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%\newpage \section{Dataset \label{sec:dataset}} \subsection{\label{sub:datasample}\boldmath Data Sample} \noindent For this analysis we used the vjets\_cafe v04-00-08 framework (Release p21.18.00) and the data set consisted of 3JET skim produced by the commom samples group and recorded between August 2002 and May 2010 (runs 151817 - 258547) \cite{3jet_data}. \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 10\% efficiency on signal selection if compared to previous p17 analysis. Since the efficiency of this trigger is not 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 2 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} \\ $Wjj+jets\rightarrow$ $\ell\nu+jj+jets$ &\multicolumn{1}{c|}{0.5821} &\multicolumn{1}{c|}{0.6337} &\multicolumn{1}{c|}{0.6586}&\multicolumn{1}{c|}{0.6652} \\ $Wbb+jets\rightarrow$ $\ell\nu+bb+jets$ &\multicolumn{1}{c|}{0.5948} &\multicolumn{1}{c|}{0.6475}&\multicolumn{1}{c|}{0.6729}&\multicolumn{1}{c|}{0.6796} \\ $Wcc+jets\rightarrow$ $\ell\nu+cc+jets$ &\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 &\multicolumn{1}{c}{Trigger name} &\multicolumn{1}{c}{Delivered $\mathcal{L}$ ($\mbox{pb}^{-1})$} &\multicolumn{1}{c}{Recorded $\mathcal{L}$ ($\mbox{pb}^{-1})$} &\multicolumn{1}{c|}{Reconstructed $\mathcal{L}$ ($\mbox{pb}^{-1})$} \tabularnewline \hline \hline V15.0 - V15.99 &\multicolumn{1}{c}{JT2\_3JT15L\_IP\_VX} &\multicolumn{1}{c}{1682.08} &\multicolumn{1}{c}{1544.71} &\multicolumn{1}{c|}{1385.99} \tabularnewline V16.0 - V16.99 &\multicolumn{1}{c}{JT2\_3JT15L\_IP\_VX} &\multicolumn{1}{c}{4059.92} &\multicolumn{1}{c}{3887.95} &\multicolumn{1}{c|}{3565.86} \tabularnewline \hline T O T A L &\multicolumn{1}{c}{} &\multicolumn{1}{c}{5742.00} &\multicolumn{1}{c}{5432.66} &\multicolumn{1}{c|}{4951.85} \tabularnewline \hline %\end{center} \end{tabular} %\end{ruledtabular} \caption{The results of luminosity calculation for the Run IIb 3JET data skim for different D0 trigger list versions} \label{lumi} \end{table} %\newpage \subsection{\label{sub:background}\boldmath Backgrounds} The largest sources of background to our signal are QCD ({}``fake $\tau$'') and $W/Z$+jets. We estimate the first from data and the second using Monte Carlo simulation. Other sources such as single top and diboson production are small enough to be ignored. A list of backgrounds process 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 reconstructed 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} is 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 correction factors to MC samples in order to get the 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 LO cross sections ($\sigma_{NLO}/\sigma_{LO}$) 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 top of k-factors in order to provide the correct normalization for processes 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 4 summarizes the correction factors applied. \begin{table}[htbp] \begin{center} \begin{tabular}{|c|r|} \hline Process & correction 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$1.67} \\ \hline \end{tabular} \caption{k-factors for MC.