\relax 
\@writefile{toc}{\contentsline {section}{\numberline {1}Motivation}{1}}
\newlabel{sec.intro}{{1}{1}}
\@writefile{toc}{\contentsline {section}{\numberline {2}Event Samples}{2}}
\newlabel{sec.samples}{{2}{2}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.1}The Data}{2}}
\newlabel{sec.data_samples}{{2.1}{2}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.2}Monte Carlo}{2}}
\newlabel{sec.mc_samples}{{2.2}{2}}
\@writefile{lot}{\contentsline {table}{\numberline {1}{\ignorespaces  Summary of Monte Carlo samples used in this analysis. $q$ refers to the light quarks $u$, $d$ or $s$.}}{3}}
\newlabel{table:MCsamples}{{1}{3}}
\@writefile{toc}{\contentsline {section}{\numberline {3}Triggers}{4}}
\newlabel{sec.triggers}{{3}{4}}
\@writefile{lot}{\contentsline {table}{\numberline {2}{\ignorespaces  Description of the three leading v12 muon triggers. Candidate signal events were required to pass MU\_JT25\_L2M0.}}{4}}
\newlabel{table:v12ORtrigdesc}{{2}{4}}
\@writefile{lot}{\contentsline {table}{\numberline {3}{\ignorespaces  Description of the three leading v11 muon triggers. Candidate signal events were required to pass MU\_JT25\_L2M0.}}{4}}
\newlabel{table:v11ORtrigdesc}{{3}{4}}
\@writefile{lot}{\contentsline {table}{\numberline {4}{\ignorespaces  v12 trigger efficiencies for MC signal events.}}{5}}
\newlabel{table:v12trigeff}{{4}{5}}
\@writefile{lot}{\contentsline {table}{\numberline {5}{\ignorespaces  v11 trigger efficiencies for MC signal events.}}{5}}
\newlabel{table:v11trigeff}{{5}{5}}
\@writefile{toc}{\contentsline {section}{\numberline {4}Event Selection}{7}}
\newlabel{sec.MCsel}{{4}{7}}
\@writefile{lot}{\contentsline {table}{\numberline {6}{\ignorespaces  Cut flow table for $Z$\nobreakspace  {}$\rightarrow $\nobreakspace  {}$b\overline {b}$ Monte Carlo events passing pre-v13 triggers. Event counts are weighted by cross-section and luminosity, the errors are statistical only.}}{7}}
\newlabel{table:cutflow_zbb}{{6}{7}}
\@writefile{lot}{\contentsline {table}{\numberline {7}{\ignorespaces  Cut flow table for events in data. Note the much higher fraction of events passing the offline criteria in the v13 data.}}{8}}
\newlabel{table:cutflow_data}{{7}{8}}
\newlabel{eq:signif}{{1}{8}}
\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces  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. }}{9}}
\newlabel{fig:signif_njets_v12OR}{{1}{9}}
\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces 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.}}{9}}
\newlabel{fig:dphi_v12OR}{{2}{9}}
\@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces  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. }}{10}}
\newlabel{fig:signif_dphi_v12OR}{{3}{10}}
\@writefile{lof}{\contentsline {figure}{\numberline {4}{\ignorespaces  Comparison of the invariant dijet mass after event selection in pre-v13 data (black) and the expected $Z$\nobreakspace  {}$\rightarrow $\nobreakspace  {}$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. }}{10}}
\newlabel{fig:invmass_final_prev13}{{4}{10}}
\citation{CDF}
\@writefile{toc}{\contentsline {section}{\numberline {5}Background Subtraction}{11}}
\newlabel{sec.bkgsub}{{5}{11}}
\@writefile{toc}{\contentsline {section}{\numberline {6}Background Estimation Method 1}{11}}
\newlabel{sec.bkgsub1}{{6}{11}}
\@writefile{toc}{\contentsline {subsection}{\numberline {6.1}Background Estimation Using an Invariant Mass Based TRF}{11}}
