Diff for /ttbar/p20_taujets_note/b_and_tau.tex between versions 1.1 and 1.2

version 1.1, 2011/05/18 21:30:39 version 1.2, 2011/06/01 01:20:54
Line 3 Line 3
   
 In the next step we applied the requirements of tight $\tau$- and $b$-tagging.  In the next step we applied the requirements of tight $\tau$- and $b$-tagging.
 Table \ref{cap:btaggingandtau} shows the selection criteria that  Table \ref{cap:btaggingandtau} shows the selection criteria that
 we applied to data and MC. The b-tag operating point used was TIGHT, which corresponds  we applied to data and MC. The $b$-tag operating point used was TIGHT, which corresponds
 to NNbtag $>$ 0.775. We chose the $\tau$ with the highest $NN_{\tau}$ as \textit{the} $\tau$ candidate.  to NNbtag $>$ 0.775. In there are more than 1 tau candidate in the event then we
   choose the one with the highets $NN_{\tau}$ as the only one. Also we apply a tau-jet matching
   condition. A tau candidate is only used in the measurement if the separation between it
   and a jet is $\Delta R = \sqrt{{(\Delta \eta})^{2} + {(\Delta \phi})^{2}} > 0.5$.
 At this stage of the analysis we separated the events dataset we deal with into parts,   At this stage of the analysis we separated the events dataset we deal with into parts, 
 according to which type of $\tau$ the candidate with highest NN belongs.   according to which type of $\tau$ the candidate with highest $NN_{\tau}$ belongs. 
 This was done primarily to separate the type 3 tau events (which are   This was done primarily to separate the type 3 tau events (which are 
 expected to have much higher fake rate and thus weaker $\ttbar$ cross section result) from the   expected to have much higher fake rate and thus weaker $\ttbar$ cross section result) from the 
 type 2 events. The separate measurement channels were later combined to get the final result   type 2 events. The separate measurement channels were later combined to get the final result 
 (Section \ref{sub:xsect}). In principle, types 1 and 2 should be separated as well  (Section \ref{sub:xsect}). In principle, types 1 and 2 should be separated as well
 but as there exists a considerable   but as there exists a considerable 
 cross-migration between them \cite{tau-id} and type 1 is a small fraction of  cross-migration between them \cite{tau-id} and type 1 is a small fraction of
 the total (10\% of type 1, 54.5\% of type 2 and 35.5\% of type 3), they were taken togetther in this analysis.   the total (10\% of type 1, 54.5\% of type 2 and 35.5\% of type 3), they were taken together in this analysis. 
 The topological NN used to enhance the signal content is described in section \ref{sub:NN-variables} .  The topological NN used to enhance the signal content is described in section \ref{sub:NN-variables} .
   
 %Table \ref{b and tau type 3} shows the same efficiencies for   %Table \ref{b and tau type 3} shows the same efficiencies for 
Line 22  The topological NN used to enhance the s Line 25  The topological NN used to enhance the s
   
   
 At this point, we used these ID algorithms to define 3 mutually exclusive and  At this point, we used these ID algorithms to define 3 mutually exclusive and
 exhastive subsamples out of the original preselected data sample:  exhastive subsamples out of the preselected data sample:
   
 \begin{itemize}  \begin{itemize}
 \item The {}``non-$b$ veto'' or {}``signal'' sample - the $\tau$ candidate has $NN_{\tau}>0.90$ ($NN_{\tau}$ denotes the NN cut commonly applied to all taus)  \item The {}``non-$b$-tag'' or {}``signal'' sample - The $\tau$ candidate has $NN_{\tau}>0.90$ 
 for taus types 1 and 2 and $NN(\tau)>0.95$ for taus type 3, and at least one NN b-tag (as in Table \ref{cap:btaggingandtau}).  ($NN_{\tau}$ denotes the NN cut commonly applied to all taus)
   for taus types 1 and 2 and $NN_{\tau}>0.95$ for taus type 3, and at least one NN b-tag (as in Table \ref{cap:btaggingandtau}).
 These $NN(\tau)$ cuts were chosen based on previous studies involving hadronic decays of taus \cite{tes,higgs_tau}.  These $NN(\tau)$ cuts were chosen based on previous studies involving hadronic decays of taus \cite{tes,higgs_tau}.
