%===============================================================================================
% Search for the Z->bb Decay at Dzero
% Amber Jenkins
% Imperial College, London
% D-Zero Experiment, Fermilab
% Created 12/02/05, Fermilab
% Modified 23/09/05, London
%===============================================================================================

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  & {D\O\ Note 4988} \\
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%=====================================================================================
\title {\textbf{Evidence for} \boldmath{$Z\rightarrow b\overline{b}$} \textbf{Decays at D\O}} \author{Amber Jenkins, Per Jonsson, Gavin Davies \\ \textit{Imperial College London, UK} \\ Andrew Haas \\ \textit{Columbia University, USA} \\ \date{\today} \\}
\maketitle
%=====================================================================================

%=====================================================================================
\begin{abstract}
%=====================================================================================

A search has been performed at D\O\ for $Z\rightarrow b\overline{b}$
decays using the initial 300 pb$^{-1}$ of data from Run II.
Candidate events are selected by triggering on muons from
semileptonic decay of $b$ quarks. Trigger and offline $b$-tagging
requirements remove background from light quarks. The remaining
$b\overline{b}$ background is harder to suppress. For this purpose,
the three most valuable handles are the number of jets per event,
the dijet angular distribution and invariant mass. The
$b\overline{b}$ background is estimated using b-tag rate functions
(TRFs) derived from data. In this analysis on $b$ production two
somewhat different background-subtraction methods are explored. Both
approaches lead to an an excess of events following background
subtraction. One method yields an excess of 1353 $\pm$ 151
{\tiny(stat.)} $\pm$ 306 {\tiny(syst.)} events in 297.5 pb$^{-1}$ of
data collected with triggerlist versions 8-12. This excess is in
good agreement with Monte Carlo predictions, and amounts to a
$Z\rightarrow b\overline{b}$ signal of 4.0 standard deviations. The
second approach, which deals with the entire pre-v13 pass1 data,
reveals an excess of 810 $\pm$ 230 {\tiny(stat.)} events.

\end{abstract}

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

The measurement of $Z\rightarrow b\overline{b}$ is an important part
of the program at D\O in that it can provide an independent
calibration and efficiency for tagging b quarks. In Run I, the D\O\
detector lacked a magnetic field, and its tracking capabilities were
not as refined; as such the potential for observing $Z\rightarrow
b\overline{b}$ was limited. With an upgraded tracking system,
improved muon triggering and the possibility of online $b$-quark
tagging the prospects for observing $Z\rightarrow b\overline{b}$ in
Run II are brighter. This paper describes the first search for
$Z\rightarrow b\overline{b}$ at D\O\ in Run II of the Tevatron
collider.

$Z\rightarrow b\overline{b}$ is a particularly important tool in the
calibration of the $b$-jet energy scale, which affects many analyses
of the high-$p_{T}$ physics at the Tevatron. The current uncertainty
on the jet energy scale - of the order of 3\% - dominates the
uncertainty on the mass of the top quark, and an improved
measurement of the $b$-jet energy scale can further constrain its
mass. In addition, $Z\rightarrow b\overline{b}$ can be used to
improve the understanding of jet energy resolution.

Another major impetus behind the search is that $Z\rightarrow
b\overline{b}$ serves as an important benchmark for Higgs physics,
since it is the closest observable process to the decay of a light
Higgs to $b\overline{b}$. The knowledge of jet energy resolution,
dijet mass resolution, $b$ tagging and kinematic handles gleaned in
studying $Z\rightarrow b\overline{b}$ can be used to refine Higgs
searches at a hadron-hadron collider.

The main challenge is to sufficiently reduce backgrounds such that
$b\overline{b}$ events from the $Z$ can be observed. To this end,
careful analysis techniques are critical and only the most effective
triggers must be employed.

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

%=====================================================================================
\subsection{The Data} \label{sec.data_samples}
%=====================================================================================

Our analysis uses data collected with several trigger lists, the
latest of which is v12. For the v13 list, channel-specific triggers
were put in place for the $Z\rightarrow b\overline{b}$ search.
However, the v13 data suffer from poor statistics, as correspond to
an integrated luminosity of only about 50.0 pb$^{-1}$. More events
are needed both to ensure statistical significance in the search and
to model the background with sufficient precision. The analysis is
therefore extended to incorporate pre-v13 data, corresponding to an
integrated luminosity of approximately 300 pb$^{-1}$. In fact, the
analysis described in the following will concentrate largely on the
pre-v13 sample. See Appendix A for more information on the v13
triggers and data.

The data arise from the ``BID'' skim, processed and fixed with the
pass2 p14 version of the reconstruction software.\footnote{The
analysis in Section 7 uses the pass1 p14 data} 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 jet of cone radius 0.5. (A cone radius is specified by $ \Delta R = \sqrt{(\Delta\phi)^{2} + (\Delta\eta)^{2}} $, with $\phi$ and $\eta$ being the azimuth and pseudorapidity.) This requirement enhances the fraction of heavy-flavour events due to the decays of $b\rightarrow \mu$ and $b\rightarrow c\rightarrow \mu$;\footnote{The BID skim provided the best data 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, each with $p_T>15$ GeV/c, but not demand any muons. Initial studies indicate that the total efficiency for signal would increase by 50--100\% using this skim.}

\item The skim contains about 90 million events, and corresponds to integrated luminosities of about 50 pb$^{-1}$ and 300 pb$^{-1}$ for the v13 and pre-v13 data, respectively.

\end{itemize}

The following selection criteria are imposed to ensure good data
quality:

\begin{itemize}
\item Events are required to be contained in acceptable luminosity blocks.
\item Good calorimeter and jet/Missing $E_{T}$ response in runs.
\item Runs with acceptable muons.
\item Runs with acceptable central-tracking information (SMT and CFT).
\end{itemize}

%=====================================================================================
\subsection{Monte Carlo} \label{sec.mc_samples}
%=====================================================================================

A range of Monte Carlo (MC) samples are used in the analysis 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     & 82,000 \\
\hline \multicolumn{3}{|c|}{\textit{Heavy-flavour 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)
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 either the RASTA
or, in Section 7, the higgs\_multijet roottuple-generating packages.
Jet energy scale corrections are applied to all jets, including
corrections for muons in jets, using version 5.3 of the jet energy
correction software.\footnote{The analysis in Section 7 used an
earlier version of the jet energy scale corrections compatible with
data from the p14 pass1.} No specific $b$-jet energy scale
corrections are applied, as no officially approved corrections exist
for these data.

Monte Carlo events are corrected throughout the analysis to account
for the $b$-tagging efficiency and jet measurement effects observed
in data. Jet energies are smeared to 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 not 100\% efficient.

\newpage

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

$Z\rightarrow b\overline{b}$ events are characterised 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 prescaled and candidate events thrown
away.

Ideally, the trigger should rely on dijet events with displaced
vertices at Level~2, but this capability was provided only recently
by the Level~2 Silicon Track Trigger (STT). Alternatively, candidate
events can be selected at the trigger level using the semileptonic
decay of the $b$-quarks. However, triggering on muons within one or
both $b$ jets from the $Z$, limits the signal efficiency 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\%.} The v8 to v12 trigger lists
ran online from 2001 to June 2004; they contain more than 60
different muon-based triggers of interest to this analysis, which
were exposed to a luminosity of about 300 pb$^{-1}$.

The leading muon triggers of the full data sample were identified
(i.e. those which were fired most often in data for candidate events
after final event selection) and the most significant trigger in the
v12 data was selected for the analysis\footnote{This trigger
selection does however not apply to the analysis presented in
Section 7, which treats the entire data as a whole}.

The most significant v12  and  v11 triggers are described in
Tables~\ref{table:v12ORtrigdesc} and~\ref{table:v11ORtrigdesc},
respectively.
%These triggers were the ones that were fired most frequently by selected candidate events in data.

