,000 \\
\hline
$q\overline{q}$              & 20--40   & 125,000 \\
\hline
$q\overline{q}$              & 40--80   & 150,000 \\
\hline
$q\overline{q}$              & 80--160  & 100,000 \\
\hline
$q\overline{q}$              & 160--320 & 25,000 \\
\hline
\end{tabular}
\caption{\label{table:MCsamples} Summary of Monte Carlo samples used
in this analysis. $q$ refers to the light quarks $u$, $d$ or $s$.}
\end{center}
\end{table}

The data skim and MC samples are processed using custom ROOT
ntuple-generating packages. Jet energy scale (JES) corrections are
applied to all jets, including corrections for muons in jets, using
version 5.3 (5.0) of the jet energy correction software for method 1
(2). No specific $b$-jet energy scale corrections are applied, as no
officially approved such correction exists for this data set.

Monte Carlo events are corrected to account for the $b$-tagging
efficiency and jet measurement effects observed in data. Jet
energies are smeared to accurately reflect the jet energy resolution
measured in data, and event weighting is applied in order to account
for the fact that jet reconstruction/identification and $b$-tagging
are less efficient in data than MC.

%=====================================================================================
\subsection{Triggers} \label{sec.triggers}
%=====================================================================================

$Z\rightarrow b\overline{b}$ events are characterized by the
presence of two $b$-tagged jets. Light quark rejection is needed at
the trigger level, prior to any offline event selection, in order to
achieve an acceptable trigger rate at instantaneous luminosities in
excess of 50 x $10^{30} $cm$^{-2}$s$^{-1}$. Without this rejection
the data would have to be undesirably prescaled, and candidate
events would be thrown away.

Ideally one would trigger on di-jet events with displaced vertices
at Level~2; such a capability is however only since recently
provided by the Level~2 Silicon Track Trigger (STT). However, a
large reduction in rate must already be achieved at Level~1.
Candidate events can be selected at the trigger level using the
semileptonic decay of the $b$-jets. Triggering on muons from one or
both of the $b$-jets from the $Z$ limits the signal efficiency
however, because of the small $b$~$\rightarrow$~$\mu$ branching
fraction\footnote{B.R.(b~$\rightarrow$~$\mu$) = 0.11. Muons from the
cascade decays $b \rightarrow c \rightarrow \mu$ and $b \rightarrow
\tau \rightarrow \mu$ are significant, and the total probability for
a $b$-jet to have a muon is nearly 20\%. For
$Z$~$\rightarrow$~$b\overline{b}$ events in which \textit{at least
one} $b$-jet has a muon which passes muon cuts, the maximum signal
efficiency hence is $1-(1-0.2)$x$(1-0.2) = 36\%$. For events with
two muons, this number reduces to 4\%. }.

\begin{table}[ht]
\begin{center}
\begin{tabular}{|c|c|c|c|}
\hline \textbf{v12 Trigger} & \multicolumn{3}{|c|}{\textbf{Trigger
Description}} \\ \cline{2-4}
                     & \textbf{Level 1}      & \textbf{Level 2}   & \textbf{Level 3} \\
\hline \hline
MU\_JT25\_L2M0      & single $\mu$ $+$ jet       & $\ge1 \mu$ $+ \ge1$ jet  & $\ge1$ jet    \\
\hline
MU\_2TRK3\_L2M0     & single $\mu$ $+$ jet       & $\ge1 \mu$               & 2~global tracks  \\
\hline
MUW\_W\_L2M3\_TRK10 & single $\mu$   & $\ge1 \mu$               & 1~global track   \\
\hline
\end{tabular}
\caption{\label{table:v12ORtrigdesc} Description of the three
leading v12 muon triggers. Candidate signal events were required to
pass MU\_JT25\_L2M0.}
\end{center}
\end{table}

\begin{table}[ht]
\begin{center}
\begin{tabular}{|c|c|c|c|}
\hline \textbf{v11 Trigger} & \multicolumn{3}{|c|}{\textbf{Trigger
Description}} \\ \cline{2-4}
                     & \textbf{Level 1}      & \textbf{Level 2}   & \textbf{Level 3} \\
\hline \hline
MU\_JT20\_L2M0      & single $\mu$ $+$ jet       & $\ge1 \mu$ $+ \ge1$ jet  & $\ge1$ jet    \\
\hline
MU\_JT25\_L2M0      & single $\mu$ $+$ jet       & $\ge1 \mu$ $+ \ge1$ jet  & $\ge1$ jet    \\
\hline
MUW\_W\_L2M3\_TRK10 & single $\mu$   & $\ge1 \mu$               & 1~global track   \\
\hline
\end{tabular}
\caption{\label{table:v11ORtrigdesc} Description of the three
leading v11 muon triggers. Candidate signal events were required to
pass MU\_JT25\_L2M0.}
\end{center}
\end{table}

