%\newpage \section{Dataset \label{sec:dataset}} \subsection{\label{sub:datasample}\boldmath Data Sample} \noindent For this analysis the framework used was vjets\_cafe v04-00-08 (Release p21.18.00) and the data set consisted of 3JET skim produced by the commom samples group \cite{3jet_data} and recorded between August 2002 and May 2010 (runs 151817 - 258547). \begin{itemize} \item CSG$\_$CAF$\_3$JET$\_$PASS2$\_$p21.10.00 \item CSG$\_$CAF$\_3$JET$\_$PASS4$\_$p21.10.00$\_$p20.12.00 \item CSG$\_$CAF$\_3$JET$\_$PASS4$\_$p21.10.00$\_$p20.12.01 \item CSG$\_$CAF$\_3$JET$\_$PASS4$\_$p21.10.00$\_$p20.12.02 \item CSG$\_$CAF$\_3$JET$\_$PASS4$\_$p21.10.00$\_$p20.12.04 \item CSG$\_$CAF$\_3$JET$\_$PASS4$\_$p21.12.00$\_$p20.12.05$\_$allfix \item CSG$\_$CAF$\_3$JET$\_$PASS4$\_$p21.10.00$\_$p20.16.07$\_$fix \item CSG$\_$CAF$\_3$JET$\_$PASS4$\_$p21.12.00$\_$p20.16.07$\_$summer2010 \end{itemize} In this analysis we chose the three jets trigger JT2\_3JT15L\_IP\_VX. This particular trigger was chosen based on our needs of looking for events with multiple jets and the fact that it represents a gain of 20\% efficiency on signal selection if compared to previous p17 analysis. Since the efficiencies for such trigger are not currently part of caf\_trigger package, in this analysis we benefit from the trigger modelling provided by the $hbb$ group \cite{bIDH_note} for the $\phi b \rightarrow b\bar{b}b$ analysis. Trigger weight distributions for all MC samples used in the analysis as a function of the number of b-tagged jets are found in %Appendix \ref{app:trig_eff} and summarized in Table \ref{trig_weight}: Appendix \ref{app:trig_eff} and Table II summarizes their mean values: \begin{table}[h] \begin{center} \begin{tabular}{|c|r|r|r|r|} \hline Process & 0 tags & 1 tag & 2 tags & 3 or more tags \\ \hline \hline $t\overline{t}\rightarrow\tau+jets$ &\multicolumn{1}{c|}{0.7923} &\multicolumn{1}{c|}{0.8620} &\multicolumn{1}{c|}{0.8953} &\multicolumn{1}{c|}{0.9039} \\ $t\overline{t}\rightarrow e+jets$ &\multicolumn{1}{c|}{0.7902} &\multicolumn{1}{c|}{0.8599} &\multicolumn{1}{c|}{0.8933}&\multicolumn{1}{c|}{0.9020} \\ $t\overline{t}\rightarrow\mu+jets$ &\multicolumn{1}{c|}{0.7942} &\multicolumn{1}{c|}{0.8639} &\multicolumn{1}{c|}{0.8973}&\multicolumn{1}{c|}{0.9058} \\ $t\overline{t}\rightarrow l+l$ &\multicolumn{1}{c|}{0.7274} &\multicolumn{1}{c|}{0.7915} &\multicolumn{1}{c|}{0.8223} &\multicolumn{1}{c|}{0.8302} \\ $Wjj+jets\rightarrow$ $l\nu+jj+jets$ &\multicolumn{1}{c|}{0.5821} &\multicolumn{1}{c|}{0.6337} &\multicolumn{1}{c|}{0.6586}&\multicolumn{1}{c|}{0.6652} \\ $Wbb+jets\rightarrow$ $l\nu+bb+jets$ &\multicolumn{1}{c|}{0.5948} &\multicolumn{1}{c|}{0.6475}&\multicolumn{1}{c|}{0.6729}&\multicolumn{1}{c|}{0.6796} \\ $Wcc+jets\rightarrow$ $l\nu+cc+jets$ &\multicolumn{1}{c|}{0.5912} &\multicolumn{1}{c|}{0.6435}&\multicolumn{1}{c|}{0.6687}&\multicolumn{1}{c|}{0.6754} \\ $Zjj+jets\rightarrow$ $ee+jj+jets$ &\multicolumn{1}{c|}{0.6769} &\multicolumn{1}{c|}{0.7363}&\multicolumn{1}{c|}{0.7646}&\multicolumn{1}{c|}{0.7719} \\ $Zbb+jets\rightarrow$ $ee+bb+jets$ &\multicolumn{1}{c|}{0.4331} &\multicolumn{1}{c|}{0.4712}&\multicolumn{1}{c|}{0.4895}&\multicolumn{1}{c|}{0.4943} \\ $Zcc+jets\rightarrow$ $ee+cc+jets$ &\multicolumn{1}{c|}{0.6167} &\multicolumn{1}{c|}{0.6746}&\multicolumn{1}{c|}{0.7035}&\multicolumn{1}{c|}{0.7127} \\ $Zjj+jets\rightarrow$ $\mu\mu+jj+jets$ &\multicolumn{1}{c|}{0.6641} &\multicolumn{1}{c|}{0.7233}&\multicolumn{1}{c|}{0.7520}&\multicolumn{1}{c|}{0.7598} \\ $Zbb+jets\rightarrow$ $\mu\mu+bb+jets$ &\multicolumn{1}{c|}{0.6057} &\multicolumn{1}{c|}{0.6598}&\multicolumn{1}{c|}{0.6860}&\multicolumn{1}{c|}{0.6931} \\ $Zcc+jets\rightarrow$ $\mu\mu+cc+jets$ &\multicolumn{1}{c|}{0.5817} &\multicolumn{1}{c|}{0.6335}&\multicolumn{1}{c|}{0.6585}&\multicolumn{1}{c|}{0.6653} \\ $Zjj+jets\rightarrow$ $\tau\tau+jj+jets$ &\multicolumn{1}{c|}{0.5712} &\multicolumn{1}{c|}{0.6220}&\multicolumn{1}{c|}{0.6465}&\multicolumn{1}{c|}{0.6530} \\ $Zbb+jets\rightarrow$ $\tau\tau+bb+jets$ &\multicolumn{1}{c|}{0.6049} &\multicolumn{1}{c|}{0.6586}&\multicolumn{1}{c|}{0.6845}&\multicolumn{1}{c|}{0.6914} \\ $Zcc+jets\rightarrow$ $\tau\tau+cc+jets$ &\multicolumn{1}{c|}{0.5889} &\multicolumn{1}{c|}{0.6410}&\multicolumn{1}{c|}{0.6661}&\multicolumn{1}{c|}{0.6727} \\ $Zjj+jets\rightarrow$ $\nu\nu+jj+jets$ &\multicolumn{1}{c|}{0.5739}&\multicolumn{1}{c|}{0.6241}&\multicolumn{1}{c|}{0.6480}&\multicolumn{1}{c|}{0.6541} \\ $Zbb+jets\rightarrow$ $\nu\nu+bb+jets$ &\multicolumn{1}{c|}{0.6012} &\multicolumn{1}{c|}{0.6539}&\multicolumn{1}{c|}{0.6790}&\multicolumn{1}{c|}{0.6854} \\ $Zcc+jets\rightarrow$ $\nu\nu+cc+jets$ &\multicolumn{1}{c|}{0.6360}&\multicolumn{1}{c|}{0.6914}&\multicolumn{1}{c|}{0.7177}&\multicolumn{1}{c|}{0.7242} \\ \hline \end{tabular} \caption{Mean values of the trigger weight for all MC samples.} \end{center} \label{trig_weight} \end{table} For this trigger we also measured the luminosity of our data sample. Table \ref{lumi} shows the results for both v15 and v16 trigger versions. %\newpage % \begin{table}[h] %\begin{ruledtabular} \begin{tabular}{|crrrr|} %\begin{center} \hline Trigger version& Trigger name& Delivered $\mathcal{L}$ ($pb^{-1})$& Recorded $\mathcal{L}$ ($pb^{-1})$& Reconstructed $\mathcal{L}$ ($pb^{-1})$ \tabularnewline \hline \hline V15.0 - V15.99& JT2\_3JT15L\_IP\_VX& 1682.08& 1544.71& 1385.99 \tabularnewline V16.0 - V16.99& JT2\_3JT15L\_IP\_VX& 4059.92& 3887.95& 3565.86 \tabularnewline \hline T O T A L& & 5742.00& 5432.66& 4951.85 \tabularnewline \hline %\end{center} \end{tabular} %\end{ruledtabular} \caption{The results of luminosity calculation for the Run2b 3JET data skim for