%\begin{table}[ht]
%\begin{center}
%\begin{tabular}{|c|c|c|c|}
%\hline
%\textbf{v13 Trigger} & \multicolumn{3}{|c|}{\textbf{Trigger Description}} \\ \cline{2-4}
%                     & \textbf{Level 1}            & \textbf{Level 2}            & \textbf{Level 3} \\
%\hline
%\hline
%MUJ1\_2JT12\_LMB\_V   & single $\mu$ $+$ 2~jets    &  $\ge1 \mu$ $+$ $\ge1$ jet  & IP tag, vtx cut, $\mu$, $\ge$2~jets \\
%\hline
%MM1\_JT25             & single $\mu$ + track       &  $\ge1 \mu$                 & $\ge$1~jet   \\
%\hline
%MUJ2\_2JT12\_LMB\_V   & single $\mu$ $+$ jet       &  $\ge1 \mu$ $+$ $\ge1$ jet                 & IP tag, vtx cut, $\mu$, $\ge$2~jets \\
%\hline
%ZBB\_TLM3\_2JBID\_V   & single $\mu$ + track       &  $\ge1 \mu$                 & $\ge1 \mu$ + track, IP tag, vtx cut, 2~jets \\
%\hline
%\end{tabular}
%\caption{\label{table:v13ORtrigdesc} Description of the four leading v13 $Z$~$\rightarrow$~$b\overline{b}$ triggers. Note that all of the three single muon based specifically designed $Z\rightarrow b\bar{b}$ triggers from Table 3 are among the four leading triggers.}
%\end{center}
%\end{table}

\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}


% NB: PASS 2 v13 lumis obtained from Per's Zbb talk, 06-01-05

Trigger efficiencies for the v12 and v11 triggers are listed in
Tables~\ref{table:v12trigeff} and~\ref{table:v11trigeff}.

\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}

\clearpage

%[The dimuon and ZBB\_TLM3\_2LM0\_2J triggers which both require two muons (either at Level~1 or at Level~3) are about 20\% efficient at selecting signal events.]

%On average, each set of triggers is 15\% efficient with respect to offline cuts.

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 were
selected from this single trigger.\footnote{As previously noted, the
analysis presented in Section 7 does not apply this trigger
selection.}
\newpage

%=====================================================================================
\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,
$\Delta\varphi$. Intuitively, for a given jet $p_{T}$, one would
expect the two leading jets to be more back-to-back in
$Z$~$\rightarrow$~$b\overline{b}$ events than in QCD background, due
to the color connection between initial and final state and hence
the presence of more gluon radiation in the QCD processes.

% DPHI PLOT HERE

With this in mind, candidate events are selected using the following
offline prescription:

\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;
\item [\textbf{Cut 3}] The two jets must both have $\mid\eta\mid < 2.5$ and corrected $p_{T}$ $>$ 15 GeV/c;
\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 to it and be located within $\pm 50$ cm in the z-direction;
\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 strongly back-to-back, i.e. $\Delta\varphi > 2.75$ radians.
\end{itemize}

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

\begin{table}[ht]
\begin{center}
\begin{tabular}{|c|c|}
\hline
\textbf{Analysis Cut}  & \textbf{Number of Events}\\
                       & \textbf{Passing Cut, pre-v13}\\
\hline \hline
No selection      & 336475 $\pm$ 1174\\
\hline
1                 & 18567 $\pm$ 276\\
\hline
2                 & 10524 $\pm$ 209 \\
\hline
3                 & 8055 $\pm$ 183\\
\hline
4                 & 6915 $\pm$ 169\\
\hline
5                 & 6643 $\pm$ 165\\
\hline
6                 & 1451 $\pm$ 77\\
\hline
7                 & 1444 $\pm$ 65 \\
\hline
\end{tabular}
\caption{\label{table:cutflow_zbb} Cut flow table for
$Z$~$\rightarrow$~$b\overline{b}$ Monte Carlo events passing pre-v13
triggers. Event counts are weighted by cross-section and luminosity,
the errors are statistical only.}
\end{center}
\end{table}

\begin{table}[ht]
\begin{center}
\begin{tabular}{|c|c|}
\hline
\textbf{Analysis Cut}  & \textbf{Number of Events}\\
                       & \textbf{Passing Cut, pre-v13}\\
\hline \hline
1            & 10882864 \\
\hline
2            & 5135730  \\
\hline
3            & 4030914 \\
\hline
4            & 2726889  \\
\hline
5            & 2698544 \\
\hline
6            & 33499 \\
\hline
7            & 31183 \\
\hline
\end{tabular}
\caption{\label{table:cutflow_data} Cut flow table for events in
data. Note the much higher fraction of events passing the offline
criteria in the v13 data.}
\end{center}
\end{table}

In the BID skim the bb/light quark fraction is about 10\% after a
single b-tag requirement (see Fig. 16). With the additional muon and
trigger selection (Cuts 1 and 2) the bb/light 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-flavour component remains which still
swamps the signal; $\textrm{S:(S+B)}$ is of the order of 1:20. 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}

\noindent 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. In what follows, the square root of $N_{tot}$ -
$N_{signal}$ is used as a conservative estimate of the size of the
statistical error on the background; see Section 6 for how this
error is calculated in the actual analysis.

Figure~\ref{fig:signif_njets_v12OR} shows the variation of effective
signal significance with the cut on the number of jets in the event
and indicates that restricting the number of jets to exactly two
provides the best significance. Requiring two and only two jets
desirably cleans up the signal by restricting the amount of
radiation between the jets.

%insert figure njets_sign_v12_top3.eps
\begin{figure}[!ht]
\begin{center}
%\includegraphics[width=12cm, height=8cm]{./njets_sign_final_prev13.eps}
\includegraphics[width=12cm, height=8cm]{./sign_vs_njets.eps}
\caption{\label{fig:signif_njets_v12OR} Effective signal
significance, before cut 7, as a function of the cut on the number
of good jets in the event, $n_{jet}$, in the pre-v13 data. The
systematic error on the number of background events was set to 1\%.
Maximum significance is obtained in events with two and only two
jets. }
\end{center}
\end{figure}

In Figure~\ref{fig:dphi_v12OR} we compare the azimuthal angle
between the two jets for signal and data, after applying cuts 1--6
and accounting for the trigger efficiency and the integrated
luminosity of 297.5 pb$^{-1}$. The signal:background ratio is 1:23
and, as expected, the jets in $Z$~$\rightarrow$~$b\overline{b}$ are
slightly more back-to-back than in the background. Effective
significance is plotted as a function of $\Delta\varphi$ cut in
Figure~\ref{fig:signif_dphi_v12OR}, while varying the systematic
part of the error on the background. Taking into account the
triggger efficiency and integrated luminosity, a significance of 4
is obtained with a cut of $\Delta\varphi > 2.75$ radians and a
background systematic uncertainty of 1\% (see Section~6 for a
discussion of background uncertainties.). Note that so far no
invariant mass cut has been applied. Since the signal events are
expected to be concentrated in an invariant mass window around the Z
mass(see Figure~\ref{fig:invmass_final_prev13}), such a cut around
the interesting region can be expected to further enhance the
significance of the signal. We can therefore conclude that an excess
of $Z\rightarrow b\overline{b}$ events of the order of 4 sigma above
the background may already be observable in the pre-v13 data sample,
if the background can be estimated with sufficient precision.


\begin{figure}[!ht]
\begin{center}
\includegraphics[width=12cm, height=8cm]{./dphi10_final_prev13_correctsigma.eps}
\caption{\label{fig:dphi_v12OR}Comparison of the angular dijet
distribution between pre-v13 data and signal MC, after passing cuts
1--6. Red (dark grey) histogram: MC signal; black points: data. The
signal is slightly more back-to-back and S:S+B is approximately
1:23.}
\end{center}
\end{figure}