 This is the sample used to extract the cross section. Jets matched to $\tau$ candidates are not $b$-tagged,  This is the sample used to extract the cross section. Jets matched to $\tau$ candidates are not $b$-tagged,
 althought they still count as jets.  althought they still count as jets.
Line 34  althought they still count as jets. Line 38  althought they still count as jets.
 $0.3<NN_{\tau}<0.7$ for all taus. $\tau$ NN lower cut of 0.3   $0.3<NN_{\tau}<0.7$ for all taus. $\tau$ NN lower cut of 0.3 
 instead of 0.0 was chosen to bias their jet properties closer to those of tight tau candidates,   instead of 0.0 was chosen to bias their jet properties closer to those of tight tau candidates, 
 in particular, so they have narrow showers. The upper cut is at 0.7 and not 0.95 or 0.90 to reduce signal contamination.   in particular, so they have narrow showers. The upper cut is at 0.7 and not 0.95 or 0.90 to reduce signal contamination. 
 In this sample, 1400000 events were used for NN training for taus type 1 and 2 and 600000 events were used   In this sample, 1400000 events were used for NN training for taus of Type 1 and 2 and 600000 events were used 
 in the case of type 3 taus. In both cases, the rest of the samples served as QCD template.  in the case of Type 3 taus. In both cases, the rest of the samples served as QCD template.
 \item The {}``$b$ veto'' sample - Require exactly 0 tight $b$-tags. This is   \item The {}``$b$ veto'' sample - Require exactly 0 tight $b$-tags. This is 
 the control sample used to verify the validity of the QCD modelling method. The b veto requirement  the control sample used to validate of the QCD modelling method. The b veto requirement
 implies this sample is almost purely background.  implies this sample is almost purely background.
 \end{itemize}  \end{itemize}
 %  %
   
 Along with the $NN_{\tau}$   One extra cut applied along with the $NN_{\tau}$ 
 cut described above, we also applied the cut NNelec $>$ 0.9 only   cut described above was the so called NNelec cut. It is meant to be applied to Type 2 taus only in order
 to type 2 taus since these are more likely to be faked by electrons. The cut NNelec $>$ 0.9 was chosen in   to reduce the probability of having these being faked by electrons. We chose a non-optimized cut of NNelec $>$ 0.9.
 order to match the lowest cut of $NN_{\tau}$ $>$ 0.9 applied to type 2 taus (Section \ref{sub:Results-of-the}).  
   
 As both b and $\tau$ ID is the step immediately after the preselection, the number of events available is   As both b and $\tau$ ID is the step immediately after the preselection, the number of events available is 
 2800000 million events. As explained above 1400000 events were used for taus type 1 and 2 NN training   2800000 events. As explained above 1400000 events were used for taus of Type 1 and 2 NN training 
 and 600000 for type 3 taus NN training. Thus, there are 1400000 events available in each sample for the  and 600000 for Type 3 taus NN training. Thus, there are 1400000 events available in each sample for the
 measurement in the case of types 1 and 2 and 2200000 in the case of type 3. Details on NN training are given  measurement in the case of Types 1 and 2 and 2200000 in the case of Type 3. Details of NN training are given
 in Section \ref{sub:NN-variables}.  in Section \ref{sub:NN-variables}.