different D0 trigger list versions} \label{lumi} \end{table} \newpage \subsection{\label{sub:background}\boldmath Backgrounds} In this analysis the largest background sources are QCD ({}``fake $\tau$''), which is estimated from data and $W/Z$+jets, which are simulated Monte Carlo samples. Other backgrounds that were not included in this analysis due to their small contribution are single top and diboson production. A list of backgrounds sources is found in Section III of \cite{p17_note}. In the following sections we describe both signal and background simulation. \subsection{\label{sub:mcsample}\boldmath Monte Carlo Samples} \noindent We use p20 certified MC samples as produced by CSG and caffed with p21.11.00 (version3) \cite{3jet_mc}. All $W/Z$ and $t\bar{t}$ were generated with ALPGEN v2.11 \cite{alpgen} interfaced with Pythia v6.409 \cite{pythia} for production of parton-level showers and hadronization. EvtGen \cite{evtgen} is used to model b hadrons decays and TAUOLA \cite{tauola} used to model tau leptons decays. \noindent ALPGEN is a leading order (LL) generator. In order to correct it to match with next-to-leading order (NLO) cross sections we apply {\it correction factors} and then provide a correct normalization. These correction factors were taken from {\tt vjets$\_$cafe} framework and are described in Ref.\cite{kfactor}. There are two kinds of correction factors: {\it k-factors}, which are the result of the ratio between NLO and LL cross sections ($\sigma_{NLO}/\sigma_{LL}$) and {\it heavy flavor factors}, which are in turn the ratio between k-factors for $HF+0lp(incl)$ and $2lp(incl)$ process from MCFM \cite{mcfm}. Here $HF$ denotes $Z + bb$, $Z + cc$, $W + bb$ or $W + cc$ and $lp$ stands for {\it light parton}. Heavy flavor factors are applied on the top of k-factors in order to provide the correct normalization for process where heavy quarks are present. For $Z$ production, samples are split into $Z$ + light jets, $Z + bb$ and $Z + cc$. $Z$ + light parton cross sections are multiplied by a k-factor of 1.3, while $Z + bb$ and $Z+ cc$ are multiplied by additional heavy flavor factors of 1.52 and 1.67 respectively. $W$ + jets samples are also split the same way: $W$ + light jets, $W + bb$ and $W + cc$. In $W$ + light jets case a k-factor of 1.3 is applied while an additional heavy flavor factor of 1.47 is applied to both $W + bb$ and $W + cc$ samples. %Table \ref{kxsec} summarizes factors applied. Table IV summarizes the correction factors applied. \begin{table}[htbp] \begin{center} \begin{tabular}{|c|r|} \hline Process & k-factor \\ \hline \hline W + light partons & \multicolumn{1}{c|}{1.3} \\ \hline W + bb & \multicolumn{1}{c|}{1.3$\times$1.47} \\ \hline W + cc & \multicolumn{1}{c|}{1.3$\times$1.47} \\ \hline Z + light partons & \multicolumn{1}{c|}{1.3} \\ \hline Z + bb & \multicolumn{1}{c|}{1.3$\times$1.52} \\ \hline Z + cc & \multicolumn{1}{c|}{1.3$\times$1.67} \\ \hline \end{tabular} \caption{k-factors for MC.