%insert figure dphi_sign_v12_top3.eps
\begin{figure}[!ht]
\begin{center}
%\includegraphics[width=12cm, height=8cm]{./dphi_sign_final_prev13.eps}
\includegraphics[width=12cm, height=8cm]{./sign_vs_dphi.eps}
\caption{\label{fig:signif_dphi_v12OR} Effective signal significance
as a function of $\Delta\varphi$ cut in pre-v13 data, for a
systematic error of (from top to bottom) 0\% (blue), 0.5\% (green),
1\% (red), and 2\% (black) on the number of background events. The
dependence on $\Delta\varphi$ is weak and a loose cut of 2.75 was
used in the pre-v13 analysis. }
\end{center}
\end{figure}

%insert figure inv_di-jet_mass_v13.eps
\begin{figure}[!ht]
\begin{center}
%\includegraphics[width=12cm, height=8cm]{./invmass_final_prev13.eps}
\includegraphics[width=12cm, height=8cm]{./fig4_correctsigma.eps}
\caption{\label{fig:invmass_final_prev13} Comparison of the
invariant dijet mass after event selection in pre-v13 data (black)
and the expected $Z$~$\rightarrow$~$b\overline{b}$ MC signal (red).
No b-jet energy scale correction is available for this data, which
explains why the Z mass peak is shifted towards lower masses. Note
that the region above 120 GeV is almost signal free. }
\end{center}
\end{figure}

\clearpage



%After triggering, and for our optimal set of kinematic cuts, we derive signal event predictions from Monte Carlo. They are shown in the following table.

\clearpage

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

Understanding the background to the $Z\rightarrow b\bar{b}$ signal
in the double b-tagged data sample is as we have seen crucial to
this analysis. The background is composed almost entirely of
heavy-flavour dijet production and mistagged gluon/light-quark jet
production, all of which cannot be accurately simulated using
current techniques. Thus the background is derived from data, using
either single-tagged and/or untagged events. Once the background
shape is well understood, one can then subtract it from the data
with confidence.

We have developed two slightly different methods for measuring the
background. The two approaches have different strengths and
weaknesses and 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 first method (Section 6) defines signal and background `zones'
in terms of $\Delta\varphi$. A TRF is constructed using information
from the signal zone and then applied, as an event weight, to the
single tagged events in the same signal zone. The final invariant
mass background template is then normalized to the double tagged
data with a fit to the signal free invariant mass region above 120
GeV. As a comparison, the result of using the TRF from a background
zone with $\Delta\varphi < 3.0$ can be found in Appendix B.

The second approach (Section 7) does not prescribe signal and
background regions and instead uses a single data sample. In
addition, two corrections are applied to account for differences
between single $b$-tagged and untagged events and also to
incorporate signal events which are not double $b$-tagged.

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

%=====================================================================================
\subsection{Background Estimation Using an Invariant Mass Based TRF} \label{subsec.invmasstrf}
%=====================================================================================

A convenient starting point to this analysis is the strategy and
method used by the CDF $Z\rightarrow b\bar{b}$ analysis in Run
I~\cite{CDF}.

One can attempt to estimate the background by defining two regions
in $\Delta\varphi$ space:
\begin{itemize}
\item[1.]\textit{``In Zone'':} A region rich in signal. Events falling into this box pass Cuts 1--5 and Cut 7 (as outlined in Section~\ref{sec.MCsel}). Cut 7, the cut of $\Delta\varphi$ $>$ 2.75 radians, ensures a more back-to-back like topology in the event.
\item[2.]\textit{``Out of Zone'':} A background-enriched region. Events only pass Cuts 1--5. They fail Cut 7, the `in zone' $\Delta\varphi$ criterion.
\end{itemize}

The data are then further divided into a double-$b$-tagged sample
(by imposing Cut 6) and a single-$b$-tagged sample. There are thus
four types of events:

\begin{itemize}
\item In Zone, double-tagged: $N_{in}^{++}$
\item In Zone, single-tagged:  $N_{in}^{+}$
\item Out of Zone, double-tagged:  $N_{out}^{++}$
\item Out of Zone, single-tagged:  $N_{out}^{+}$
\end{itemize}

In the signal-enhanced region, $N_{in}^{++}$ is an admixture of
genuine signal events plus background events. The amount of
background in-zone can be naively determined by calculating the
tag-ratio of double to single $b$-tags outside the zone and then
applying this TRF into the zone. Here the TRF is defined as the
ratio between $N_{out}^{++}$ and $N_{out}^{+}$. An estimate of the
expected background in-zone is then for each invariant mass bin
given by

\begin{equation} \label{eq:exp_bkg}
(N_{in}^{++})_{exp}^{bkg} = (N_{in}^{+})_{obs} \textrm{ x }
\frac{(N_{out}^{++})_{obs}}{(N_{out}^{+})_{obs}}.
\end{equation}

\noindent $(N_{in}^{++})_{exp}^{bkg}$ can then be subtracted
bin-by-bin from the invariant mass spectrum obtained after applying
Cuts 1--7. After subtraction, provided the number of events
occupying the side-band regions is consistent with zero, an excess
around the mass of the $Z$ constitutes evidence for a signal.

Underpinning this method is the assumption that it is valid to
extrapolate a TRF measured \textit{outside} the signal zone
\textit{into} the signal zone. This in turn assumes that the TRF is
independent of the choice of signal box, in particular of the choice
of $\Delta\varphi$ between the two leading jets in the event, and is
discussed further in Section~\ref{subsec.trfcor}. In addition,
signal events that appear out-of-zone are neglected, resulting in a
somewhat conservative signal estimate. In reality, a small amount of
$Z$~$\rightarrow$~$b\overline{b}$ will also be present outside the
zone (see Figure~\ref{fig:dphi_v12OR}).

%=====================================================================================
\subsection{Correction for the $\Delta\varphi$ Dependence of the TRF} \label{subsec.trfcor}
%=====================================================================================

Up to this point, it has been assumed that the ratio of double- to
single-tags outside the signal zone is independent of where the
signal box is placed, i.e. is independent of the particular
$\Delta\varphi$ value chosen to differentiate signal from
background. Figure~\ref{fig:black_red2} which shows the double to
single tag rate as a function of $\Delta\varphi$, however suggests a
strong linear dependence.

%Figure~\ref{fig:black_red2}, which shows the TRF as a function of invariant mass for signal and background-defined $\Delta\varphi$ values, suggests that this assumption is not valid, and that the TRF varies according to where in $\Delta\varphi$ space it is measured.

%insert figure black_red2.ps
\begin{figure}[!ht]
\begin{center}
\includegraphics[width=12cm, height=8cm]{./trf_dphi_prev13.eps}
\caption{\label{fig:black_red2} The variation of tag-rate function
with $\Delta\varphi$ between the two leading $b$-jets in each event,
for pre-v13 data. A linear dependence of the TRF upon
$\Delta\varphi$ is observed.}
\end{center}
\end{figure}

%In Figure~\ref{fig:black_red2}, the red points show the variation of the TRF with dijet mass for signal-enriched events. The black points correspond to the TRF of events in a signal-depleted zone where the jets are less back-to-back. As expected the TRF of signal-like events peaks around the $Z$ mass, while the TRF of background-like events peaks at a lower mass. Away from the $Z$ mass one would expect the two TRFs to converge, if the TRF is indeed independent of $\Delta\varphi$. Such convergence is, however, not seen, implying that the ratio of double- to single-tags depends on the $\Delta\varphi$ cut imposed.

