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\@writefile{toc}{\contentsline {section}{\numberline {1}Background Subtraction}{1}}
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\@writefile{toc}{\contentsline {subsection}{\numberline {1.1}Invariant Mass Based TRF Method for Background Estimation (a.k.a. - The CDF Method)}{1}}
\newlabel{subsec.invmasstrf}{{1.1}{1}}
\newlabel{eq:exp_bkg}{{1}{2}}
\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces  Invariant dijet mass distribution in the v12 dataset \textit  {before} background subtraction. Green shaded histogram: Expected background, estimated using an invariant-mass based TRF. Black points: Total dijet mass distribution observed in v12 data.}}{2}}
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\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces  Invariant dijet mass spectrum from v12 data \textit  {after} background subtraction. The background is estimated using a tag-rate function calculated in the invariant-mass plane. An excess of events around the $Z$-peak is observed.}}{3}}
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\@writefile{toc}{\contentsline {subsection}{\numberline {1.2}Correction for the $\Delta \phi $ dependence of the TRF}{3}}
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\@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces  TRF as a function of invariant mass, for $\Delta \phi > 3.0$ radians (red points) and $2.8 < \Delta \phi < 3.0$ radians (black points). The distributions are derived from v12 data.}}{4}}
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\@writefile{toc}{\contentsline {subsection}{\numberline {1.3}The Jet-Based TRF Method with $\Delta \phi $ Correction}{4}}
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\@writefile{lof}{\contentsline {figure}{\numberline {4}{\ignorespaces  The variation of tag-rate function with $\Delta \phi $ between the two leading $b$-jets in each event, for v12 data. A linear dependence on $\Delta \phi $ is observed and the corresponding correction is derived.}}{5}}
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\@writefile{lof}{\contentsline {figure}{\numberline {5}{\ignorespaces  Invariant dijet mass in the v12 dataset \textit  {before} background subtraction. Green shaded histogram: Expected background, estimated using a jet-based TRF and scaling for the TRF dependence on $\Delta \phi $. Black points: total dijet mass distribution observed in data.}}{6}}
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\@writefile{lof}{\contentsline {figure}{\numberline {6}{\ignorespaces  Invariant dijet mass in the v12 dataset \textit  {after} background subtraction. An excess of 490 $\pm $ 22 events around the $Z$ mass is observed.}}{6}}
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\@writefile{toc}{\contentsline {subsection}{\numberline {1.4}The Full TRF Method with 0$\rightarrow $1 and Z Corrections}{7}}
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\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.4.1}Event Samples and Selection}{8}}
\newlabel{subsubsec. fulltrfsamples}{{1.4.1}{8}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.4.2}The $0\rightarrow 1$ tag Shift}{9}}
\newlabel{subsubsec. fulltrf01corr}{{1.4.2}{9}}
\@writefile{lof}{\contentsline {figure}{\numberline {7}{\ignorespaces  Comparison between the single-tagged data and the background expected using the TRF method. Comparisons are also shown to the $b\mathaccent "7016\relax {b}$ MC di-jet invariant mass spectrum (which was normalized using double-tagged data) and to the $Z\rightarrow b\mathaccent "7016\relax {b}$ 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.}}{10}}
\newlabel{fig:singletag_trf}{{7}{10}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.4.3}The Double-tag TRF}{10}}
\newlabel{subsubsec. fulltrfdoubletrf}{{1.4.3}{10}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.4.4}The 0- and 1-tag Z Peak Correction}{10}}
\newlabel{subsubsec. fulltrfzcorr}{{1.4.4}{10}}
\@writefile{lof}{\contentsline {figure}{\numberline {8}{\ignorespaces  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 $Z\rightarrow b\mathaccent "7016\relax {b}$ events in the un-tagged and single-tagged data samples, using the methods described below in Section 1.4.4\hbox {}.}}{11}}
\newlabel{fig:singletag_diff}{{8}{11}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.4.5}Results and Conclusions of the Full-TRF Method}{11}}
\newlabel{subsubsec. fulltrfresults}{{1.4.5}{11}}
\@writefile{lof}{\contentsline {figure}{\numberline {9}{\ignorespaces  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 3 $\eta $-bins: $\eta <1.1$, $1.1<\eta <1.5$, and $1.5<\eta <2.5$.}}{12}}
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\@writefile{lof}{\contentsline {figure}{\numberline {10}{\ignorespaces  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).}}{12}}
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\@writefile{lof}{\contentsline {figure}{\numberline {11}{\ignorespaces  The estimated fraction of $Z\rightarrow b\mathaccent "7016\relax {b}$ 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.}}{13}}
\newlabel{fig:histo200}{{11}{13}}
\@writefile{lof}{\contentsline {figure}{\numberline {12}{\ignorespaces  Comparison of the background-subtracted double-tagged data to the observed 0$\rightarrow $1 tag shift. The slightly different shape of the 0$\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.}}{14}}
\newlabel{fig:diff_cdiff_300_dphi_2.9_01}{{12}{14}}
\@writefile{lof}{\contentsline {figure}{\numberline {13}{\ignorespaces  The final $Z\rightarrow b\mathaccent "7016\relax {b}$ peak derived from data, after all corrections, compared to the shape of the $Z\rightarrow b\mathaccent "7016\relax {b}$ distribution in MC. (The slightly different shape of the Z peak in data without the 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.)}}{15}}
\newlabel{fig:diff_cdiff_300_dphi_2.9_01_diff}{{13}{15}}