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%\section{Systematics Uncertainties on the Background Prediction}
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%\label{sec:systematics}
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[DESCRIBE HERE ONE BY ONE THE UNCERTAINTIES THAT ARE PRESENT IN THE SPREADSHHET
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FROM WHICH WE CALCULATE THE TOTAL UNCERTAINTY. WE KNOW HOW TO DO THIS
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AND
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WE HAVE THE TECHNOLOGY FROM THE 7 TEV ANALYSIS TO PROPAGATE ALL
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UNCERTAINTIES
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CORRECTLY THROUGH. WE WILL DO IT ONCE WE HAVE SETTLED ON THE
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INDIVIDUAL PIECES WHICH ARE STILL IN FLUX]
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In this Section we discuss the systematic uncertainty on the BG
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prediction. This prediction is assembled from the event
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counts in the peak region of the transverse mass distribution as
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well as Monte Carlo
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with a number of correction factors, as described previously.
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The
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final uncertainty on the prediction is built up from the uncertainties in these
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individual
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components.
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The calculation is done for each signal
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region,
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for electrons and muons separately.
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The choice to normalizing to the peak region of $M_T$ has the
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advantage that some uncertainties, e.g., luminosity, cancel.
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It does however introduce complications because it couples
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some of the uncertainties in non-trivial ways. For example,
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the primary effect of an uncertainty on the rare MC cross-section
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is to introduce an uncertainty in the rare MC background estimate
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which comes entirely from MC. But this uncertainty also affects,
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for example,
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the $t\bar{t} \to$ dilepton BG estimate because it changes the
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$t\bar{t}$ normalization to the peak region (because some of the
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events in the peak region are from rare processes). These effects
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are carefully accounted for. The contribution to the overall
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uncertainty from each BG source is tabulated in
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Section~\ref{sec:bgunc-bottomline}.
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First, however, we discuss the uncertainties one-by-one and we comment
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on their impact on the overall result, at least to first order.
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Second order effects, such as the one described, are also included.
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\subsection{Statistical uncertainties on the event counts in the $M_T$
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peak regions}
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These vary between XX and XX \%, depending on the signal region
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(different
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signal regions have different \met\ requirements, thus they also have
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different $M_T$ regions used as control.
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Since
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the major BG, eg, $t\bar{t}$ are normalized to the peak regions, this
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fractional uncertainty is pretty much carried through all the way to
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the end. There is also an uncertainty from the finite MC event counts
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in the $M_T$ peak regions. This is also included, but it is smaller.
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\subsection{Uncertainty from the choice of $M_T$ peak region}
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IN 7 TEV DATA WE HAD SOME SHAPE DIFFERENCES IN THE MTRANS REGION THAT
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LED US TO CONSERVATIVELY INCLUDE THIS UNCERTAINTY. WE NEED TO LOOK
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INTO THIS AGAIN
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\subsection{Uncertainty on the Wjets cross-section and the rare MC cross-sections}
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These are taken as 50\%, uncorrelated.
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The primary effect is to introduce a 50\%
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uncertainty
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on the $W +$ jets and rare BG
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background predictions, respectively. However they also
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have an effect on the other BGs via the $M_T$ peak normalization
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in a way that tends to reduce the uncertainty. This is easy
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to understand: if the $W$ cross-section is increased by 50\%, then
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the $W$ background goes up. But the number of $M_T$ peak events
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attributed to $t\bar{t}$ goes down, and since the $t\bar{t}$ BG is
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scaled to the number of $t\bar{t}$ events in the peak, the $t\bar{t}$
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BG goes down.
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\subsection{Scale factors for the tail-to-peak ratios for lepton +
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jets top and W events}
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These tail-to-peak ratios are described in Section~\ref{sec:ttp}.
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They are studied in CR1 and CR2. The studies are described
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in Sections~\ref{sec:cr1} and~\ref{sec:cr2}), respectively, where
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we also give the uncertainty on the scale factors.