A similar dependence of the TRF is also observed in Monte Carlo.

%insert figure trf_vs_dphi_bbqcd2040_notfulljes_fullsmear_notrig_notweighted_01radbins_fornote.eps
%\begin{figure}[!ht]
%\begin{center}
%\includegraphics[width=12cm, height=8cm]{./trf_vs_dphi_bbqcd2040_notfulljes_fullsmear_notrig_notweighted_01radbins_fornote.eps}
%\caption{\label{fig:TRF_dphifit_v12OR} The variation of tag-rate function with $\Delta\varphi$ between the two leading $b$-jets in each event, for $b\overline{b}$ Monte Carlo. As with data, a linear dependence of the TRF upon $\Delta\varphi$ is observed.}
%\end{center}
%\end{figure}

Having demonstrated that a clear $\Delta\varphi$ dependence exists,
it is natural to evaluate and apply a correction for this
dependence.
Our initial approach involved deriving the correction by fitting a plot of the tag ratio against $\Delta\varphi$ from data outside the signal zone. As $\Delta\varphi$ increases, the ratio of double- to single-tags increases linearly. This linear dependence can be fitted and extrapolated from the mean value of $\Delta\varphi$ outside the zone to the average $\Delta\varphi$ value inside the zone. This method, however, results in a rather large systematic uncertainty on the number of background events.\\
A more accurate method to take the $\Delta\varphi$ dependence into
account is instead to normalize the TRF weighted invariant mass
distribution to the double-tagged data by fitting it to the observed
signal depleted region above 120 GeV. A possible weakness of this
method is that it does not account for any $\Delta\varphi$ dependent
invariant mass bias. Another approach, which will remove any such
$\Delta\varphi$ dependent difference between the events used for the
TRF and the selected in-zone events and also result in larger
statistics for the background determination, is to calculate the TRF
from the same in-zone events to which it will be applied and then
again fix the overall normalisation by fitting the invariant mass
distribution to the data above 120 GeV. In the following we will use
this method to model the background.

%In Figure~\ref{fig:black_red2} it can be seen that the fall-off of the TRF as a function of invariant mass is similar regardless of $\Delta\varphi$ (since the black and red graphs have similar shapes). As such, it is valid to average the TRF over all invariant masses while measuring the dependence on $\Delta\varphi$.

% Background systematic discussion
The main challenge arising from this method is the difficulty of
obtaining a sufficiently precise normalisation fit of the invariant
mass to the double tagged data. The systematic uncertainty of the
background which, as we have seen, is critcal to extract a signal of
any significance, is dominated by the error on this fit.

%The $\Delta\varphi$ correction yields an overall factor which is used to scale up the estimated background. For the v12 data the fit is shown in Figure~\ref{fig:TRF_dphifit_v12OR}. An extrapolation from a $\Delta\varphi$ of 2.77?? radians out-of-zone to 3.08?? radians inside the zone yields a correction of 18.8 $\pm$ 1.4\%??, where the uncertainty is taken from the error on the fit. For v13 and v11 data the correction factors are 33.0 $\pm$ 3.8\%??, respectively [CHANGE THIS?].

%It is not surprising that a similar dependence of the TRF upon $n_{jet}$ is also observed. An $n_{jet}$ correction to the TRF, which takes into account the effect of moving from $n_{jet}$ = 2 to $n_{jet}$ $\ge$ 2, is devised and found to be 10\%. This is then combined with the $\Delta\varphi$ correction to yield an overall factor which is used to scale up the estimated background. The total systematic error on the background is estimated to be 4\%. Thus the full TRF correction factors are 1.40 $\pm$ 0.04 for v13 data and 1.31 $\pm$ 0.04 for v12 events.

%insert figure tagrate_vs_dphi_v12_top3.eps
%\begin{figure}[!ht]
%\begin{center}
%\includegraphics[width=12cm, height=8cm]{./tagrate_vs_dphi_v12_top3.eps}
%\caption{\label{fig:TRF_dphifit_v12OR} The variation of tag-rate function with $\Delta\varphi$ between the two leading $b$-jets in each event, for v12 data. A linear dependence of the TRF upon $\Delta\varphi$ is observed and a correction factor of 1.31 $\pm$ 0.04 (syst.)?? is derived. For v13, the correction is 1.40 $\pm$ 0.04 (syst.).??}
%\end{center}
%\end{figure}


%=====================================================================================
\subsection{Improving the TRF Further: The Jet-Based TRF Method} \label{subsec.jettrf}
%=====================================================================================

%We have seen that an invariant-mass based constant TRF does not model the background shape correctly at higher masses.
In addition to correcting for the $\Delta\varphi$ dependency of the
TRF, we can improve the way in which the TRF is calculated. Instead
of an invariant-mass based TRF, a TRF can be constructed on a
jet-by-jet basis. This is a similar approach to that adopted in the
D\O\ Run II $hb\overline{b}$ analysis~\cite{hbb}.

This approach can still be based on either events inside or outside
the signal zone. Consider events in which the first-leading jet is
single-SVT loose tagged. For these events, the second leading jet is
categorised 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 parametrised as a function of the $p_{T}$ of the second
leading jet. This generates a TRF \textit{per jet}.

To estimate the background in-zone, each event passing Cuts 1--5 and
7 and with the leading jet loose SVT $b$-tagged is weighted by the
TRF corresponding to the second leading jet. This is likely to be a
more accurate method as it provides a finer resolution to the
correction. 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 (as discussed
in Section~\ref{subsec.trfcor}). Figure~\ref{fig:et67_v12OR.eps}
illustrate the jet-based TRF as a function of the second leading jet
$p_{T}$, for jets in three different $\eta$-bins: $\mid\eta\mid
<1.1$, $1.1< \mid\eta\mid <1.5$, and $1.5< \mid\eta\mid <2.5$ for
in-zone events (See Appendix B for the TRF from the out-zone).


%insert figure et67_v12_top3.eps
\begin{figure}[!ht]
\begin{center}
%\includegraphics[width=12cm, height=8cm]{./trf_dphi_gt_3_prev13.eps}
\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 in-zone events in pre-v13
data.}
\end{center}
\end{figure}

%insert figure et68_v12_top3.eps
%\begin{figure}[!ht]
%\begin{center}
%\includegraphics[width=12cm, height=8cm]{./et68_v12_top3.eps}
%\caption{\label{fig:et68_v12OR.eps} TRF as a function of second-leading jet $E_{T}$ for jets in the region $1.1$ $<$ $\mid\eta\mid$ $<$ $1.5$??[WHICH REGION IS THIS PER?], evaluated in v12 data.}
%\end{center}
%\end{figure}



\clearpage

%=====================================================================================
%\subsection{Systematic Error on the Background Estimation} \label{subsec.systerr}
%=====================================================================================

%Per - please could you add a discussion of the systematics here? Thanks.