\begin{table}[ht]
\begin{center}
\begin{tabular}{|c|c|c|}
\hline \textbf{v12 Trigger} & \multicolumn{2}{|c|}{\textbf{L1L2L3
Trigger Efficiency(\%)}} \\  \cline{2-3}
                     & \textbf{Absolute}  & \textbf{w.r.t. Offline Cuts}           \\
\hline \hline
MU\_JT25\_L2M0      & 5.5  & 15.6\\
\hline
MU\_2TRK3\_L2M0     & 7.0  & 18.1\\
\hline
MUW\_W\_L2M3\_TRK10 & 3.4  & 8.9\\
\hline
OR of the above 3 triggers & 8.7 & 20.2  \\
\hline
\end{tabular}
\caption{\label{table:v12trigeff} v12 trigger efficiencies for MC
signal events.}
\end{center}
\end{table}

\begin{table}[ht]
\begin{center}
\begin{tabular}{|c|c|c|}
\hline \textbf{v11 Trigger} & \multicolumn{2}{|c|}{\textbf{L1L2L3
Trigger Efficiency(\%)}} \\  \cline{2-3}
                     & \textbf{Absolute} & \textbf{w.r.t. Offline Cuts}              \\
\hline \hline
MU\_JT20\_L2M0      & 7.4   & 18.3\\
\hline
MU\_JT25\_L2M0      & 5.5   & 15.6\\
\hline
MUW\_W\_L2M3\_TRK10 & 3.4   & 8.9\\
\hline
OR of the above 3 triggers & 8.4 & 19.7  \\
\hline
\end{tabular}
\caption{\label{table:v11trigeff} v11 trigger efficiencies for MC
signal events.}
\end{center}
\end{table}

Trigger efficiencies for the v12 and v11 triggers are listed in
Tables~\ref{table:v12trigeff} and~\ref{table:v11trigeff}. The most
frequently fired v12 trigger, MU\_JT25\_L2M0, was exposed to a
luminosity of 297.5 pb$^{-1}$. To simplify the analysis and the
comparison to the MC predictions all events in the pre-v13 data-set
were selected from this single trigger. The second method presented
does not apply this trigger selection, and is thus not able to
measure a Z cross-section.

%=====================================================================================
\section{Event Selection} \label{sec.MCsel}
%=====================================================================================

There are few kinematic handles with which to discriminate between
the $Z$~$\rightarrow$~$b\overline{b}$ signal and the QCD
$b\overline{b}$ background. The two most powerful variables, besides
the invariant di-jet mass, are the number of jets in the event,
$n_{jet}$ and the angular separation of the two leading $b$-jets in
the plane perpendicular to the beam, $\Delta\varphi$. Both of these
variables are sensitive to the prediction that QCD background, due
to the color connection between initial and final state in the QCD
processes, should have more gluon radiation. With this in mind,
candidate events are selected offline using the following
prescriptions:

\begin{itemize}

\item [\textbf{Cut 1}] Trigger selection: MU\_JT25\_L2M0;
\item [\textbf{Cut 2}] The event must contain two and only two good quality jets
and at least one loose offline muon. (No offline muon is explicitly
required in method 2);
\item [\textbf{Cut 3}] The two jets must both have $\mid\eta\mid < 2.5$
and corrected $p_{T}$ $>$ 15 GeV/c. (Method 2 requires applies the
$p_{T}$ cut before jet energy scale corrections.);
\item [\textbf{Cut 4}] For $b$-tagging, the two jets must both be taggable;
\item [\textbf{Cut 5}] The primary vertex of the event must have more than 2 tracks
attached and be located within $\pm 50$ cm in the z-direction ($\pm
35$ cm for method 2);
\item [\textbf{Cut 6}] The two jets must both be ``loose'' SVT-tagged
(using the standard p14 definitions);
\item [\textbf{Cut 7}] The two $b$-jets must be nearly back-to-back
in the plane perpendicular to the beam-line, i.e. $\Delta\varphi >
2.75$ radians (2.9 radians in method 2).
\end{itemize}

Tables~\ref{table:cutflow_zbb} shows the number of events passing
each analysis cut in signal MC and data for method 1. Monte Carlo
event counts are weighted by cross-section and luminosity.