\newlabel{subsec.invmasstrf}{{6.1}{11}}
\newlabel{eq:exp_bkg}{{2}{12}}
\@writefile{toc}{\contentsline {subsection}{\numberline {6.2}Correction for the $\Delta \varphi $ Dependence of the TRF}{12}}
\newlabel{subsec.trfcor}{{6.2}{12}}
\@writefile{lof}{\contentsline {figure}{\numberline {5}{\ignorespaces  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.}}{12}}
\newlabel{fig:black_red2}{{5}{12}}
\citation{hbb}
\@writefile{toc}{\contentsline {subsection}{\numberline {6.3}Improving the TRF Further: The Jet-Based TRF Method}{13}}
\newlabel{subsec.jettrf}{{6.3}{13}}
\@writefile{lof}{\contentsline {figure}{\numberline {6}{\ignorespaces  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.}}{14}}
\newlabel{fig:et67_v12OR.eps}{{6}{14}}
\@writefile{toc}{\contentsline {subsection}{\numberline {6.4}Comparing The Background Models to Data}{15}}
\newlabel{subsec.data}{{6.4}{15}}
\@writefile{lof}{\contentsline {figure}{\numberline {7}{\ignorespaces  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 $Z\rightarrow b\mathaccent "7016\relax {b}$ signal from MC. The fit results in a correction to the background scale of 0.9538 $\pm $ 0.0116.}}{15}}
\newlabel{fig:bkg_fit}{{7}{15}}
\@writefile{lof}{\contentsline {figure}{\numberline {8}{\ignorespaces  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 $Z\rightarrow b\mathaccent "7016\relax {b}$ signal from MC.}}{16}}
\newlabel{fig:invmass621_dphi_gt_3}{{8}{16}}
\@writefile{lof}{\contentsline {figure}{\numberline {9}{\ignorespaces  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\nobreakspace  {}$GeV/c^{2}$ and a width of 11.27\nobreakspace  {}$GeV/c^{2}$.}}{16}}
\newlabel{fig:invmass627_dphi_gt_3}{{9}{16}}
\citation{ambers}
\@writefile{lot}{\contentsline {table}{\numberline {8}{\ignorespaces  Signal candidate counts before and after background subtraction in the pre-v13 data and MC. The errors are statistical only.}}{17}}
\newlabel{table:excessnums_v12}{{8}{17}}
\@writefile{lot}{\contentsline {table}{\numberline {9}{\ignorespaces  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.}}{18}}
\newlabel{table:excesssummary_v12}{{9}{18}}
\@writefile{toc}{\contentsline {subsection}{\numberline {6.5}Closure Test}{19}}
\newlabel{subsec.clostest}{{6.5}{19}}
\@writefile{lof}{\contentsline {figure}{\numberline {10}{\ignorespaces  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.}}{19}}
\newlabel{fig:closure}{{10}{19}}
\@writefile{toc}{\contentsline {section}{\numberline {7}Background Estimation Method 2: The Full TRF Method with 0$\rightarrow $1 and Z Corrections}{20}}
\newlabel{sec.bkgsub2}{{7}{20}}
\@writefile{toc}{\contentsline {subsection}{\numberline {7.1}The $0\rightarrow 1$ tag Shift}{20}}
\newlabel{subsec.fulltrf01corr}{{7.1}{20}}
\@writefile{lof}{\contentsline {figure}{\numberline {11}{\ignorespaces  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 $1.5<\eta <2.5$. }}{21}}
\newlabel{fig:notag_trf}{{11}{21}}
\@writefile{toc}{\contentsline {subsection}{\numberline {7.2}The Double-tag TRF}{21}}
\newlabel{subsec.fulltrfdoubletrf}{{7.2}{21}}
\@writefile{lof}{\contentsline {figure}{\numberline {12}{\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 dijet invariant mass spectrum (which was normalized using double-tagged data) and to the $Z\rightarrow b\mathaccent "7016\relax {b}$ 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.}}{22}}
\newlabel{fig:singletag_trf}{{12}{22}}