   
   
Line 66  know whether this sample is totally QCD Line 69  know whether this sample is totally QCD
 Numbers showing the composition of such sample are shown on Tables \ref{loosetight1_2} and \ref{loosetight_3}  Numbers showing the composition of such sample are shown on Tables \ref{loosetight1_2} and \ref{loosetight_3}
 with their respective statistical uncertainties. From the $t\bar{t}$ content in each case we are able  with their respective statistical uncertainties. From the $t\bar{t}$ content in each case we are able
 estimate the signal contamination in the loose-tight sample. Such contaminations are 5.4\%   estimate the signal contamination in the loose-tight sample. Such contaminations are 5.4\% 
 and 3.0\% for taus type 1 and 2 and type 3 respectively when a cross section of 7.46 pb is assumed   and 3.0\% for taus of Type 1 and 2 and Type 3 respectively when $\sigma_{t\bar{t}}$ = 7.46 pb is assumed 
 (Section \ref{sub:mcsample}). Likewise we see that electroweak contaminations  (Section \ref{sub:mcsample}). Likewise we see that electroweak contaminations
 are 2.2\% and 0.9\%. As this is the sample used to model the QCD background  are 2.2\% and 0.9\%. As this is the sample used to model the QCD background
 both signal and electroweak contaminations were taken into account when measuring the   both signal and electroweak contaminations were taken into account when measuring the 
Line 96  cross section in Section \ref{sub:xsect} Line 99  cross section in Section \ref{sub:xsect}
 \caption{$b$-tagging and $\tau$ ID. In the MC, we use the $b$-tagging certified  \caption{$b$-tagging and $\tau$ ID. In the MC, we use the $b$-tagging certified
 parameterization rather than actual $b$-tagging, that is, we applied the  parameterization rather than actual $b$-tagging, that is, we applied the
 $b$-tagging weight. We also used the triggering weight  $b$-tagging weight. We also used the triggering weight
 as computed by the trigger efficiency parameterization as well as luminosity profile and $PV_Z$ reweighting weights. $  as computed by the trigger efficiency parameterization as well as luminosity profile, $PV_Z$ reweighting
 mcweight$ is the MC normalization factors (to luminosity), which are different for MC   and $WZPt$ reweighting weights. $mcweight$ is the MC normalization factor (to luminosity), which is different for MC 
 samples with different parton multiplicities in ALPGEN MC samples.}%\end{ruledtabular}  samples with different parton multiplicities in ALPGEN MC samples.}%\end{ruledtabular}