\begin{table}[ht]
\begin{center}
\begin{tabular}{|c|c|c|}
\hline
\textbf{Analysis Cut} & \textbf{MC $Z$~$\rightarrow$~$b\overline{b}$} & \textbf{Data Passing Cut} \\
\hline \hline
No selection      & 336475 $\pm$ 1174 & $\sim$ 90000000 \\
\hline
1                 & 18567 $\pm$ 276 & 10882864 \\
\hline
2                 & 10524 $\pm$ 209 & 5135730 \\
\hline
3                 & 8055 $\pm$ 183 & 4030914  \\
\hline
4                 & 6915 $\pm$ 169 & 2726889 \\
\hline
5                 & 6643 $\pm$ 165 & 2698544 \\
\hline
6                 & 1451 $\pm$ 77 & 33499\\
\hline
7                 & 1444 $\pm$ 65 & 31183 \\
\hline
\end{tabular}
\caption{\label{table:cutflow_zbb} Cut flow table for
$Z$~$\rightarrow$~$b\overline{b}$ events in Monte Carlo and events
in data. Event counts are weighted by cross-section and luminosity,
the errors are statistical only.}
\end{center}
\end{table}

The $b$- / light-jet fraction is about 10\% after a single $b$-tag
requirement. With the additional muon and trigger selection (Cuts 1
and 2) the fraction is about 20\% and after requiring a double
offline $b$-tag in the data (Cut 6) the light-quark QCD background
component is reduced to about 10\% of the sample. However, a large
heavy-flavor component remains which still swamps the signal;
$\textrm{S:(S+B)}$ is of the order of 1:30. By restricting the
number of jets and the angle between the two $b$-jets (i.e. cuts 2
and 7) the signal significance can be improved. We have investigated
the effect of these two cuts on the effective signal significance,
where effective significance is defined as:
\begin{equation} \label{eq:signif}
\textrm{\textit{Effective Significance}} =
\frac{N_{signal}}{\sigma_{bkg}^{stat} \oplus \sigma_{bkg}^{syst}
\oplus \sqrt{N_{tot}}}
\end{equation}
Here $N_{signal}$ is the number of MC signal events passing the
cuts, weighted by cross-section and luminosity,
$\sigma_{bkg}^{stat}$ and $\sigma_{bkg}^{syst}$ are the statistical
and systematic errors on the estimated number of background events
passing all cuts and $N_{tot}$ is the total number of events in data
passing the cuts. The square root of $N_{tot}$ - $N_{signal}$ is
used as a conservative estimate of the size of the statistical error
on the background.


%=====================================================================================
\section{Background Subtraction} \label{sec.bkgsub}
%=====================================================================================

Understanding the shape of the background to the $Z\rightarrow
b\bar{b}$ signal in the double $b$-tagged data sample is central to
this analysis. The background is composed of heavy-flavor di-jet
production and mis-tagged gluon/light-quark jet production, all of
which cannot be accurately simulated using current techniques,
particularly in the quantities needed for the statistical accuracy
required. Thus the background is derived from data, using either
single-tagged and/or un-tagged events.

We have developed two slightly different methods for measuring the
background. The two approaches are discussed in
sections~\ref{sec.bkgsub1} and~\ref{sec.bkgsub2} respectively. Both
methods use a \textit{tag rate function (TRF)} to estimate the
amount of double $b$-tagged background in the data. We measure the
\textit{tag ratio} of double to single $b$-tags as a function of jet
$p_{T}$ and jet $\eta$ to form the TRF. The TRFs are applied, as an
event weight, to the single tagged events.

In the first method, the final invariant mass background template is
normalized to the double tagged data with a fit to the signal free
invariant mass region above 120 GeV. The second approach instead
makes use of the difference in shape between single $b$-tagged and
un-tagged invariant mass distributions.

%=====================================================================================
\section{Background Estimation Method 1} \label{sec.bkgsub1}
%=====================================================================================

A TRF can be constructed on a jet-by-jet basis, a similar approach
to that adopted in the D\O\ Run II $hb\overline{b}$
analysis~\cite{hbb}. Consider those events in which the
first-leading-\pt\ jet is $b$-tagged. For these events, the
second-leading-\pt\ jet is categorized according to its location in
one of three different eta regions of the detector:
\\$\mid\eta\mid$~$<$~$1.1$, $1.1$~$<$~$\mid\eta\mid$~$<$~$1.5$ and
$1.5$~$<$~$\mid\eta\mid$~$<$~$2.5$. For each $\eta$ region, the TRF
is then parameterized as a function of the $p_{T}$ of the
second-leading-\pt\ jet. This generates a TRF \textit{per jet}.