\@writefile{lof}{\contentsline {figure}{\numberline {13}{\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 7.3\hbox {}.}}{22}}
\newlabel{fig:singletag_diff}{{13}{22}}
\@writefile{toc}{\contentsline {subsection}{\numberline {7.3}The 0- and 1-tag Z Peak Correction}{22}}
\newlabel{subsec.fulltrfzcorr}{{7.3}{22}}
\@writefile{lof}{\contentsline {figure}{\numberline {14}{\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 three $\eta $-bins: $\eta <1.1$, $1.1<\eta <1.5$, and $1.5<\eta <2.5$.}}{23}}
\newlabel{fig:TRFs}{{14}{23}}
\@writefile{lof}{\contentsline {figure}{\numberline {15}{\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).}}{23}}
\newlabel{fig:doubletag_beforeZtrf}{{15}{23}}
\@writefile{lof}{\contentsline {figure}{\numberline {16}{\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.}}{24}}
\newlabel{fig:histo200}{{16}{24}}
\@writefile{toc}{\contentsline {subsection}{\numberline {7.4}Applying This Full-TRF Method to Data}{24}}
\newlabel{subsec.fulltrfresults}{{7.4}{24}}
\@writefile{lof}{\contentsline {figure}{\numberline {17}{\ignorespaces  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.}}{25}}
\newlabel{fig:diff_cdiff_300_dphi_2.9_01}{{17}{25}}
\@writefile{lof}{\contentsline {figure}{\numberline {18}{\ignorespaces  The final $Z\rightarrow b\mathaccent "7016\relax {b}$ peak derived from data, after all corrections (green), compared to the shape of the $Z\rightarrow b\mathaccent "7016\relax {b}$ 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.)}}{25}}
\newlabel{fig:diff_cdiff_300_dphi_2.9_01_diff}{{18}{25}}
\bibcite{CDF}{1}
\@writefile{toc}{\contentsline {section}{\numberline {8}Summary of Results}{26}}
\newlabel{sec.results}{{8}{26}}
\@writefile{toc}{\contentsline {section}{\numberline {9}Conclusions}{26}}
\newlabel{sec.conclusions}{{9}{26}}
\bibcite{hbb}{2}
\bibcite{ambers}{3}
\@writefile{toc}{\contentsline {section}{References}{27}}
\newlabel{sec.refs}{{9}{27}}
\@writefile{lot}{\contentsline {table}{\numberline {10}{\ignorespaces  Description of the new v13 $Z$\nobreakspace  {}$\rightarrow $\nobreakspace  {}$b\overline {b}$ triggers. ``trk-matched'' means track-matched; ``vtx cut'' means vertex cut.}}{28}}
\newlabel{table:v13trigdesc}{{10}{28}}
\@writefile{lot}{\contentsline {table}{\numberline {11}{\ignorespaces  Delivered, recorded and good luminosity for the v13 $Z$\nobreakspace  {}$\rightarrow $\nobreakspace  {}$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.}}{28}}
\newlabel{table:v13lumistats}{{11}{28}}
\@writefile{lot}{\contentsline {table}{\numberline {12}{\ignorespaces  The trigger rates and signal candidate yields, in the v13 portion of the data, for the four leading v13 $Z$\nobreakspace  {}$\rightarrow $\nobreakspace  {}$b\overline {b}$ triggers. Note that all of the three single muon based specifically designed $Z\rightarrow b\mathaccent "7016\relax {b}$ triggers from Table 3 are among the four leading triggers and that MM1\_JT25, which is a B-phyics trigger, has a higher rate.}}{29}}
\newlabel{table:v13ORtrigdesc}{{12}{29}}
\@writefile{lot}{\contentsline {table}{\numberline {13}{\ignorespaces  v13 trigger efficiencies for MC signal events.}}{29}}
\newlabel{table:v13trigeff}{{13}{29}}
\@writefile{lot}{\contentsline {table}{\numberline {14}{\ignorespaces  Cut flow table for $Z$\nobreakspace  {}$\rightarrow $\nobreakspace  {}$b\overline {b}$ Monte Carlo events passing v13 triggers. Event counts are weighted by cross-section and luminosity, the errors are statistical only.}}{29}}