\newpage

%=====================================================================================
\subsection{Comparing The Background Models to Data} \label{subsec.data}
%=====================================================================================

The described background model - with a jet-based TRF - is now
applied to the entire pre-v13 data. Figure~\ref{fig:bkg_fit} shows
the fit of the background prediction (from the in-zone TRF) to the
double tagged data in the high mass region. The normalization
correction is given by the single fit parameter ``bkg''.\footnote{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 0.96 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.}

%insert figure bkg_fit.eps
\begin{figure}[!ht]
\begin{center}
%\includegraphics[width=12cm, height=8cm]{./bkg_fit.eps}
\includegraphics[width=12cm, height=8cm]{./massfit_dphi_2.75.eps}
\caption{\label{fig:bkg_fit} Invariant dijet mass in the pre-v13
data \textit{before} background subtraction. Green (light gray)
shaded histogram: expected background, estimated using a jet-based
TRF from in-zone events and fit with a one parameter fit to the
observed data above 120 GeV. Black points: total dijet 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 0.9538 $\pm$ 0.0116.}
\end{center}
\end{figure}

The normalised invariant mass background compared to data and signal
MC is shown in Figure~\ref{fig:invmass621_dphi_gt_3}. Figure
~\ref{fig:invmass627_dphi_gt_3} shows the invariant mass after
subtraction of the background.


\begin{figure}[!ht]
\begin{center}
%\includegraphics[width=12cm, height=8cm]{./invmass621_dphi_gt_3.eps}
\includegraphics[width=12cm, height=8cm]{./invmass121_dphi_2.75.eps}
\caption{\label{fig:invmass621_dphi_gt_3} Invariant dijet mass in
the pre-v13 data \textit{before} background subtraction. Green
(light gray) shaded histogram: expected background, estimated using
a jet-based TRF from in-zone events. The dark blue band indicates
the $\pm$ 1.7 \% systematic error on the background. Black points:
total dijet mass distribution observed in data. Red (dark grey)
histogram: expected $Z\rightarrow b\bar{b}$ signal from MC.}
\end{center}
\end{figure}

%insert figure invmass627_dphi_gt_3.eps
\begin{figure}[!ht]
\begin{center}
%\includegraphics[width=12cm, height=8cm]{./invmass627_dphi_gt_3.eps}
\includegraphics[width=12cm, height=8cm]{./627_dphi_2.75.eps}
\caption{\label{fig:invmass627_dphi_gt_3} The invariant dijet mass
spectrum in the pre-v13 data \textit{after} background (from in-zone
TRF) 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 pre-v13
data and Monte Carlo is presented in
Table~\ref{table:excessnums_v12}. After background subtraction we
observe an excess of

\begin{center}
1352.8 $\pm$ 151.33 (stat.) $\pm$ 305.70 (syst.) events
[\textit{pre-v13 data, 297.5 pb$^{-1}$}]
\end{center}

\noindent in the 50--100~GeV/c$^{2}$ mass window, as plotted in
Figure~\ref{fig:invmass627_dphi_gt_3}. The excess peak is fitted
with a Gaussian and compared to the number of events expected from
Monte Carlo. We expect to see

\begin{center}
1388.92 $\pm$ 107.09 (stat.) events   [\textit{Signal Monte Carlo,
with pre-v13 trigger}]
\end{center}

\noindent and therefore observe good agreement between data and
Monte Carlo within the errors. Table~\ref{table:excesssummary_v12}
summarizes the overall pre-v13 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, similar to the 0 to
1 tag correction in Section 7, reveals a net uncertainty on the
number of background events of less than 1\% in the 50-100 GeV $Z$
mass region. 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. 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}.

%For completeness, Table~\ref{table:excessnums_mc} summarises the signal event predictions per 30~GeV/c$^{2}$ mass bin, for the v13 set of triggers.



\begin{table}[ht]
\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}[ht]
\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}



\clearpage

%=====================================================================================
\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 in-zone TRF were fitted 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 Figure~\ref{fig:closure}).

%insert figure invmass_template_fit.eps
\begin{figure}[!ht]
\begin{center}
%\includegraphics[width=12cm, height=8cm]{./closure_dphi_gt_3.eps}
\includegraphics[width=12cm, height=8cm]{./closure_2.75.eps}
\caption{\label{fig:closure} Closure test of the final invariant
dijet mass spectrum observed in the pre-v13 data after background
subtraction.  Green (light gray) shaded histogram: expected
background, estimated using a jet-based TRF from in-zone events.
Black points: total dijet 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}

As can be seen, the fitted background scale parameter is 0.9541
$\pm$ 0.0091, which within the error is compatible with the value
obtained from Figure~\ref{fig:bkg_fit}. The fitted signal scale
parameter is within errors compatible with the expected value 1, we
therefore conclude that the sum of the signal MC and the background
as calculated with our in-zone TRF based model and normalised 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.

\newpage

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

Another method of background estimation will now be discussed; it
differs from the previous method in the following ways:

\begin{itemize}
\item The full pass1 pre-v13 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 than the pass2 data.

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

\item The method does not assume that the signal or background is dependent on $\Delta\varphi$. The jet-based TRF is measured in, and applied to, the same data sample, as was done in the "in-zone TRF" method discussed above.

%\item Because there is only one data sample used, no $\Delta\varphi$ correction is applied to the TRF. This eliminates the systematic error which would be associated with that correction.

%\item The use of a single data sample allows the method to use larger statistics and include the signal events which would have been classified in the background-rich data sample by the previous method.

\item A slightly wider $\Delta\varphi$ cut was used, $> 2.9$ instead of $> 3.0$.

\end{itemize}

In addition, two corrections are applied to this background
estimation:

\begin{itemize}

\item Because the TRF is applied to the single-tagged data sample, which is less rich in heavy-flavour 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-flavour 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. The shift is observed and measured using an \emph{untagged} data sample. A TRF is derived for the un-tagged data and applied to the untagged 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-flavour by the same amount. This is verified by comparing the data with MC $b\bar{b}$ events.

\item 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$1 correction and the TRF are derived, respectively, are corrected for. A signal peak is first measured in double-tagged data, using this background subtraction method, including the 0$\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.

\end{itemize}

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

As described above, the shift in the invariant mass spectrum of the
dijet 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 (see
Figure~\ref{fig:notag_trf}) 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 dijet 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.

\begin{center}\begin{figure}[!ht]\begin{center}
\includegraphics[width=12cm]{./TRFs_1tag.eps}
\caption{\label{fig:notag_trf} The TRF's derived on the un-tagged
data sample, which are used to estimate the single-tagged
background. Each TRF is a function of corrected jet $p_T$ in one of
three $\eta$-bins: $\eta<1.1$, $1.1<\eta<1.5$, and $1.5<\eta<2.5$. }
\end{center}\end{figure}\end{center}

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-flavour jets to light-jets as a function of dijet 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 dijet invariant mass
spectrum (which was normalized using double-tagged data) and to the
$Z\rightarrow b\bar{b}$ MC dijet 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 Double-tag TRF} \label{subsec.fulltrfdoubletrf}
%=====================================================================================

To estimate the double b-tagged background, a set of TRFs are
derived as a function of corrected jet $p_T$ for 3 $\eta$-bins from
the single-tagged data and reapplied to the same data. The TRFs are
shown in Figure~\ref{fig:TRFs}. The resulting estimate of the
double-tagged background is compared to double-tagged data and shown
in Figure~\ref{fig:doubletag_beforeZtrf}.

\begin{center}\begin{figure}[!ht]\begin{center}
\includegraphics[width=12cm]{./TRFs.eps}
\caption{\label{fig:TRFs} The TRF's derived on the single-tagged
data sample, which are used to estimate the double-tagged
background. Each TRF is a function of corrected jet $p_T$ in one of
three $\eta$-bins: $\eta<1.1$, $1.1<\eta<1.5$, and $1.5<\eta<2.5$.}
\end{center}\end{figure}\end{center}

\begin{center}\begin{figure}[!ht]\begin{center}
\includegraphics[width=12cm]{./doubletag_beforeZtrf.eps}
\caption{\label{fig:doubletag_beforeZtrf} The comparison between
double b-tagged data (points) and the expected background, from the
TRF method using single-tagged data, before either of the background
corrections ($0\rightarrow 1$ or Z peak).}
\end{center}\end{figure}\end{center}

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

As mentioned above, 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, as shown in
Figure~\ref{fig:histo200}.