To estimate the background, each event passing cuts with the
leading-\pt\ jet $b$-tagged is weighted by the TRF corresponding to
the second-leading-\pt\ jet. The resulting background distribution
is then corrected for the dependence of the TRF upon $\Delta\varphi$
by fitting it to the observed invariant mass distribution above 120
GeV. Figure \ref{fig:et67_v12OR.eps} illustrates the jet-based TRF
as a function of the second leading jet $p_{T}$, for jets in the
three different $\eta$-bins.

\begin{figure}[!ht]
\begin{center}
\includegraphics[width=12cm, height=8cm]{./trf_2.75.eps}
\caption{\label{fig:et67_v12OR.eps} TRF as a function of
second-leading jet $p_{T}$ for jets in the regions $\mid\eta\mid
<1.1$ (black), $1.1$ $<$ $\mid\eta\mid$ $<$ $1.5$ (red) and $1.5<
\mid\eta\mid <2.5$ (green), evaluated for events in data with the
leading-\pt\ jet $b$-tagged.}
\end{center}
\end{figure}

Figure \ref{fig:bkg_fit} shows the fit of the background prediction
to the double tagged data in the high mass region. By construction
this method produces a background invariant mass template with an
identical number of integrated events as the observed double-tags.
If the invariant mass shape of the background and observed data were
identical then the normalization would be equal to 1. The fact that
the fit yields 0.95 indicates a difference in the relative fraction
of events above and below 120 GeV in the background template and the
double-tagged data. (We have more events in the Z mass region in the
double-tagged data.)

\begin{figure}[!ht]
\begin{center}
\includegraphics[width=12cm, height=8cm]{./massfit_dphi_2.75.eps}
\caption{\label{fig:bkg_fit} Invariant di-jet mass in the pre-v13
data-set \textit{before} background subtraction. Green (light gray)
shaded histogram: expected background, estimated using a jet-based
TRF from data and fit with one parameter to the observed data above
120 GeV. Black points: total di-jet mass distribution observed in
data. Red (dark gray) histogram: expected $Z\rightarrow b\bar{b}$
signal from MC. The fit results in a correction to the background
scale of 0.95 $\pm$ 0.01. }
\end{center}
\end{figure}

The normalized invariant mass background compared to data and signal
MC is shown in Figure \ref{fig:invmass621_dphi_gt_275}. Figure
\ref{fig:invmass627_dphi_gt_275} shows the invariant mass after
subtraction of the background, compared to Monte Carlo.

\begin{figure}[!ht]
\begin{center}
\includegraphics[width=12cm, height=8cm]{./invmass121_dphi_2.75.eps}
\caption{\label{fig:invmass621_dphi_gt_275} Invariant di-jet mass in
the data \textit{before} background subtraction. Green (light gray)
shaded histogram: expected background, estimated using a jet-based
TRF from data. The dark blue band indicates the $\pm$ 1.7 \%
systematic error on the background. Black points: total di-jet mass
distribution observed in data. Red (dark grey) histogram: expected
$Z\rightarrow b\bar{b}$ signal from MC.}
\end{center}
\end{figure}

\begin{figure}[!ht]
\begin{center}
\includegraphics[width=12cm, height=8cm]{./627_dphi_2.75.eps}
\caption{\label{fig:invmass627_dphi_gt_275} The invariant di-jet
mass spectrum in the data \textit{after} background subtraction.
Black points: excess observed in data, fitted with a Gaussian. Error
bars show statistical errors only. Red (dark gray) histogram:
expected signal from MC. The excess peak has a mean mass of
73.18~$GeV/c^{2}$ and a width of 11.27~$GeV/c^{2}$.}
\end{center}
\end{figure}

A complete mass-bin-by-mass-bin breakdown of the excess in data and
predicted from Monte Carlo is presented in
Table~\ref{table:excessnums_v12}. After background subtraction we
observe an excess of 1352.8 $\pm$ 151.33 (stat.) $\pm$ 305.70
(syst.) events in the 50--100~GeV/c$^{2}$ mass window. The excess is
fit with a Gaussian and compared to the number of events expected
from Monte Carlo. We expect to see 1388.92 $\pm$ 107.09 (stat.)
events and therefore observe good agreement between data and Monte
Carlo within the errors. Table~\ref{table:excesssummary_v12}
summarizes the overall excess.

The total statistical error is calculated by combining in quadrature
the statistical errors on the number of observed events and expected
background events. The main source of systematic uncertainty on the
observed excess comes from the normalization fit of the background
and is taken, from the error on the fitted parameter, to be 1.3\% of
the number of background events. The contribution from the invariant
mass shape of the TRF based background not being modeled perfectly,
is estimated to be small from the small $\chi^{2}$/NDF of the
normalization fit at masses above 120 GeV. A study of the difference
of the invariant mass shape of an un-tagged (light quark dominated)
and single-tagged ($b$ contaminated) event sample reveals a net
uncertainty on the number of background events of less than 1\% in
the $Z$ mass region (50-100 GeV). Hence, an additional 1\%
systematic uncertainty was added to the error on the background.

The systematic error on the background is added in quadrature to the
total statistical error in the last column of
Table~\ref{table:excesssummary_v12}. Taking the systematic
uncertainty of the background into account, the observed excess has
a significance of 4.0 standard deviations.