} \end{center} \label{kxsec} \end{table} All MC samples used in this analysis are shown in Table \ref{used_mc} with their respective cross sections and number of events. The cross sections shown are the averages of the cross sections of each set of MC process generated and are calculated from /caf$\_$mc$\_$util/mc$\_$sample$\_$info/MC.list \cite{caf_mc_util}. \clearpage \begin{table}[h] %\begin{center} \begin{tabular}{|crr|} \hline Sample & $\sigma(pb)$ & \# of Events \\ \hline $t\bar{t}+0lp-\ell\nu+b\bar{b}+2lpc\_\mbox{excl}\_m172.5$ & 1.392196 & $ 793267 $ \\ $t\bar{t}+1lp-\ell\nu+b\bar{b}+3lpc\_\mbox{excl}\_m172.5$ & .576927 & $ 456317 $ \\ $t\bar{t}+2lp-\ell\nu+b\bar{b}+4lpc\_\mbox{incl}\_m172.5$ & .281831 & $ 277912 $ \\ $W+0lp\rightarrow \ell\nu+0lp\_\mbox{excl}$ & 4530.269741 & $ 47070044 $ \\ $W+1lp\rightarrow \ell\nu+1lp\_\mbox{excl}$ & 1283.094130 & $ 20683540 $ \\ $W+2lp\rightarrow \ell\nu+2lp\_\mbox{excl}$ & 306.073315 & $ 19686862 $ \\ $W+3lp\rightarrow \ell\nu+3lp\_\mbox{excl}$ & 73.494491 & $ 4269023 $ \\ $W+4lp\rightarrow \ell\nu+4lp\_\mbox{excl}$ & 16.958254 & $ 3084707 $\\ $W+5lp\rightarrow \ell\nu+5lp\_\mbox{incl}$ & 5.218917 & $ 2565942 $ \\ $W+b\bar{b}+0lp\rightarrow \ell\nu+b\bar{b}+0lp\_\mbox{excl}$ & 9.315458 & $ 1120570 $ \\ $W+b\bar{b}+1lp\rightarrow \ell\nu+b\bar{b}+1lp\_\mbox{excl}$ & 4.288365 & $ 812095 $ \\ $W+b\bar{b}+2lp\rightarrow \ell\nu+b\bar{b}+2lp\_\mbox{excl}$ & 1.554786 & $ 563315 $ \\ $W+b\bar{b}+3lp\rightarrow \ell\nu+b\bar{b}+3lp\_\mbox{incl}$ & 0.716175& $ 464475 $ \\ $W+c\bar{c}+0lp\rightarrow \ell\nu+c\bar{c}+0lp\_\mbox{excl}$ & 24.404153 & $ 934253 $ \\ $W+c\bar{c}+1lp\rightarrow \ell\nu+c\bar{c}+1lp\_\mbox{excl}$ & 13.486806 & $ 738709 $ \\ $W+c\bar{c}+2lp\rightarrow \ell\nu+c\bar{c}+2lp\_\mbox{excl}$ & 5.459005 & $ 554236 $ \\ $W+c\bar{c}+3lp\rightarrow \ell\nu+c\bar{c}+3lp\_\mbox{incl}$ & 2.526973 & $ 469900 $ \\ $\gamma /Z+0lp\rightarrow ee+0lp\_\mbox{excl}\_75\_130$ & 132.086811 & $ 1212214 $ \\ $\gamma /Z+1lp\rightarrow ee+1lp\_\mbox{excl}\_75\_130$ & 40.060963 & $ 599588 $ \\ $\gamma /Z+2lp\rightarrow ee+2lp\_\mbox{excl}\_75\_130$ & 9.981935 & $ 298494 $ \\ $\gamma /Z+3lp\rightarrow ee+3lp\_\mbox{incl}\_75\_130$ & 3.297072 & $ 150267 $ \\ $\gamma /Z+b\bar{b}+0lp\rightarrow ee+b\bar{b}+0lp\_\mbox{excl}\_75\_130$ & 0.400826 & $ 200121 $ \\ $\gamma /Z+b\bar{b}+1lp\rightarrow ee+b\bar{b}+1lp\_\mbox{excl}\_75\_130$ & 0.173438 & $ 97474 $ \\ $\gamma /Z+b\bar{b}+2lp\rightarrow ee+b\bar{b}+2lp\_\mbox{incl}\_75\_130$ & 0.107248 & $ 48269 $ \\ $\gamma /Z+c\bar{c}+0lp\rightarrow ee+c\bar{c}+0lp\_\mbox{excl}\_75\_130$ & 0.900923 & $ 182485 $ \\ $\gamma /Z+c\bar{c}+1lp\rightarrow ee+c\bar{c}+1lp\_\mbox{excl}\_75\_130$ & 0.506337 & $ 89293 $ \\ $\gamma /Z+c\bar{c}+2lp\rightarrow ee+c\bar{c}+2lp\_\mbox{incl}\_75\_130$ & 0.285871 & $ 47357 $ \\ $\gamma /Z+0lp\rightarrow \mu \mu+0lp\_\mbox{excl}\_75\_130$ & 133.850906 & $ 1553222 $ \\ $\gamma /Z+1lp\rightarrow \mu \mu+1lp\_\mbox{excl}\_75\_130$ & 41.677185 & $ 639392 $ \\ $\gamma /Z+2lp\rightarrow \mu \mu+2lp\_\mbox{excl}\_75\_130$ & 9.822132 & $ 446737 $ \\ $\gamma /Z+3lp\rightarrow \mu \mu+3lp\_\mbox{incl}\_75\_130$ & 3.195801 & $ 172628 $ \\ $\gamma /Z+b\bar{b}+0lp\rightarrow \mu \mu+b\bar{b}+0lp\_\mbox{excl}\_75\_130$ & 0.424239 & $ 210139 $ \\ $\gamma /Z+b\bar{b}+1lp\rightarrow \mu \mu+b\bar{b}+1lp\_\mbox{excl}\_75\_130$ & 0.195271 & $ 101055 $ \\ $\gamma /Z+b\bar{b}+2lp\rightarrow \mu \mu+b\bar{b}+2lp\_\mbox{incl}\_75\_130$ & 0.099004 & $ 49600 $ \\ $\gamma /Z+c\bar{c}+0lp\rightarrow \mu \mu+c\bar{c}+0lp\_\mbox{excl}\_75\_130$ & 0.932203 & $ 193928 $ \\ $\gamma /Z+c\bar{c}+1lp\rightarrow \mu \mu+c\bar{c}+1lp\_\mbox{excl}\_75\_130$ & 0.548182 & $ 92744 $ \\ $\gamma /Z+c\bar{c}+2lp\rightarrow \mu \mu+c\bar{c}+2lp\_\mbox{incl}\_75\_130$ & 0.280795 & $ 51277 $ \\ $\gamma /Z+0lp\rightarrow \tau \tau+0lp\_\mbox{excl}\_75\_130$ & 131.564780 & $ 1556389 $ \\ $\gamma /Z+1lp\rightarrow \tau \tau+1lp\_\mbox{excl}\_75\_130$ & 40.300291 & $ 595169 $ \\ $\gamma /Z+2lp\rightarrow \tau \tau+2lp\_\mbox{excl}\_75\_130$ & 10.072067 & $ 305312 $ \\ $\gamma /Z+3lp\rightarrow \tau \tau+3lp\_\mbox{excl}\_75\_130$ & 3.089442 & $ 205365 $ \\ $\gamma /Z+b\bar{b}+0lp\rightarrow \tau \tau+b\bar{b}+0lp\_\mbox{excl}\_75\_130$ & 0.423679 & $ 196943 $ \\ $\gamma /Z+b\bar{b}+1lp\rightarrow \tau \tau+b\bar{b}+1lp\_\mbox{excl}\_75\_130$ & 0.196527 & $ 103105 $ \\ $\gamma /Z+b\bar{b}+2lp\rightarrow \tau \tau+b\bar{b}+2lp\_\mbox{incl}\_75\_130$ & 0.103561 & $ 48476 $ \\ $\gamma /Z+c\bar{c}+0lp\rightarrow \tau \tau+c\bar{c}+0lp\_\mbox{excl}\_75\_130$ & 0.898135 & $ 260243 $ \\ $\gamma /Z+c\bar{c}+1lp\rightarrow \tau \tau+c\bar{c}+1lp\_\mbox{excl}\_75\_130$ & 0.487548 & $ 100802 $ \\ $\gamma /Z+c\bar{c}+2lp\rightarrow \tau \tau+c\bar{c}+2lp\_\mbox{incl}\_75\_130$ & 0.297808 & $ 50711 $ \\ $Z+0lp\rightarrow \nu \nu+0lp\_\mbox{excl}$ & 806.552968 & $ 2368495 $ \\ $Z+1lp\rightarrow \nu \nu+1lp\_\mbox{excl}$ & 244.651772 & $ 2591505 $ \\ $Z+2lp\rightarrow \nu \nu+2lp\_\mbox{excl}$ & 61.014112 & $ 657110 $ \\ $Z+3lp\rightarrow \nu \nu+3lp\_\mbox{excl}$ & 14.091090 & $ 194705 $ \\ $Z+4lp\rightarrow \nu \nu+4lp\_\mbox{excl}$ & 3.277295 & $ 100158 $ \\ $Z+5lp\rightarrow \nu \nu+5lp\_\mbox{incl}$ & 0.936465 & $ 49660 $ \\ $Z+b\bar{b}+0lp\rightarrow \nu \nu+b\bar{b}+0lp\_\mbox{excl}$ & 2.562976 & $ 375572$ \\ $Z+b\bar{b}+1lp\rightarrow \nu \nu+b\bar{b}+1lp\_\mbox{excl}$ & 1.143703 & $ 180558 $ \\ $Z+b\bar{b}+2lp\rightarrow \nu \nu+b\bar{b}+2lp\_\mbox{incl}$ & 0.617265 & $ 91588 $ \\ $Z+c\bar{c}+0lp\rightarrow \nu \nu+c\bar{c}+0lp\_\mbox{excl}$ & 5.634504 & $ 376456 $ \\ $Z+c\bar{c}+1lp\rightarrow \nu \nu+c\bar{c}+1lp\_\mbox{excl}$ & 3.002712 & $ 199012 $ \\ $Z+c\bar{c}+2lp\rightarrow \nu \nu+c\bar{c}+2lp\_\mbox{incl}$ & 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 D0 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}: properly model the occurence of multiple interactions at higher instantaneous luminosities, simulated samples are overlaid on Zero Bias data. Due to a difference in instantaneous 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}: vertex $z$ 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 distributions 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 Removal (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 {\it off} to signal $t\bar{t}$ and {\it on} to $W/Z$ + jets samples. \noindent {\bf Tau Energy Scale (TES)}: A $E/p$ correction is applied to the energy of the hadronically decaying taus 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