 \label{cap:btaggingandtau}   \label{cap:btaggingandtau} 
 \end{table}  \end{table}
Line 136  $Wcc+jets\rightarrow$ $l\nu+cc+jets$& Line 139  $Wcc+jets\rightarrow$ $l\nu+cc+jets$&
 $Wjj+jets\rightarrow$ $l\nu+jj+jets$&  $Wjj+jets\rightarrow$ $l\nu+jj+jets$&
 &  &
 5.66 $\pm$ 0.11 \\  5.66 $\pm$ 0.11 \\
 $Zbb+jets\rightarrow$ $\tau\tau+bb+jets$&  $\gamma Zbb+jets\rightarrow$ $\tau\tau+bb+jets$&
 &  &
 0.93 $\pm$ 0.08\\  0.93 $\pm$ 0.08\\
 $Zcc+jets\rightarrow$ $\tau\tau+cc+jets$&  $\gamma Zcc+jets\rightarrow$ $\tau\tau+cc+jets$&
 &  &
 0.51 $\pm$ 0.04\\  0.51 $\pm$ 0.04\\
 $Zjj+jets\rightarrow$ $\tau\tau+jj+jets$&  $\gamma Zjj+jets\rightarrow$ $\tau\tau+jj+jets$&
 &  &
 1.07 $\pm$ 0.10 \\  1.07 $\pm$ 0.10 \\
 $Zbb+jets\rightarrow$ $ee+bb+jets$&  $\gamma Zbb+jets\rightarrow$ $ee+bb+jets$&
 &  &
 0.03 $\pm$ 0.01\\  0.03 $\pm$ 0.01\\
 $Zcc+jets\rightarrow$ $ee+cc+jets$&  $\gamma Zcc+jets\rightarrow$ $ee+cc+jets$&
 &  &
 0.00 $\pm$ 0.00\\  0.00 $\pm$ 0.00\\
 $Zjj+jets\rightarrow$ $ee+jj+jets$&  $\gamma Zjj+jets\rightarrow$ $ee+jj+jets$&
 &  &
 0.02 $\pm$ 0.01 \\  0.02 $\pm$ 0.01 \\
 $Zbb+jets\rightarrow$ $\mu\mu+bb+jets$&  $\gamma Zbb+jets\rightarrow$ $\mu\mu+bb+jets$&
 &  &
 0.07 $\pm$ 0.02\\  0.07 $\pm$ 0.02\\
 $Zcc+jets\rightarrow$ $\mu\mu+cc+jets$&  $\gamma Zcc+jets\rightarrow$ $\mu\mu+cc+jets$&
 &  &
 0.02 $\pm$ 0.01\\  0.02 $\pm$ 0.01\\
 $Zjj+jets\rightarrow$ $\mu\mu+jj+jets$&  $\gamma Zjj+jets\rightarrow$ $\mu\mu+jj+jets$&
 &  &
 0.01 $\pm$ 0.01 \\   0.01 $\pm$ 0.01 \\ 
 $Zbb+jets\rightarrow$ $\nu\nu+bb+jets$&  $Zbb+jets\rightarrow$ $\nu\nu+bb+jets$&
Line 173  $Zjj+jets\rightarrow$ $\nu\nu+jj+jets$& Line 176  $Zjj+jets\rightarrow$ $\nu\nu+jj+jets$&
 &  &
 0.04 $\pm$ 0.01\\ \hline  0.04 $\pm$ 0.01\\ \hline
 \end{tabular}  \end{tabular}
 \caption{Final number of events in each channel for taus types 1 and 2 $\tau$ after b-tagging, $\tau$ ID and trigger  \caption{Final number of events in each channel for taus of Types 1 and 2 $\tau$ after b-tagging, $\tau$ ID and trigger
 in the signal sample when the assumed cross section is 7.46 pb. An estimate of QCD background is not included.}  in the signal sample when $\sigma_{t\bar{t}}$ = 7.46 pb is assumed. An estimate of QCD background is not included.}
 %\end{ruledtabular}  %\end{ruledtabular}
 \label{b_and_tau_type1_2}   \label{b_and_tau_type1_2} 
 \end{table}  \end{table}
Line 213  $Wcc+jets\rightarrow$ $l\nu+cc+jets$& Line 216  $Wcc+jets\rightarrow$ $l\nu+cc+jets$&
 $Wjj+jets\rightarrow$ $l\nu+jj+jets$&  $Wjj+jets\rightarrow$ $l\nu+jj+jets$&
 &  &