The peak of the distribution lies at approximately 75 GeV/c$^{2}$,
in both Monte Carlo and data, after jet energy scale corrections
have been applied. At the time of this analysis no official $b$-jet
JES correction, other than the correction for muons in jets, is
available for this data-set. Applying an unofficial $b$-jet JES
correction to the MC shifts the peak to 79 GeV. The remaining mass
shift could be explained by energy loss to hard final state
radiation as suggested in ~\cite{ambers}.


\begin{table}[h]
\begin{center}
\begin{tabular}{|c|c|c|c|c|}
\hline
\textbf{Invariant Mass Bin} & \textbf{No. Events} & \textbf{No. Events}  & \textbf{Excess} & \textbf{Expected $Z\rightarrow b\overline{b}$} \\
\textbf{(}\boldmath{GeV/c$^{2}$}\textbf{)}    & \textbf{Observed} & \textbf{Expected}    &      &  \\
\hline \hline
0--30 & 0 & 0 & 0 & 0 \\
\hline
30--60 & 2336 & 2138.45 $\pm$ 20.59 & 197.56 $\pm$ 52.54 & 166.74 $\pm$ 29.21 \\
\hline
60--90 & 13543 & 12549.70 $\pm$ 49.88 & 993.30 $\pm$ 126.62 & 1064.96 $\pm$ 73.82 \\
\hline
90--120 & 8465 & 8215.07 $\pm$ 40.36 & 249.93 $\pm$ 100.47 & 191.41 $\pm$ 31.30\\
\hline
120--150 & 3682 & 3589.04 $\pm$ 26.68 & 92.96 $\pm$ 66.28 & 4.23 $\pm$ 4.65 \\
\hline
150--180 & 1590 & 1600.98 $\pm$ 17.82 & -10.98 $\pm$ 43.67 & 16.15 $\pm$ 9.09 \\
\hline
180--210 & 731 & 752.03 $\pm$ 12.21 & -21.03 $\pm$ 29.67 & 0 \\
\hline
210--240 & 354 & 377.46 $\pm$ 8.65 & -23.46 $\pm$ 20.71 & 0\\
\hline
240--270 & 201 & 218.26 $\pm$ 6.58 & -17.26 $\pm$ 15.63 & 0 \\
\hline
270--300 & 117 & 121.73 $\pm$ 4.91 & -4.73 $\pm$ 11.88 & 0\\
\hline
300--330 & 67 & 67.51 $\pm$ 3.66 & -0.51 $\pm$ 8.97 & 0\\
\hline
330--360 & 44 & 39.39 $\pm$ 2.79 & 4.61 $\pm$ 7.20 & 0\\
\hline
360--390 & 19 & 20.54 $\pm$ 2.02 & -1.54 $\pm$ 4.80 & 0\\
\hline
\end{tabular}
\caption{\label{table:excessnums_v12} Signal candidate counts before
and after background subtraction in the pre-v13 data and MC. The
errors are statistical only.}
\end{center}
\end{table}

\begin{table}[h]
\begin{center}
\begin{tabular}{|c|c|c|c|c|c|c|}
\hline
\textbf{Search Window}&\textbf{No. Events}&\textbf{No. Events}&\textbf{Overall}&\textbf{Total Stat.}&\textbf{Total Syst.}&\textbf{Overall}\\
\textbf{(}\boldmath{GeV/c$^{2}$}\textbf{)}&\textbf{Observed}&\textbf{Expected}&\textbf{Excess}&\textbf{Error}&\textbf{Error}&\textbf{Error}\\
\hline \hline
50--100 & 19335 & 17982.20 & 1352.80 & 151.33 & 305.70 & 341.10 \\
\hline \multicolumn{7}{|c|}{\textbf{Prediction from MC:
}\boldmath{1388.92 $\pm$ 107.09}} \\ \cline{1-7} \hline
\multicolumn{7}{|c|}{\textbf{Significance of Result: }\boldmath{3.97
$\sigma$}} \\ \cline{1-7}
\end{tabular}
\caption{\label{table:excesssummary_v12} Excess of events observed
in the 50--100 GeV/c$^{2}$ search window after background
subtraction has been performed in the pre-v13 data, along with the
signal prediction from MC. Agreement is seen between the excess
observed and the number of signal events predicted.}
\end{center}
\end{table}


%=====================================================================================
\subsection{Closure Test} \label{subsec.clostest}
%=====================================================================================

As a closure test, the sum of the invariant mass templates of the
signal MC and background from the TRF were fit to the whole
invariant mass range of the observed double tagged candidates. The
scale of the two templates were fitted with two unbound scale
parameters: ``bkg'' and ``signal'' (see Fig.~\ref{fig:closure}).