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}.

\begin{center}\begin{figure}[!ht]\begin{center}
\includegraphics[width=12cm]{./histo200.eps}
\caption{\label{fig:histo200} The estimated fraction of
$Z\rightarrow b\bar{b}$ events in the single-tagged data sample, as
estimated from the peak observed in the double-tagged data sample
after subtracting the background estimated via the TRF method. This
fraction of events will be subtracted from the single-tagged data,
and then the final TRFs are derived and re-applied to this corrected
single-tagged data set.}
\end{center}\end{figure}\end{center}

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 This Full-TRF Method to Data} \label{subsec.fulltrfresults}
%=====================================================================================

After Z peak corrections to the un-tagged and single-tagged data
samples, the comparison of the background-subtracted double-tagged
data to the observed 0$\rightarrow$1 tag shift is shown in
Figure~\ref{fig:diff_cdiff_300_dphi_2.9_01}. (The slightly different
shape of the 0$\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.eps}
\caption{\label{fig:diff_cdiff_300_dphi_2.9_01} Comparison of the
background-subtracted double-tagged data (white squares) to the
observed 0$\rightarrow$1 tag shift (green). The slightly different
shape of the 0$\rightarrow$1 tag shift without Z peak corrections to
the un-tagged and single-tagged data samples is also shown (black),
to give a feel for the size of the effect.}
\end{center}\end{figure}\end{center}

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 is able to use a larger $\Delta\varphi$ range (2.9
as opposed to 3.0), spans the pre-v13 trigger-list data in the Pass1
skim, 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}). This
efficiency is reasonable since the trigger/skimming require a muon,
and the signal has two $b$-jets, each with a 10\% branching ratio to
muons.

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

We have investigated different methods to extract an observable
$Z\rightarrow b\bar{b}$ signal in the p14 data from the BID skim.
Using a jet based TRF from events in the back to back $\Delta\varphi$ region to model the background we observe 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, but correcting for the
$Z$ contribution to the TRF, also confirms the observed excess:
\begin{center}
810 $\pm$ 230 {\tiny(stat.)}
\end{center}

The position and width of the observed mass peak are in both cases
in agreement with MC expectations. 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. MC
studies have shown that the reconstructed peak position is sensitive
to both trigger as well as muon and jet $p_{T}$ requirements.

Worth noting is also the interesting small excess around di-jet
masses of 140 GeV, which is seen in the data with both methods.

%Systematics/Errors:

%The integrated luminosity can only be roughly approximated, since the data are not selected by any given set of triggers, and prescales and overlaps are largely unknown. An estimate of the integrated luminosity can be obtained by comparing the invariant mass spectrum of dijet events in the full data sample to that obtained from a smaller data sample selected by requiring a trigger with known luminosity.

%Both TRF methods take a 10\% error on (v12) lumi.

%The main problem is to beat down the systematic error.

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

%=====================================================================================
\section{Conclusions} \label{sec.conclusions}
We have demonstrated that a $Z\rightarrow b\bar{b}$ di-jet mass resonance indeed successfully can be isolated from the massive QCD background, already with the first 300 pb$^{-1}$ of RunII data collected by the D\O\ experiment. The observed excess agrees well with the expectations from $Z\rightarrow b\bar{b}$ MC. \\
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 $Z$ peak but also enable a
more precise background determination.
%=====================================================================================


%=====================================================================================
%\section{References} \label{sec.refs}
\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.
\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.
\end{thebibliography}
%=====================================================================================
\newpage
\section*{Appendix A: Trigger list v13}
A set of five dedicated $Z\rightarrow b\overline{b}$ triggers were
designed to run unprescaled up to luminosities of about 80 x
$10^{30}$ cm$^{-2}$s$^{-1}$ as part of the v13 trigger list.
Table~\ref{table:v13trigdesc} provides a description of these new
trigger terms. Three of the triggers identify single-muon events
using either $b$-tagging or muon selection at Level~3. The other two
triggers select clean but rare dimuon events. The aim was to
construct a versatile set of triggers which cover different
characteristics of the $Z$~$\rightarrow$~$b\overline{b}$ decay.

\begin{table}[ht]
\begin{center}
\begin{tabular}{|c|c|c|c|}
\hline \textbf{v13 Trigger} & \multicolumn{3}{|c|}{\textbf{Trigger
Description}} \\ \cline{2-4}
                     & \textbf{Level 1}            & \textbf{Level 2}            & \textbf{Level 3} \\
\hline \hline
ZBB\_TLM3\_2JBID\_V   & single $\mu$ + track       &  $\ge1 \mu$                 & $\ge1 \mu$, IP tag, vtx cut, 2~jets \\
\hline
ZBB\_TLM3\_2LM0\_2J   & single $\mu$ + track       &  $\ge1 \mu$                 & $\ge2$~medium~$\mu$, 2~jets\\
\hline
MUJ1\_2JT12\_LMB\_V   & single $\mu$ $+$ 2~jets    &  $\ge1 \mu$ $+$ $\ge1$ jet  & IP tag, vtx cut, $\mu$, $\ge$2~jets \\
\hline
MUJ2\_2JT12\_LMB\_V   & single $\mu$ $+$ jet       &  $\ge1 \mu$                 & IP tag, vtx cut, $\mu$, $\ge$2~jets \\
\hline
DMU1\_JT12\_TLM3      & dimuon term                & $\ge1 \mu$                  & $\ge$$1$ trk-matched $\mu$, jet  \\
\hline
\end{tabular}
\caption{\label{table:v13trigdesc} Description of the new v13
$Z$~$\rightarrow$~$b\overline{b}$ triggers. ``trk-matched'' means
track-matched; ``vtx cut'' means vertex cut.}
\end{center}
\end{table}

%With an array of muon-based triggers in hand - including the new v13 ones and older pre-existing triggers - we then determined which of the many muon-based triggers were most useful for selecting candidate events.

%The leading triggers of the full data sample were identified (i.e. those which were fired most often in data for candidate events after final event selection) and the most significant muon triggers for the v13 and the v12 data were then selected for the analysis.

%We then determined the minimum number of top triggers that, when combined in an ORed term, at least 95\% of the $Z$~$\rightarrow$~$b\overline{b}$ signal. In this way, we optimise the signal yield while minimising the amount of background noise events that filter through on insignificant triggers.
%Ultimately, the study revealed that for the v13 data an ORed combination of the top four triggers was sufficient to collect most of the signal, while for the v12 and v11 data a combination of the top three triggers was optimal.

The v13 data exploited in this study were collected between early
June 2004 and the end of August 2004, when the Tevatron shutdown
commenced. Each v13 trigger was exposed to approximately 50--60
pb$^{-1}$ of integrated luminosity, which reduces to about 50
pb$^{-1}$ after good run selection (see
Table~\ref{table:v13lumistats}).

\begin{table}[ht]
\begin{center}
\begin{tabular}{|c|c|c|c|}
\hline \textbf{v13 Trigger} &
\multicolumn{3}{|c|}{\textbf{Luminosity \boldmath (pb$^{-1}$)}}  \\
\cline{2-4}
                     & \textbf{Delivered} & \textbf{Recorded}  & \textbf{Good} \\
\hline \hline
ZBB\_TLM3\_2JBID\_V   & 68.9 & 49.7 & 45.9 \\
\hline
ZBB\_TLM3\_2LM0\_2J   & 68.9 & 49.7 & 45.9 \\
\hline
MUJ1\_2JT12\_LMB\_V   & 68.9 & 53.8 & 48.9 \\
\hline
MUJ2\_2JT12\_LMB\_V   & 68.9 & 51.6 & 47.4 \\
\hline
DMU1\_JT12\_TLM3      & 68.9 & 62.0 & 54.2 \\
\hline
\end{tabular}
\caption{\label{table:v13lumistats} Delivered, recorded and good
luminosity for the v13 $Z$~$\rightarrow$~$b\overline{b}$ triggers.
This analysis incorporates only good luminosity data. The dimuon
trigger was exposed to a larger integrated luminosity as it remained
unprescaled. The single-muon triggers were prescaled or turned off
at the very highest luminosities.}
\end{center}
\end{table}