} \end{center} \label{kxsec} \end{table} All MC samples used in this analysis are shown in Table \ref{used_mc} with theirs respective cross sections and number of events. The cross sections shown are the averages of the cross-sections of each set of MC process generated and are calculated from /caf$\_$mc$\_$util/mc$\_$sample$\_$info/MC.list \clearpage \begin{table}[h] %\begin{center} \begin{tabular}{|crr|} \hline Sample & $\sigma(pb)$ & \# of Events \\ \hline $t+t+0lp-l\nu+2b+2lpc\_\mbox{excl}\_m172$ & 1.392196 & $ 793267 $ \\ $t+t+1lp-l\nu+2b+3lpc\_\mbox{excl}\_m172$ & .576927 & $ 456317 $ \\ $t+t+2lp-l\nu+2b+4lpc\_\mbox{incl}\_m172$ & .281831 & $ 277912 $ \\ $\mbox{W}+0lp\rightarrow lnu+0lp\_\mbox{excl}$ & 4530.269741 & $ 47070044 $ \\ $\mbox{W}+1lp\rightarrow lnu+1lp\_\mbox{excl}$ & 1283.094130 & $ 20683540 $ \\ $\mbox{W}+2lp\rightarrow lnu+2lp\_\mbox{excl}$ & 306.073315 & $ 19686862 $ \\ $\mbox{W}+3lp\rightarrow lnu+3lp\_\mbox{excl}$ & 73.494491 & $ 4269023 $ \\ $\mbox{W}+4lp\rightarrow lnu+4lp\_\mbox{excl}$ & 16.958254 & $ 3084707 $\\ $\mbox{W}+5lp\rightarrow lnu+5lp\_\mbox{incl}$ & 5.218917 & $ 2565942 $ \\ $\mbox{W}+2b+0lp\rightarrow l\nu+2b+0lp\_\mbox{excl}$ & 9.315458 & $ 1120570 $ \\ $\mbox{W}+2b+1lp\rightarrow l\nu+2b+1lp\_\mbox{excl}$ & 4.288365 & $ 812095 $ \\ $\mbox{W}+2b+2lp\rightarrow l\nu+2b+2lp\_\mbox{excl}$ & 1.554786 & $ 563315 $ \\ $\mbox{W}+2b+3lp\rightarrow l\nu+2b+3lp\_\mbox{incl}$ & 0.716175& $ 464475 $ \\ $\mbox{W}+2b+0lp\rightarrow l\nu+2c+0lp\_\mbox{excl}$ & 24.404153 & $ 934253 $ \\ $\mbox{W}+2b+1lp\rightarrow l\nu+2c+1lp\_\mbox{excl}$ & 13.486806 & $ 738709 $ \\ $\mbox{W}+2b+2lp\rightarrow l\nu+2c+2lp\_\mbox{excl}$ & 5.459005 & $ 554236 $ \\ $\mbox{W}+2b+3lp\rightarrow l\nu+2c+3lp\_\mbox{incl}$ & 2.526973 & $ 469900 $ \\ $\gamma \mbox{Z}+0lp\rightarrow ee+0lp\_\mbox{excl}\_75\_130$ & 132.086811 & $ 1212214 $ \\ $\gamma \mbox{Z}+1lp\rightarrow ee+1lp\_\mbox{excl}\_75\_130$ & 40.060963 & $ 599588 $ \\ $\gamma \mbox{Z}+2lp\rightarrow ee+2lp\_\mbox{excl}\_75\_130$ & 9.981935 & $ 298494 $ \\ $\gamma \mbox{Z}+3lp\rightarrow ee+3lp\_\mbox{incl}\_75\_130$ & 3.297072 & $ 150267 $ \\ $\gamma \mbox{Z}+2b+0lp\rightarrow ee+2b+0lp\_\mbox{excl}\_75\_130$ & 0.400826 & $ 200121 $ \\ $\gamma \mbox{Z}+2b+1lp\rightarrow ee+2b+1lp\_\mbox{excl}\_75\_130$ & 0.173438 & $ 97474 $ \\ $\gamma \mbox{Z}+2b+2lp\rightarrow ee+2b+2lp\_\mbox{incl}\_75\_130$ & 0.107248 & $ 48269 $ \\ $\gamma \mbox{Z}+2c+0lp\rightarrow ee+2c+0lp\_\mbox{excl}\_75\_130$ & 0.900923 & $ 182485 $ \\ $\gamma \mbox{Z}+2c+1lp\rightarrow ee+2c+1lp\_\mbox{excl}\_75\_130$ & 0.506337 & $ 89293 $ \\ $\gamma \mbox{Z}+2b+2lp\rightarrow ee+2b+2lp\_\mbox{incl}\_75\_130$ & 0.285871 & $ 47357 $ \\ $\gamma \mbox{Z}+0lp\rightarrow \mu \mu+0lp\_\mbox{excl}\_75\_130$ & 133.850906 & $ 1553222 $ \\ $\gamma \mbox{Z}+1lp\rightarrow \mu \mu+1lp\_\mbox{excl}\_75\_130$ & 41.677185 & $ 639392 $ \\ $\gamma \mbox{Z}+2lp\rightarrow \mu \mu+2lp\_\mbox{excl}\_75\_130$ & 9.822132 & $ 446737 $ \\ $\gamma \mbox{Z}+3lp\rightarrow \mu \mu+3lp\_\mbox{incl}\_75\_130$ & 3.195801 & $ 172628 $ \\ $\gamma \mbox{Z}+2b+0lp\rightarrow \mu \mu+2b+0lp\_\mbox{excl}\_75\_130$ & 0.424239 & $ 210139 $ \\ $\gamma \mbox{Z}+2b+1lp\rightarrow \mu \mu+2b+1lp\_\mbox{excl}\_75\_130$ & 0.195271 & $ 101055 $ \\ $\gamma \mbox{Z}+2b+2lp\rightarrow \mu \mu+2b+2lp\_\mbox{incl}\_75\_130$ & 0.099004 & $ 49600 $ \\ $\gamma \mbox{Z}+2c+0lp\rightarrow \mu \mu+2c+0lp\_\mbox{excl}\_75\_130$ & 0.932203 & $ 193928 $ \\ $\gamma \mbox{Z}+2c+1lp\rightarrow \mu \mu+2c+1lp\_\mbox{excl}\_75\_130$ & 0.548182 & $ 92744 $ \\ $\gamma \mbox{Z}+2b+2lp\rightarrow \mu \mu+2b+2lp\_\mbox{incl}\_75\_130$ & 0.280795 & $ 51277 $ \\ $\gamma \mbox{Z}+0lp\rightarrow \tau \tau+0lp\_\mbox{excl}\_75\_130$ & 131.564780 & $ 1556389 $ \\ $\gamma \mbox{Z}+1lp\rightarrow \tau \tau+1lp\_\mbox{excl}\_75\_130$ & 40.300291 & $ 595169 $ \\ $\gamma \mbox{Z}+2lp\rightarrow \tau \tau+2lp\_\mbox{excl}\_75\_130$ & 10.072067 & $ 305312 $ \\ $\gamma \mbox{Z}+3lp\rightarrow \tau \tau+3lp\_\mbox{excl}\_75\_130$ & 3.089442 & $ 205365 $ \\ $\gamma \mbox{Z}+2b+0lp\rightarrow \tau \tau+2b+0lp\_\mbox{excl}\_75\_130$ & 0.423679 & $ 196943 $ \\ $\gamma \mbox{Z}+2b+1lp\rightarrow \tau \tau+2b+1lp\_\mbox{excl}\_75\_130$ & 0.196527 & $ 103105 $ \\ $\gamma \mbox{Z}+2b+2lp\rightarrow \tau \tau+2b+2lp\_\mbox{incl}\_75\_130$ & 0.103561 & $ 48476 $ \\ $\gamma \mbox{Z}+2c+0lp\rightarrow \tau \tau+2c+0lp\_\mbox{excl}\_75\_130$ & 0.898135 & $ 260243 $ \\ $\gamma \mbox{Z}+2c+1lp\rightarrow \tau \tau+2c+1lp\_\mbox{excl}\_75\_130$ & 0.487548 & $ 100802 $ \\ $\gamma \mbox{Z}+2b+2lp\rightarrow \tau \tau+2b+2lp\_\mbox{incl}\_75\_130$ & 0.297808 & $ 50711 $ \\ $\gamma \mbox{Z}+0lp\rightarrow \nu \nu+0lp\_\mbox{excl}$ & 806.552968 & $ 2368495 $ \\ $\gamma \mbox{Z}+1lp\rightarrow \nu \nu+1lp\_\mbox{excl}$ & 244.651772 & $ 2591505 $ \\ $\gamma \mbox{Z}+2lp\rightarrow \nu \nu+2lp\_\mbox{excl}$ & 61.014112 & $ 657110 $ \\ $\gamma \mbox{Z}+3lp\rightarrow \nu \nu+3lp\_\mbox{excl}$ & 14.091090 & $ 194705 $ \\ $\gamma \mbox{Z}+4lp\rightarrow \nu \nu+4lp\_\mbox{excl}$ & 3.277295 & $ 100158 $ \\ $\gamma \mbox{Z}+5lp\rightarrow \nu \nu+5lp\_\mbox{incl}$ & 0.936465 & $ 49660 $ \\ $\gamma \mbox{Z}+2b+0lp\rightarrow \nu \nu+2b+0lp\_\mbox{excl}$ & 2.562976 & $ 375572$ \\ $\gamma \mbox{Z}+2b+1lp\rightarrow \nu \nu+2b+1lp\_\mbox{excl}$ & 1.143703 & $ 180558 $ \\ $\gamma \mbox{Z}+2b+2lp\rightarrow \nu \nu+2b+2lp\_\mbox{incl}$ & 0.617265 & $ 91588 $ \\ $\gamma \mbox{Z}+2c+0lp\rightarrow \nu \nu+2c+0lp\_\mbox{excl}$ & 5.634504 & $ 376456 $ \\ $\gamma \mbox{Z}+2c+1lp\rightarrow \nu \nu+2c+1lp\_\mbox{excl}$ & 3.002712 & $ 199012 $ \\ $\gamma \mbox{Z}+2b+2lp\rightarrow \nu \nu+2b+2lp\_\mbox{incl}$ & 1.635746 & $ 96147 $ \\\hline \end{tabular} \caption{MC Samples. Here $l$ stands for the three lepton flavor ($e$, $\mu$ and $\tau$). $\tau$ decays are not restricted.