 4.08 $\pm$ 0.11\\  4.08 $\pm$ 0.11\\
 $Zbb+jets\rightarrow$ $\tau\tau+bb+jets$&  $\gamma Zbb+jets\rightarrow$ $\tau\tau+bb+jets$&
 &  &
 0.74 $\pm$ 0.07\\  0.74 $\pm$ 0.07\\
 $Zcc+jets\rightarrow$ $\tau\tau+cc+jets$&  $\gamma Zcc+jets\rightarrow$ $\tau\tau+cc+jets$&
 &  &
 0.41 $\pm$ 0.03\\  0.41 $\pm$ 0.03\\
 $Zjj+jets\rightarrow$ $\tau\tau+jj+jets$&  $\gamma Zjj+jets\rightarrow$ $\tau\tau+jj+jets$&
 &  &
 0.80 $\pm$ 0.10 \\  0.80 $\pm$ 0.10 \\
 $Zbb+jets\rightarrow$ $ee+bb+jets$&  $\gamma Zbb+jets\rightarrow$ $ee+bb+jets$&
 &  &
 0.00 $\pm$ 0.00\\  0.00 $\pm$ 0.00\\
 $Zcc+jets\rightarrow$ $ee+cc+jets$&  $\gamma Zcc+jets\rightarrow$ $ee+cc+jets$&
 &  &
 0.01 $\pm$ 0.01\\  0.01 $\pm$ 0.01\\
 $Zjj+jets\rightarrow$ $ee+jj+jets$&  $\gamma Zjj+jets\rightarrow$ $ee+jj+jets$&
 &  &
 0.01 $\pm$ 0.01 \\  0.01 $\pm$ 0.01 \\
 $Zbb+jets\rightarrow$ $\mu\mu+bb+jets$&  $\gamma Zbb+jets\rightarrow$ $\mu\mu+bb+jets$&
 &  &
 0.04 $\pm$ 0.02\\  0.04 $\pm$ 0.02\\
 $Zcc+jets\rightarrow$ $\mu\mu+cc+jets$&  $\gamma Zcc+jets\rightarrow$ $\mu\mu+cc+jets$&
 &  &
 0.01 $\pm$ 0.01\\  0.01 $\pm$ 0.01\\
 $Zjj+jets\rightarrow$ $\mu\mu+jj+jets$&  $\gamma Zjj+jets\rightarrow$ $\mu\mu+jj+jets$&
 &  &
 0.00 $\pm$ 0.00 \\   0.00 $\pm$ 0.00 \\ 
 $Zbb+jets\rightarrow$ $\nu\nu+bb+jets$&  $Zbb+jets\rightarrow$ $\nu\nu+bb+jets$&
Line 250  $Zjj+jets\rightarrow$ $\nu\nu+jj+jets$& Line 253  $Zjj+jets\rightarrow$ $\nu\nu+jj+jets$&
 &  &
 0.06 $\pm$ 0.01 \\ \hline  0.06 $\pm$ 0.01 \\ \hline
 \end{tabular}  \end{tabular}
 \caption{Final number of events in each channel for taus type 3 $\tau$ After b-tagging, $\tau$ ID and trigger  \caption{Final number of events in each channel for taus Type 3 $\tau$ After b-tagging, $\tau$ ID and trigger
 in the signal sample when the assumed cross section is 7.46 pb. An estimate of QCD background is not included.}%\end{ruledtabular}  in the signal sample when $\sigma_{t\bar{t}}$ = 7.46 pb is assumed. An estimate of QCD background is not included.}%\end{ruledtabular}
 \label{b_and_tau_type_3}   \label{b_and_tau_type_3} 
 \end{table}  \end{table}
   
Line 288  $Wcc+jets\rightarrow$ $l\nu+cc+jets$& Line 291  $Wcc+jets\rightarrow$ $l\nu+cc+jets$&
 $Wjj+jets\rightarrow$ $l\nu+jj+jets$&  $Wjj+jets\rightarrow$ $l\nu+jj+jets$&
 &  &
 169.95 $\pm$ 2.68\\  169.95 $\pm$ 2.68\\
 $Zbb+jets\rightarrow$ $\tau\tau+bb+jets$&  $\gamma Zbb+jets\rightarrow$ $\tau\tau+bb+jets$&
 &  &
 1.30 $\pm$ 0.11\\  1.30 $\pm$ 0.11\\
 $Zcc+jets\rightarrow$ $\tau\tau+cc+jets$&  $\gamma Zcc+jets\rightarrow$ $\tau\tau+cc+jets$&
 &  &
 3.15 $\pm$ 0.20\\  3.15 $\pm$ 0.20\\