\newlabel{table:cutflow_zbb_v13}{{14}{29}}
\@writefile{lot}{\contentsline {table}{\numberline {15}{\ignorespaces  Cut flow table for events in data. Note the much higher fraction of events passing the offline criteria in the v13 data.}}{30}}
\newlabel{table:cutflow_data_v13}{{15}{30}}
\@writefile{lof}{\contentsline {figure}{\numberline {19}{\ignorespaces  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.}}{30}}
\newlabel{fig:et66_v12OR.eps}{{19}{30}}
\@writefile{lof}{\contentsline {figure}{\numberline {20}{\ignorespaces  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 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 dijet mass distribution observed in data. Red (dark gray) histogram: expected $Z\rightarrow b\mathaccent "7016\relax {b}$ signal from MC. The fit results in a correction to the background scale of 1.177 $\pm $ 0.017. }}{31}}
\newlabel{fig:bkg_fit_dphi_gt_3}{{20}{31}}
\@writefile{lof}{\contentsline {figure}{\numberline {21}{\ignorespaces  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 out-of-zone ($\Delta \varphi < 3.0$) events. The dark blue band indicates the $\pm $ 1.5 \% systematic error from the normalisation fit. Black points: total dijet mass distribution observed in data. Red (dark grey) histogram: expected $Z\rightarrow b\mathaccent "7016\relax {b}$ signal from MC.}}{32}}
\newlabel{fig:invmass621}{{21}{32}}
\@writefile{lof}{\contentsline {figure}{\numberline {22}{\ignorespaces  The invariant dijet 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 $Z\rightarrow b\mathaccent "7016\relax {b}$ signal from MC. The excess peak has a mean mass of 70.6\nobreakspace  {}$GeV/c^{2}$ and a width of 10.7\nobreakspace  {}$GeV/c^{2}$.}}{33}}
\newlabel{fig:invmass627}{{22}{33}}
\@writefile{lof}{\contentsline {figure}{\numberline {23}{\ignorespaces  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)}}{33}}
\newlabel{fig:MbbPerAndy_nomuJES_zoom}{{23}{33}}
\@writefile{lof}{\contentsline {figure}{\numberline {24}{\ignorespaces  The TRF as measured in the untagged data sample, used for measuring the 0$\rightarrow $1 tag shift.}}{34}}
\newlabel{fig:TRFs_1tag}{{24}{34}}
\@writefile{lof}{\contentsline {figure}{\numberline {25}{\ignorespaces  The final Z-peak after correcting approximately for the W$\rightarrow $cs contribution to the single-tagged data sample.}}{34}}
\newlabel{fig:zplot_2.9_Wcs}{{25}{34}}
\@writefile{lof}{\contentsline {figure}{\numberline {26}{\ignorespaces  The final Z-peak after reversing the $\Delta \phi $ cut to $<$2.9.}}{35}}
\newlabel{fig:zplot_-2.9}{{26}{35}}
\@writefile{lof}{\contentsline {figure}{\numberline {27}{\ignorespaces  The final Z-peak after removing the muon-JES corrections -- only the standard JES was used.}}{35}}
\newlabel{fig:zplot_2.9_nomuJES}{{27}{35}}
\@writefile{lof}{\contentsline {figure}{\numberline {28}{\ignorespaces  The final Z-peak after restricting the jet $| \eta |<1.0$.}}{36}}
\newlabel{fig:zplot_2.9_eta1.0}{{28}{36}}
\@writefile{lof}{\contentsline {figure}{\numberline {29}{\ignorespaces  The final Z-peak after restricting the jet $| \eta |>1.0$.}}{36}}
\newlabel{fig:zplot_2.9_eta-1.0}{{29}{36}}
\@writefile{lof}{\contentsline {figure}{\numberline {30}{\ignorespaces  The final Z-peak after relaxing the $\Delta \phi $ cut to $>$2.5.}}{37}}
\newlabel{fig:zplot_2.5}{{30}{37}}