\begin{figure}[!ht]
\begin{center}
\includegraphics[width=12cm, height=8cm]{./closure_2.75.eps}
\caption{\label{fig:closure} Closure test of the final invariant
di-jet mass spectrum observed in the data after background
subtraction.  Green (light gray) shaded histogram: expected
background, estimated using a jet-based TRF. Black points: total
di-jet mass distribution observed in data. Red (dark gray)
histogram: expected signal from MC. The bold black line shows the
fitted sum of the scaled background and MC templates.}
\end{center}
\end{figure}

The fitted background scale parameter is 0.9541 $\pm$ 0.0091, which
within the error is compatible with the value obtained from
Fig.~\ref{fig:bkg_fit}, 0.95 $\pm$ 0.01. Also, the signal scale
parameter is within errors compatible with the expected value of
unity. We therefore conclude that the sum of the signal MC and the
background as calculated with our TRF-based model and normalized to
the high mass region are compatible with the observed double tagged
invariant mass over the full region. Furthermore, adding the signal
MC to the background template is necessary in order to obtain a good
fit to the data.

%=====================================================================================
\section{Background Estimation Method 2: with 0$\rightarrow$1 and Z Corrections} \label{sec.bkgsub2}
%=====================================================================================

The data sample used for the second method of background estimation
differs from that used for method 1 in the following ways:

\begin{itemize}
\item The full PASS 1 data set is used, with no trigger selection.
(Pass1 data did not use the T42 correction and has a different
version of the jet energy scale corrections (v5.0).)

\item A slightly tighter primary vertex requirement is made,
with $\ge$4 tracks attached, and $|z|$ $<$ 35 cm (the fiducial
$b$-tagging region).

\item A slightly narrower $\Delta\varphi$ cut was used,
$>2.9$ instead of $>2.75$.
\end{itemize}

Because the TRF is applied to the single-tagged data sample, which
is less rich in heavy-flavor jets than the data sample to which it
is compared (the double $b$-tagged data), any differences in either
the jet-energy-scale of heavy-flavor jets as opposed to gluon and
light-quark jets or their natural invariant mass spectrum will
result in a shift of the invariant mass distribution expected for
the background, as compared to the data. (In method 1 this is
accounted for by fitting the background to double-$b$-tagged data
above invariant mass of 120 GeV.) In this method, this shift is
observed and measured using an \emph{un-tagged} data sample. A TRF
is derived for the un-tagged data and applied to the un-tagged data,
and then compared to the actual single-tagged data. The shift which
is derived is called the ``0$\rightarrow$1'' correction, which is
then subtracted from the expected background in the double-tagged
data sample. This correction relies on the fact that each successive
$b$-tag that is required increases the fraction of heavy-flavor by
the same amount. This is verified by comparing the data with MC
$b\bar{b}$ events.

This method also makes an additional correction for the effects of
$Z\rightarrow b\bar{b}$ events which are present in both the
un-tagged and single-tagged data samples from which the
0$\rightarrow$1 correction and the single-tag TRF are derived,
respectively. A signal peak is first measured in double-tagged data,
including the 0$\rightarrow$1 correction. The number of events which
would exist from this signal peak in the un-tagged and single-tagged
data samples is then extrapolated using a $Z\rightarrow b\bar{b}$ MC
sample with no, one, and two $b$-tags required. The signal peak,
\emph{measured in data}, is then scaled by these factors and
subtracted from the un-tagged and single-tagged samples. Then the
TRF and the 0$\rightarrow$1 correction are re-derived, the expected
background in the double-tagged data is re-calculated, and a new
signal peak is observed. This correction process is then repeated,
using the new signal peak to estimate the $Z\rightarrow b\bar{b}$
events in the un-tagged and single-tagged data samples, a total of
three times, after which the correction and signal peak are stable.
Effects of contributions from W\rarrow cs production and decay have
been investigated and determined to be small.

%=====================================================================================
\subsection{The $0\rightarrow 1$ tag Shift} \label{subsec.fulltrf01corr}
%=====================================================================================

The shift in the invariant mass spectrum of the di-jet system caused
by applying a single $b$-tag is first measured. Later this will be
subtracted from the estimated background of the double $b$-tagged
data. A TRF is derived on the un-tagged sample and re-applied to the
same un-tagged data sample, to predict the background to the
single-tagged data sample, as shown in
Figure~\ref{fig:singletag_trf}. A comparison is also shown in this
figure to the $b\bar{b}$ MC di-jet invariant mass spectrum (which
was normalized using double-tagged data). The $b\bar{b}$ events make
up about 10\% of the single-tagged data sample, as opposed to about
2\% in the un-tagged data sample. The small contribution of
$Z\rightarrow b\bar{b}$ expected in the single-tagged data is also
shown. Most of the events in the single-tagged data sample contain
only gluon/light-quark jets.