 $Zjj+jets\rightarrow$ $\tau\tau+jj+jets$&  $\gamma Zjj+jets\rightarrow$ $\tau\tau+jj+jets$&
 &  &
 16.86 $\pm$ 1.14 \\  16.86 $\pm$ 1.14 \\
 $Zbb+jets\rightarrow$ $ee+bb+jets$&  $\gamma Zbb+jets\rightarrow$ $ee+bb+jets$&
 &  &
 0.02 $\pm$ 0.01\\  0.02 $\pm$ 0.01\\
 $Zcc+jets\rightarrow$ $ee+cc+jets$&  $\gamma Zcc+jets\rightarrow$ $ee+cc+jets$&
 &  &
 0.00 $\pm$ 0.00\\  0.00 $\pm$ 0.00\\
 $Zjj+jets\rightarrow$ $ee+jj+jets$&  $\gamma Zjj+jets\rightarrow$ $ee+jj+jets$&
 &  &
 0.74 $\pm$ 0.33 \\  0.74 $\pm$ 0.33 \\
 $Zbb+jets\rightarrow$ $\mu\mu+bb+jets$&  $\gamma Zbb+jets\rightarrow$ $\mu\mu+bb+jets$&
 &  &
 0.08 $\pm$ 0.02\\  0.08 $\pm$ 0.02\\
 $Zcc+jets\rightarrow$ $\mu\mu+cc+jets$&  $\gamma Zcc+jets\rightarrow$ $\mu\mu+cc+jets$&
 &  &
 0.07 $\pm$ 0.03\\  0.07 $\pm$ 0.03\\
 $Zjj+jets\rightarrow$ $\mu\mu+jj+jets$&  $\gamma Zjj+jets\rightarrow$ $\mu\mu+jj+jets$&
 &  &
 0.38 $\pm$ 0.22 \\   0.38 $\pm$ 0.22 \\ 
 $Zbb+jets\rightarrow$ $\nu\nu+bb+jets$&  $Zbb+jets\rightarrow$ $\nu\nu+bb+jets$&
Line 325  $Zjj+jets\rightarrow$ $\nu\nu+jj+jets$& Line 328  $Zjj+jets\rightarrow$ $\nu\nu+jj+jets$&
 &  &
 1.36 $\pm$ 0.49 \\ \hline  1.36 $\pm$ 0.49 \\ \hline
 \end{tabular}  \end{tabular}
 \caption{$b$-veto data set composition for types 1 and 2 $\tau$ when the assumed cross section is 7.46 pb.}%\end{ruledtabular}  \caption{$b$-veto data set composition for Types 1 and 2 $\tau$ when $\sigma_{t\bar{t}}$ = 7.46 pb is assumed.}%\end{ruledtabular}
 \label{bveto_type1_2}   \label{bveto_type1_2} 
 \end{table}  \end{table}
   
Line 362  $Wcc+jets\rightarrow$ $l\nu+cc+jets$& Line 365  $Wcc+jets\rightarrow$ $l\nu+cc+jets$&
 $Wjj+jets\rightarrow$ $l\nu+jj+jets$&  $Wjj+jets\rightarrow$ $l\nu+jj+jets$&
 &  &
 126.41   $\pm$ 2.60 \\  126.41   $\pm$ 2.60 \\
 $Zbb+jets\rightarrow$ $\tau\tau+bb+jets$&  $\gamma Zbb+jets\rightarrow$ $\tau\tau+bb+jets$&
 &  &
 0.92 $\pm$ 0.09\\  0.92 $\pm$ 0.09\\
 $Zcc+jets\rightarrow$ $\tau\tau+cc+jets$&  $\gamma Zcc+jets\rightarrow$ $\tau\tau+cc+jets$&
 &  &
 2.86 $\pm$ 0.20\\  2.86 $\pm$ 0.20\\
 $Zjj+jets\rightarrow$ $\tau\tau+jj+jets$&  $\gamma Zjj+jets\rightarrow$ $\tau\tau+jj+jets$&
 &  &
 14.53 $\pm$ 1.15 \\  14.53 $\pm$ 1.15 \\
 $Zbb+jets\rightarrow$ $ee+bb+jets$&  $\gamma Zbb+jets\rightarrow$ $ee+bb+jets$&
 &  &
 0.00 $\pm$ 0.00\\  0.00 $\pm$ 0.00\\
 $Zcc+jets\rightarrow$ $ee+cc+jets$&  $\gamma Zcc+jets\rightarrow$ $ee+cc+jets$&
 &  &
 0.08 $\pm$ 0.04\\  0.08 $\pm$ 0.04\\
 $Zjj+jets\rightarrow$ $ee+jj+jets$&  $\gamma Zjj+jets\rightarrow$ $ee+jj+jets$&
 &  &
 0.31 $\pm$ 0.18 \\  0.31 $\pm$ 0.18 \\