} %\end{center} \label{used_mc} \end{table} \clearpage \subsection{\label{sub:mcsample_xseccorr}\boldmath MC samples corrections} Standard D\O\ corrections are applied to MC in order to obtain a better MC-data agreement \cite{top_sys}. \noindent {\bf Trigger efficiency}: an additional scale factor (weight) is applied to MC to account for the trigger efficiency in data. Further details are given in Section \ref{sec:trig_param}. \noindent {\bf Luminosity reweighting}: in order to reproduce luminosity effects from real data, simulated samples are overlaid to Zero Bias data Due to a difference in intantaneous luminosity between the overlay and real data, the luminosity profile of all MC samples is reweighted to match the luminosity profile in data \cite{lumireweight}. \noindent {\bf Primary vertex reweighting}: $z$ vertex distributions are different between data and MC.This difference is corrected by reweighting MC $z$ vertex distributions using the reweight processor from the {\tt caf\_mc\_util} package \cite{PVz_re}. \noindent {\bf $W$ and $Z$ $p_{T}$ reweighting}: for both $W$ + jets and $Z$ + jets, the $p_{T}$ distribution from MC samples is reweighted to match the equivalent distribution in data, accordingly to the standard way \cite{WZPt_re}. \noindent {\bf b fragmentation}: the systematics on the reweight of the b-fragmentation function from the default in Pythia to the value tuned to reproduce collider data was assumed to be the symmetrized difference between the AOD and SLD tunes \cite{bfrag}. \noindent {\bf Jet Shifting Smearing and Removing (JSSR)}: due to differences in energy scale, resolution, reconstruction and identification between data and MC, MC jets are shifted, smeared and possibly removed using standard JSSR processor \cite{jssr}. In this analysis shifting is turned off to signal $t\bar{t}$ and on to $W/Z$ + jets samples. \noindent {\bf Tau Energy Scale (TES)}: due to the analysis sensitivity to any difference between data and MC in the energy scale of taus decaying hadronically we apply a $E/p$ correction to this energy scale as described in \cite{tes}. %\subsubsection{\label{sub:hadtau_corr}\boldmath Hadronic $\tau$ corrections} %\begin{itemize} %\item E/p correction for hadronic tau relative tau energy scale from package {\tt caf\_util}. %\item NN corrections from package {\tt tauid\_eff}. %\item Track corrections from package {\tt muid\_eff}. %\end{itemize} %\clearpage