The difference between the single-tagged data and the expected
background from the TRF is shown in Figure~\ref{fig:singletag_diff}.
A comparison of the background-subtracted single-tagged data to the
MC $Z\rightarrow b\bar{b}$ invariant mass distribution shows that it
is not the result of a signal peak in the single-tagged data, but
rather an overall shift in the invariant mass distribution. As
mentioned above, this shift is understood to come from either a
difference between the gluon/light-quark and the $b$-quark jet
energy scale factors or a difference in the ratio of true
cross-section of heavy-flavor jets to light-jets as a function of
di-jet invariant mass.

\begin{center}\begin{figure}[!ht]\begin{center}
\includegraphics[width=12cm]{./singletag_trf.eps}
\caption{\label{fig:singletag_trf} Comparison between the
single-tagged data and the background expected using the TRF method.
Comparisons are also shown to the $b\bar{b}$ MC di-jet invariant
mass spectrum (which was normalized using double-tagged data) and to
the $Z\rightarrow b\bar{b}$ MC di-jet invariant mass spectrum, to
give a feel for the composition of the sample. The rest of the
events are thought to be gluon/light-quark jet events.}
\end{center}\end{figure}\end{center}

\begin{center}\begin{figure}[!ht]\begin{center}
\includegraphics[width=12cm]{./singletag_diff.eps}
\caption{\label{fig:singletag_diff} Difference between the
single-tagged data and the background expected using the TRF method,
a measure of the 0$\rightarrow$1 tag shift, which will be subtracted
from the expected double $b$-tagged data (after proper
normalization). The difference is also shown after correcting for
the expected $Z\rightarrow b\bar{b}$ events in the un-tagged and
single-tagged data samples, using the methods described below in
Section \ref{subsec.fulltrfzcorr}.}
\end{center}\end{figure}\end{center}

%=====================================================================================
\subsection{The 0- and 1-tag Z Peak Correction} \label{subsec.fulltrfzcorr}
%=====================================================================================

The un-tagged and single-tagged data samples contain signal events,
which will now be corrected for. The signal peak observed in
double-tagged data, after subtracting the estimated background using
the TRF method, is scaled by a factor of 6.5, which is the ratio of
single-tagged to double-tagged events in the $Z\rightarrow b\bar{b}$
MC sample. It is important to note that the MC is only used for an
overall normalization (the $b$-tagging efficiency), and does not
affect the shape of the signal peak. This scaled signal peak is then
divided (bin by bin) by the single-tag data, to determine the
estimated fraction of $Z\rightarrow b\bar{b}$ events in each bin of
the single-tag data.

The expected fraction of $Z\rightarrow b\bar{b}$ events in each
invariant mass bin is then subtracted from the signal-tagged data
(the events are weighted by 1-f, where f is the fraction of
$Z\rightarrow b\bar{b}$ expected). Then the TRFs are re-derived and
re-applied to this corrected, weighted, single-tagged data. The
0$\rightarrow$1 tag correction is also re-derived, using the same
principles to estimate the fraction of $Z\rightarrow b\bar{b}$ in
the un-tagged data sample. The effect from $Z\rightarrow b\bar{b}$
events in the un-tagged sample is relatively small, as expected, so
the modification to the 0$\rightarrow$1 tag correction is slight, as
seen in Figure~\ref{fig:singletag_diff}.

Since the size and shape of the original Z peak in data changes
slightly after the corrections to the un-tagged and single-tagged
data, the corrections themselves can be re-derived using the new Z
peak observed. This cyclic process could be continued ad-infinitum,
but in practice the solution is stable after only a few iterations,
which results in a final Z peak and set of corrections.

%=====================================================================================
\subsection{Applying to Data} \label{subsec.fulltrfresults}
%=====================================================================================

The final $Z\rightarrow b\bar{b}$ peak derived from data, after all
corrections, is considered to be the difference between the
background-subtracted double-tagged data and the corrected
0$\rightarrow$1 tag shift. This invariant mass distribution
difference is shown in
Figure~\ref{fig:diff_cdiff_300_dphi_2.9_01_diff}, and compared to
the shape of the $Z\rightarrow b\bar{b}$ distribution in MC. (The
slightly different shape of the difference between the
background-subtracted double-tagged data and the 0$\rightarrow$1 tag
shift without Z peak corrections to the un-tagged and single-tagged
data samples is also shown, to give a feel for the size of the
effect.)

\begin{center}\begin{figure}[!ht]\begin{center}
\includegraphics[width=12cm]{./diff_cdiff_300_dphi_2.9_01_diff.eps}
\caption{\label{fig:diff_cdiff_300_dphi_2.9_01_diff} The final
$Z\rightarrow b\bar{b}$ peak derived from data, after all
corrections (green), compared to the shape of the $Z\rightarrow
b\bar{b}$ distribution in MC (blue). (The slightly different shape
of the Z peak in data without the Z peak corrections to the
un-tagged and single-tagged data samples (black) is also shown, to
give a feel for the size of the effect.)}
\end{center}\end{figure}\end{center}

The final Z peak in data (with all corrections included) is fit to a
Gaussian distribution, which describes the shape of the
$Z\rightarrow b\bar{b}$ peak well in MC. Both the mean (79$\pm$3
GeV) and width (9$\pm$3 GeV) of the distribution observed for data
are comparable to those derived from $Z\rightarrow b\bar{b}$ MC: 81
GeV and 11 GeV, respectively.