The trigger rates and signal candidate yield of the most significant
v13 triggers are described in Table~\ref{table:v13ORtrigdesc}.

\begin{table}[ht]
\begin{center}
\begin{tabular}{|c|c|c|c|}
\hline
\textbf{v13 Trigger} & \textbf{Trigger rate at L=60E30} & \textbf{Signal candidate yield} \\
\hline \hline
MUJ1\_2JT12\_LMB\_V   & 1.24 Hz & 3741\\
\hline
MUJ2\_2JT12\_LMB\_V   & 1.09 Hz & 3349\\
\hline
MM1\_JT25             & 2.09 Hz & 2874\\
\hline
ZBB\_TLM3\_2JBID\_V   & 0.95 Hz & 2727\\
\hline
\end{tabular}
\caption{\label{table:v13ORtrigdesc} The trigger rates and signal
candidate yields, in the v13 portion of the data,  for the four
leading v13 $Z$~$\rightarrow$~$b\overline{b}$ triggers. Note that
all of the three single muon based specifically designed
$Z\rightarrow b\bar{b}$ triggers from Table 3 are among the four
leading triggers and that MM1\_JT25, which is a B-phyics trigger,
has a higher rate.}
\end{center}
\end{table}

Table~\ref{table:v13trigeff} lists the trigger efficiencies for the
v13 triggers, evaluated by passing signal Monte Carlo events through
a full trigger simulation ({\tt d0trigsim}). Trigger efficiencies
are quoted for each trigger individually and in combination (as an
ORed term). The fraction of events passing all three trigger levels
is calculated with respect to both absolute number of events and
events passing offline cuts.

\begin{table}[ht]
\begin{center}
\begin{tabular}{|c|c|c|}
\hline \textbf{v13 Trigger} & \multicolumn{2}{|c|}{\textbf{L1L2L3
Trigger Efficiency(\%)}} \\ \cline{2-3}
                     & \textbf{Absolute}         & \textbf{w.r.t. Offline Cuts}     \\
\hline \hline
MUJ1\_2JT12\_LMB\_V   & 3.3 & 11.1\\
\hline
MM1\_JT25             & 3.8 & 11.8 \\
\hline
MUJ2\_2JT12\_LMB\_V   & 3.3 & 11.6 \\
\hline
ZBB\_TLM3\_2JBID\_V   & 2.7 & 9.3 \\
\hline
OR of the above 4 triggers & 6.0 & 16.9 \\
\hline
\end{tabular}
\caption{\label{table:v13trigeff} v13 trigger efficiencies for MC
signal events.}
\end{center}
\end{table}

The v12 and v11 triggers are slightly more efficient than the v13
triggers as a result of looser L3 conditions (in particular no
IP-tag or primary vertex requirements). The tighter v13 conditions
are needed to avoid prescales at instantaneous luminosities above
50E30. The events from the v13 data were selected exclusively from
the MUJ1\_2JT12\_LMB\_V trigger which was exposed to a luminosity of
48.9 pb$^{-1}$. Tables~\ref{table:cutflow_zbb_v13}
and~\ref{table:cutflow_data_v13} show the number of events passing
each analysis cut in signal MC and data. Monte Carlo event counts
are weighted by cross-section and luminosity.

\begin{table}[ht]
\begin{center}
\begin{tabular}{|c|c|}
\hline
\textbf{Analysis Cut}  & \textbf{Number of Events}\\
                       & \textbf{Passing Cut, v13}\\
\hline \hline
No selection      & 55204 $\pm$193 \\
\hline
1  (MUJ1\_2JT12\_LMB\_V)                & 1814 $\pm$ 36 \\
\hline
2                 & 1012 $\pm$ 26 \\
\hline
3                 & 783.7 $\pm$ 23 \\
\hline
4                 & 745.8 $\pm$ 22 \\
\hline
5                 & 716.0 $\pm$ 22 \\
\hline
6                 & 183.3 $\pm$ 11 \\
\hline
7($\Delta\phi > 3.0$) & 120.4 $\pm$ 10 \\
\hline
\end{tabular}
\caption{\label{table:cutflow_zbb_v13} Cut flow table for
$Z$~$\rightarrow$~$b\overline{b}$ Monte Carlo events passing v13
triggers. Event counts are weighted by cross-section and luminosity,
the errors are statistical only.}
\end{center}
\end{table}

\begin{table}[ht]
\begin{center}
\begin{tabular}{|c|c|}
\hline
\textbf{Analysis Cut}  & \textbf{Number of Events}\\
                       & \textbf{Passing Cut, v13}\\
\hline \hline
1    (MUJ1\_2JT12\_LMB\_V)         & 536170  \\
\hline
2            & 259653 \\
\hline
3            & 218002  \\
\hline
4            & 179654  \\
\hline
5            & 177472  \\
\hline
6            & 7409 \\
\hline
7($\Delta\phi > 3.0$)            & 3741 \\
\hline
\end{tabular}
\caption{\label{table:cutflow_data_v13} Cut flow table for events in
data. Note the much higher fraction of events passing the offline
criteria in the v13 data.}
\end{center}
\end{table}
The small v13 sample has much lower statistics than the pre-v13 data
and also new triggers with different systematics, which at this time
makes it difficult to extract a $Z\rightarrow b\overline{b}$ signal
of any significance in this data\footnote{In the near future (the 1
fb$^{-1}$ p17 analysis) it will be possible to take full advantage
of the several times larger data sample which now has been collected
with the new v13 and v14 $Z$~$\rightarrow$~$b\overline{b}$ triggers,
and to exploit the potential of a significantly larger signal.}.

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

\section*{Appendix B: Estimating the background from the out-of-zone ($\Delta\varphi < 3.0$) TRF}

\begin{figure}[!ht]
\begin{center}
\includegraphics[width=12cm, height=8cm]{./trf_lt3.eps}
\caption{\label{fig:et66_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  out of zone events in
pre-v13 data.}
\end{center}
\end{figure}

%insert figure bkg_fit_dphi_gt_3.eps
\begin{figure}[!ht]
\begin{center}
\includegraphics[width=12cm, height=8cm]{./bkg_fit.eps}
\caption{\label{fig:bkg_fit_dphi_gt_3} Invariant di-jet mass in the
pre-v13 data \textit{before} background subtraction. Green (light
gray) shaded histogram: expected background, estimated using a
jet-based TRF from out-of-zone ($\Delta\varphi < 3.0$) events and
fit with a one parameter fit 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 1.177
$\pm$ 0.017. }
\end{center}
\end{figure}

%insert figure invmass621.eps
\begin{figure}[!ht]
\begin{center}
\includegraphics[width=12cm, height=8cm]{./invmass621.eps}
\caption{\label{fig:invmass621} Invariant di-jet mass in the pre-v13
data \textit{before} background subtraction. Green (light gray)
shaded histogram: expected background, estimated using a jet-based
TRF from out-of-zone ($\Delta\varphi < 3.0$) events. The dark blue
band indicates the $\pm$ 1.5 \% systematic error from the
normalization fit. 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}

%insert figure invmass627.eps

\begin{figure}[!ht]
\begin{center}
%\includegraphics[width=12cm, height=8cm]{./invmass627.eps}
\includegraphics[width=12cm, height=8cm]{./invmass627.eps}
\caption{\label{fig:invmass627} The invariant di-jet mass spectrum
in the pre-v13 data \textit{after} background (from out-of-zone,
$\Delta\varphi < 3.0$, TRF) subtraction. Black points: excess
observed in data, fitted with a Gaussian. Error bars show
statistical errors only. Red (dark gray) histogram: expected
$Z\rightarrow b\bar{b}$ signal from MC. The excess peak has a mean
mass of 70.6~$GeV/c^{2}$ and a width of 10.7~$GeV/c^{2}$.}
\end{center}
\end{figure}

As can be seen from plots~\ref{fig:invmass627} and
\ref{fig:invmass627_dphi_gt_3}, the agreement between data and
signal MC is better in the case where the background was modeled
with a TRF from in-zone events. The out-of-zone TRF results in a 4
GeV lower mass peak indicating that there indeed is a
$\Delta\varphi$ dependent invariant mass bias. In combination with
the larger statistics for the TRF determination, better data
agreement at high masses and the smaller normalization correction
for the in-zone TRF case, seen in Figure~\ref{fig:bkg_fit}, we
conclude that this method gives the most accurate result and is
hence used to extract the following results. The effect of applying
the out-of-zone TRF indicates that the $\Delta\varphi$ dependence is
small in terms of the observed excess, but gives shifts the observed
mass.