 $Zbb+jets\rightarrow$ $\mu\mu+bb+jets$&  $\gamma Zbb+jets\rightarrow$ $\mu\mu+bb+jets$&
 &  &
 0.04 $\pm$ 0.02\\  0.04 $\pm$ 0.02\\
 $Zcc+jets\rightarrow$ $\mu\mu+cc+jets$&  $\gamma Zcc+jets\rightarrow$ $\mu\mu+cc+jets$&
 &  &
 0.05 $\pm$ 0.02\\  0.05 $\pm$ 0.02\\
 $Zjj+jets\rightarrow$ $\mu\mu+jj+jets$&  $\gamma Zjj+jets\rightarrow$ $\mu\mu+jj+jets$&
 &  &
 0.05 $\pm$ 0.04 \\   0.05 $\pm$ 0.04 \\ 
 $Zbb+jets\rightarrow$ $\nu\nu+bb+jets$&  $Zbb+jets\rightarrow$ $\nu\nu+bb+jets$&
Line 400  $Zjj+jets\rightarrow$ $\nu\nu+jj+jets$& Line 403  $Zjj+jets\rightarrow$ $\nu\nu+jj+jets$&
 2.31 $\pm$ 0.46 \\ \hline  2.31 $\pm$ 0.46 \\ \hline
 \end{tabular}  \end{tabular}
 %\end{ruledtabular}  %\end{ruledtabular}
 \caption{$b$-veto data set composition for type 3 $\tau$ when the assumed cross section is 7.46 pb.}  \caption{$b$-veto data set composition for Type 3 $\tau$ when $\sigma_{t\bar{t}}$ = 7.46 pb is assumed.}
 \label{b_veto_type_3}   \label{b_veto_type_3} 
 \end{table}  \end{table}
   
Line 436  $Wcc+jets\rightarrow$ $l\nu+cc+jets$& Line 439  $Wcc+jets\rightarrow$ $l\nu+cc+jets$&
 $Wjj+jets\rightarrow$ $l\nu+jj+jets$&  $Wjj+jets\rightarrow$ $l\nu+jj+jets$&
 &  &
 11.34 $\pm$ 0.26\\  11.34 $\pm$ 0.26\\
 $Zbb+jets\rightarrow$ $\tau\tau+bb+jets$&  $\gamma Zbb+jets\rightarrow$ $\tau\tau+bb+jets$&
 &  &
 0.50 $\pm$ 0.06\\  0.50 $\pm$ 0.06\\
 $Zcc+jets\rightarrow$ $\tau\tau+cc+jets$&  $\gamma Zcc+jets\rightarrow$ $\tau\tau+cc+jets$&
 &  &
 0.58 $\pm$ 0.06\\  0.58 $\pm$ 0.06\\
 $Zjj+jets\rightarrow$ $\tau\tau+jj+jets$&  $\gamma Zjj+jets\rightarrow$ $\tau\tau+jj+jets$&
 &  &
 1.10 $\pm$ 0.13 \\  1.10 $\pm$ 0.13 \\
 $Zbb+jets\rightarrow$ $ee+bb+jets$&  $\gamma Zbb+jets\rightarrow$ $ee+bb+jets$&
 &  &
 0.01 $\pm$ 0.01\\  0.01 $\pm$ 0.01\\
 $Zcc+jets\rightarrow$ $ee+cc+jets$&  $\gamma Zcc+jets\rightarrow$ $ee+cc+jets$&
 &  &
 0.01 $\pm$ 0.01\\  0.01 $\pm$ 0.01\\
 $Zjj+jets\rightarrow$ $ee+jj+jets$&  $\gamma Zjj+jets\rightarrow$ $ee+jj+jets$&
 &  &
 0.00 $\pm$ 0.00 \\  0.00 $\pm$ 0.00 \\
 $Zbb+jets\rightarrow$ $\mu\mu+bb+jets$&  $\gamma Zbb+jets\rightarrow$ $\mu\mu+bb+jets$&
 &  &
 0.03 $\pm$ 0.01\\  0.03 $\pm$ 0.01\\
 $Zcc+jets\rightarrow$ $\mu\mu+cc+jets$&  $\gamma Zcc+jets\rightarrow$ $\mu\mu+cc+jets$&
 &  &
 0.04     $\pm$ 0.01\\  0.04     $\pm$ 0.01\\
 $Zjj+jets\rightarrow$ $\mu\mu+jj+jets$&  $\gamma Zjj+jets\rightarrow$ $\mu\mu+jj+jets$&
 &  &
 0.02 $\pm$ 0.01 \\   0.02 $\pm$ 0.01 \\ 
 $Zbb+jets\rightarrow$ $\nu\nu+bb+jets$&  $Zbb+jets\rightarrow$ $\nu\nu+bb+jets$&
Line 473  $Zjj+jets\rightarrow$ $\nu\nu+jj+jets$& Line 476  $Zjj+jets\rightarrow$ $\nu\nu+jj+jets$&