810$\pm$230 $Z\rightarrow b\bar{b}$ events are observed, where the
error is taken from the uncertainty in the height of the Gaussian
fit. Recall that the data set used to test this background
estimation method uses a smaller $\Delta\varphi$ range (2.9 as
opposed to 2.75), makes no explicit trigger requirements, and
corrects for the signal events in the data from which the TRFs were
derived. (570$\pm$160 events are observed if the signal events in
the data from which the TRFs were derived are not corrected for.)
The total number of events expected from $Z\rightarrow b\bar{b}$ MC
can not be estimated very accurately, because the data were not
selected by a given trigger. However, for an assumed luminosity of
300 pb$^-1$, the size of the $Z\rightarrow b\bar{b}$ peak observed
in data would correspond to an overall trigger/skimming efficiency
of about 15\% (note that this agrees with the efficiencies presented
in Section~\ref{sec.triggers}).

%=====================================================================================
\section{Summary of Results} \label{sec.results}
%=====================================================================================

We have investigated two slightly different methods for extracting
an observable $Z\rightarrow b\bar{b}$ signal. The first method shows
the following excess in 297.5 pb$^{-1}$ of data collected with the
MU\_JT25\_L2M0 trigger:
\begin{center}
1352.80 $\pm$ 151.33 {\tiny(stat.)} $\pm$ 305.70 {\tiny(syst.)}
\end{center}
compared to MC expectations of:
\begin{center}
1388.92 $\pm$ 107.09 {\tiny(stat.)}
\end{center}
The observed signal amounts to a significance of 4.0 standard
deviations.

A second approach, without trigger selection, in a slightly narrower
$\Delta\phi$ range, and correcting for the $Z$ contribution to the
TRFs, also confirms the observed excess:
\begin{center}
810 $\pm$ 230 {\tiny(stat.)}
\end{center}

The position and width of the observed mass peaks are in agreement
with MC expectations in both cases. Method 1 finds a peak with a
fitted mean of 73$\pm$2 GeV and method 2 a fitted mean of 79$\pm$3
GeV. The difference between the observed mass peaks can be
attributed to the different data samples and JES corrections (p14
pass2 versus pass1) and to the different event selection applied.

%=====================================================================================
\section{Conclusions} \label{sec.conclusions}
%=====================================================================================

We have demonstrated that a $Z\rightarrow b\bar{b}$ di-jet mass
resonance can be successfully extracted from the massive QCD
background, already with the first 300 pb$^{-1}$ of Run II data
collected by the D\O\ experiment. The observed excess agrees well
with the expectations from Monte Carlo simulations of the Standard
Model.

Thanks to the new dedicated $Z\rightarrow b\bar{b}$ triggers we have
already collected a several times larger data sample which is now
waiting to be analyzed. The larger statistics from this sample is
not only expected to provide a larger $Z\rightarrow b\bar{b}$ peak
but also enable a more precise background determination, thus
enabling a precision measurement.


%=====================================================================================

\begin{acknowledgments}

\input acknowledgement_paragraph_r2.tex   % input acknowledgement

\end{acknowledgments}

%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{thebibliography}{99}

\addcontentsline{toc}{section}{References}\label{sec.refs}

\bibitem{CDF} T. Dorigo,{\it Observation of Z Decays to
b Quark Pairs at the Tevatron Collider}, hep-ex/9806022.

\bibitem{hbb} A. Haas {\it et.al.},{\it D\O\ Search for Neutral Higgs
Bosons at High tan$\beta$ in Multi-jet Events Using p14 Data}, D\O
Note 4671, hep-ex/0504018.

\bibitem{ambers}A. Jenkins and A. Goussiou, {\it An Investigation
of $b$-jet Energy Resolution in $Z^{0}H^{0} \rightarrow eeb\bar{b}$
and $Z^{0}\rightarrow b\bar{b}$}, D\O Note 4136.

\bibitem{RunIIcone}
G.~C.~Blazey {\sl et al.}, in
     {\sl Proceedings of the Workshop:
     ``QCD and Weak Boson Physics in Run II,''}
     edited by U.~Baur, R.~K.~Ellis, and D.~Zeppenfeld,
     (Fermilab, Batavia, IL, 2000) p.~47;
     see Sec. 3.5 for details.

\end{thebibliography}

\end{document}