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

\section*{Appendix C: Some additional studies from Method 2}

The candidate events passing all cuts and double b-tagged in the
mass range 50--100 GeV were compared between Method 1 and Method 2.
As long as similar JES corrections were applied, the invariant mass
reconstructed in the two analyses was very similar, as expected.
Shown in Figure \ref{fig:MbbPerAndy_nomuJES_zoom} is a comparison of
the mass from Method 1 - the mass from Method 2, after just standard
JES corrections.

Also investigated was the efficiency and overlap between the two
analyses. Of the approximately 11,000 candidate events from Method
1:
\begin{itemize}
\item 739 are in bad luminosity blocks as determined
from the DQ criteria for pass 1
\item 1952 had the second-leading pT jet below Method 2's
threshold of 15 GeV (uncorrected). Recall that Method 1
applies jet pT cuts after JES corrections.
\item 5707 were not double-tagged by Method 2
(of these, 1409 had no b-tagged jets, and 4298 had one b-tagged jet)
\item 21 had a poor PV (<4 tracks)
\item 99 fell outside the 50-100 $M_{bb}$ range for Method 2
\item 3101 pass all selections for Method 2
\end{itemize}
We feel that all these losses are sensible between the two analyses.
Perhaps the only slightly surprising number is b-tagging. However,
b-tagging did change significantly between PASS1 and PASS2, with
different reconstruction and selection criteria.

\begin{figure}[!ht]
\begin{center}
\includegraphics[width=12cm, height=8cm]{./MbbPerAndy_nomuJES_zoom.eps}
\caption{\label{fig:MbbPerAndy_nomuJES_zoom} A comparison of the
reconstructed di-jet invariant mass between candidate events in
Method 1 and 2. (Mass in method 1 - Mass in method 2)}
\end{center}
\end{figure}

Figure \ref{fig:TRFs_1tag} shows the TRF derived from the un-tagged
data sample.

\begin{figure}[!ht]
\begin{center}
\includegraphics[width=12cm, height=8cm]{./TRFs_1tag.eps}
\caption{\label{fig:TRFs_1tag} The TRF as measured in the un-tagged
data sample, used for measuring the 0$\rightarrow$1 tag shift.}
\end{center}
\end{figure}

The cross-section for W$\rightarrow$cs is approximately 16 times
greater than Z$\rightarrow$bb, after including the larger W
cross-section and larger BR. However, the tag rate for
W$\rightarrow$cs should be about 8 times lower than for
Z$\rightarrow$bb due to the 1/4 tag-rate for c- compared to b-jets
and the fact that there's very little tag rate for the s-jet.
However, this still leaves twice the contamination from
W$\rightarrow$cs as Z$\rightarrow$bb in the single-tagged data
sample. This was previously ignored in the analysis, but can be
corrected for in a manner similar to the Z$\rightarrow$bb correction
in the un-tagged and single-tagged samples for TRF's. To simulate
the W$\rightarrow$cs contribution, the Z peak used for the
Z-correction was tripled in size. (This makes the approximation that
the peaks of W and Z have the same mass and width, compared to the
resolutions available to the analysis.) Figure
\ref{fig:zplot_2.9_Wcs} shows the final Z-peak after making this
increased correction. The peak is not significantly affected. We
also note that the trigger efficiency should be lower for
W$\rightarrow$cs, since the BR to muons is lower than for bb events,
so the true corrections would be even less significant. We also
mention that W$\rightarrow$cs can be safely ignored in the final
double-tagged data sample, to a good approximation. W$\rightarrow$cs
will be fully simulated and included at all steps in a future
incarnation of this analysis.

\begin{figure}[!ht]
\begin{center}
\includegraphics[width=12cm, height=8cm]{./zplot_2.9_Wcs.eps}
\caption{\label{fig:zplot_2.9_Wcs} The final Z-peak after correcting
approximately for the W$\rightarrow$cs contribution to the
single-tagged data sample.}
\end{center}
\end{figure}

Several additional tests were performed, varying the analysis cuts
and checking that the final Z-peak extracted from data agreed with
expectations from MC in terms of size, position, and width, as shown
in Figures \ref{fig:zplot_-2.9} - \ref{fig:zplot_2.5}. The extracted
peak always agreed well with expectations from MC, giving us
confidence that the peak truly is from Z$\rightarrow b\bar{b}$
production. After the $\Delta\phi$ cut was reversed to $<2.9$, the
peak largely disappears, as expected. When the muon-JES corrections
were removed, the peak became wider, as expected, since the
resolution of the jets is poorer without the correction. The peak is
also of course shifted down in mass, since the corrections increase
the observed jet energy. The $| \eta |$ cuts were restricted to the
central ($<1.0$) region and the forward ($>1.0)$ region, and in both
cases the observed number of events behaved as expected, although
statistics are poor in both cases. In addition, the Z-peak
corrections were not recalculated for any of these cases, thus the
shape of the background is slightly incorrect. The lack of the right
Z-peak corrections explains the systematic excess or deficit of
events in the region just above the Z-peak. Finally, the
$\Delta\phi$ cut was loosened to $>2.5$ (it was $>2.9$), and more
candidate events were observed, as expected.


\begin{figure}[!ht]
\begin{center}
\includegraphics[width=12cm, height=8cm]{./zplot_-2.9.eps}
\caption{\label{fig:zplot_-2.9} The final Z-peak after reversing the
$\Delta\phi$ cut to $<$2.9.}
\end{center}
\end{figure}

\begin{figure}[!ht]
\begin{center}
\includegraphics[width=12cm, height=8cm]{./zplot_2.9_nomuJES.eps}
\caption{\label{fig:zplot_2.9_nomuJES} The final Z-peak after
removing the muon-JES corrections -- only the standard JES was
used.}
\end{center}
\end{figure}

\begin{figure}[!ht]
\begin{center}
\includegraphics[width=12cm, height=8cm]{./zplot_2.9_eta1.0.eps}
\caption{\label{fig:zplot_2.9_eta1.0} The final Z-peak after
restricting the jet $| \eta |<1.0$.}
\end{center}
\end{figure}

\begin{figure}[!ht]
\begin{center}
\includegraphics[width=12cm, height=8cm]{./zplot_2.9_eta-1.0.eps}
\caption{\label{fig:zplot_2.9_eta-1.0} The final Z-peak after
restricting the jet $| \eta |>1.0$.}
\end{center}
\end{figure}


\begin{figure}[!ht]
\begin{center}
\includegraphics[width=12cm, height=8cm]{./zplot_2.5.eps}
\caption{\label{fig:zplot_2.5} The final Z-peak after relaxing the
$\Delta\phi$ cut to $>$2.5.}
\end{center}
\end{figure}


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






\end{document}