 &  &
 0.36 $\pm$ 0.04 \\ \hline  0.36 $\pm$ 0.04 \\ \hline
 \end{tabular}  \end{tabular}
 \caption{loose-tight data set composition for types 1 and 2 $\tau$ when the assumed cross section is 7.46 pb.}%\end{ruledtabular}  \caption{loose-tight data set composition for Types 1 and 2 $\tau$ when $\sigma_{t\bar{t}}$ = 7.46 pb is assumed.}%\end{ruledtabular}
 \label{loosetight1_2}   \label{loosetight1_2} 
 \end{table}  \end{table}
   
Line 511  $Wcc+jets\rightarrow$ $l\nu+cc+jets$& Line 514  $Wcc+jets\rightarrow$ $l\nu+cc+jets$&
 $Wjj+jets\rightarrow$ $l\nu+jj+jets$&  $Wjj+jets\rightarrow$ $l\nu+jj+jets$&
 &  &
 16.32    $\pm$ 0.30 \\  16.32    $\pm$ 0.30 \\
 $Zbb+jets\rightarrow$ $\tau\tau+bb+jets$&  $\gamma Zbb+jets\rightarrow$ $\tau\tau+bb+jets$&
 &  &
 0.52 $\pm$ 0.05\\  0.52 $\pm$ 0.05\\
 $Zcc+jets\rightarrow$ $\tau\tau+cc+jets$&  $\gamma Zcc+jets\rightarrow$ $\tau\tau+cc+jets$&
 &  &
 0.46 $\pm$ 0.04\\  0.46 $\pm$ 0.04\\
 $Zjj+jets\rightarrow$ $\tau\tau+jj+jets$&  $\gamma Zjj+jets\rightarrow$ $\tau\tau+jj+jets$&
 &  &
 1.16 $\pm$ 0.12 \\  1.16 $\pm$ 0.12 \\
 $Zbb+jets\rightarrow$ $ee+bb+jets$&  $\gamma Zbb+jets\rightarrow$ $ee+bb+jets$&
 &  &
 0.00 $\pm$ 0.00\\  0.00 $\pm$ 0.00\\
 $Zcc+jets\rightarrow$ $ee+cc+jets$&  $\gamma Zcc+jets\rightarrow$ $ee+cc+jets$&
 &  &
 0.00 $\pm$ 0.00\\  0.00 $\pm$ 0.00\\
 $Zjj+jets\rightarrow$ $ee+jj+jets$&  $\gamma Zjj+jets\rightarrow$ $ee+jj+jets$&
 &  &
 0.01 $\pm$ 0.01 \\  0.01 $\pm$ 0.01 \\
 $Zbb+jets\rightarrow$ $\mu\mu+bb+jets$&  $\gamma Zbb+jets\rightarrow$ $\mu\mu+bb+jets$&
 &  &
 0.06 $\pm$ 0.01\\  0.06 $\pm$ 0.01\\
 $Zcc+jets\rightarrow$ $\mu\mu+cc+jets$&  $\gamma Zcc+jets\rightarrow$ $\mu\mu+cc+jets$&
 &  &
 0.07 $\pm$ 0.01\\  0.07 $\pm$ 0.01\\
 $Zjj+jets\rightarrow$ $\mu\mu+jj+jets$&  $\gamma Zjj+jets\rightarrow$ $\mu\mu+jj+jets$&
 &  &
 0.11 $\pm$ 0.02 \\   0.11 $\pm$ 0.02 \\ 
 $Zbb+jets\rightarrow$ $\nu\nu+bb+jets$&  $Zbb+jets\rightarrow$ $\nu\nu+bb+jets$&
Line 549  $Zjj+jets\rightarrow$ $\nu\nu+jj+jets$& Line 552  $Zjj+jets\rightarrow$ $\nu\nu+jj+jets$&
 1.28 $\pm$ 0.08 \\ \hline  1.28 $\pm$ 0.08 \\ \hline
 \end{tabular}  \end{tabular}
 %\end{ruledtabular}  %\end{ruledtabular}
 \caption{loose-tight data set composition for type 3 $\tau$ when the assumed cross section is 7.46 pb.}  \caption{loose-tight data set composition for Type 3 $\tau$ when $\sigma_{t\bar{t}}$ = 7.46 pb is assumed.}
 \label{loosetight_3}   \label{loosetight_3} 
 \end{table}  \end{table}
   

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