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\subsection{Uncertainty on extra jet radiation for dilepton
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background}
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As discussed in Section~\ref{sec:jetmultiplicity}, the
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jet distribution in
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$t\bar{t} \to$
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dilepton MC is rescaled by the factors $K_3$ and $K_4$ to make
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it agree with the data. The XX\% uncertainties on $K_3$ and $K_4$
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comes from data/MC statistics. This
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result directly in a XX\% uncertainty on the dilepton BG, which is by far
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the most important one.
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\subsection{Uncertainty on the \ttll\ Acceptance}
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The \ttbar\ background prediction is obtained from MC, with corrections
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derived from control samples in data. The uncertainty associated with
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the theoretical modeling of the \ttbar\ production and decay is
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estimated by comparing the background predictions obtained using
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alternative MC samples. It should be noted that the full analysis is
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performed with the alternative samples under consideration,
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including the derivation of the various data-to-MC scale factors.
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The variations considered are
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\begin{itemize}
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\item Top mass: The alternative values for the top mass differ
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from the central value by $5~\GeV$: $m_{\mathrm{top}} = 178.5~\GeV$ and $m_{\mathrm{top}}
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= 166.5~\GeV$.
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\item Jet-parton matching scale: This corresponds to variations in the
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scale at which the Matrix Element partons from Madgraph are matched
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to Parton Shower partons from Pythia. The nominal value is
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$x_q>20~\GeV$. The alternative values used are $x_q>10~\GeV$ and
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$x_q>40~\GeV$.
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\item Renormalization and factorization scale: The alternative samples
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correspond to variations in the scale $\times 2$ and $\times 0.5$. The nominal
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value for the scale used is $Q^2 = m_{\mathrm{top}}^2 +
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\sum_{\mathrm{jets}} \pt^2$.
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\item Alternative generators: Samples produced with different
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generators include MC@NLO and Powheg (NLO generators) and
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Pythia (LO). It may also be noted that MC@NLO uses Herwig6 for the
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hadronisation, while POWHEG uses Pythia6.
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\item Modeling of taus: The alternative sample does not include
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Tauola and is otherwise identical to the Powheg sample.
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This effect was studied earlier using 7~TeV samples and found to be negligible.
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\item The PDF uncertainty is estimated following the PDF4LHC
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recommendations[CITE]. The events are reweighted using alternative
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PDF sets for CT10 and MSTW2008 and the uncertainties for each are derived using the
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alternative eigenvector variations and the ``master equation''. In
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addition, the NNPDF2.1 set with 100 replicas. The central value is
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determined from the mean and the uncertainty is derived from the
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$1\sigma$ range. The overall uncertainty is derived from the envelope of the
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alternative predictions and their uncertainties.
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This effect was studied earlier using 7~TeV samples and found to be negligible.
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\end{itemize}
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\begin{table}[!h]
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\begin{center}
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{\footnotesize
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\begin{tabular}{l||c||c|c|c|c|c|c|c}
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\hline
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Sample & Powheg & Madgraph & Mass Up & Mass Down & Scale Up & Scale Down &
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Match Up & Match Down \\
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\hline
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\hline
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SRA & $579 \pm 10$ & $569 \pm 16$ & $591 \pm 18$ & $610 \pm 22$ & $651 \pm 22$ & $537 \pm 16$ & $578 \pm 18$ & $570 \pm 17$ \\
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\hline
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SRB & $328 \pm 7$ & $307 \pm 11$ & $329 \pm 13$ & $348 \pm 15$ & $344 \pm 15$ & $287 \pm 10$ & $313 \pm 13$ & $307 \pm 12$ \\
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\hline
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SRC & $111 \pm 4$ & $99 \pm 5$ & $107 \pm 7$ & $113 \pm 8$ & $124 \pm 8$ & $95 \pm 6$ & $93 \pm 6$ & $106 \pm 6$ \\
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\hline
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SRD & $39 \pm 2$ & $35 \pm 3$ & $41 \pm 4$ & $41 \pm 5$ & $47 \pm 5$ & $33 \pm 3$ & $31 \pm 3$ & $39 \pm 4$ \\
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\hline
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SRE & $14 \pm 1$ & $15 \pm 2$ & $17 \pm 3$ & $12 \pm 3$ & $15 \pm 3$ & $13 \pm 2$ & $12 \pm 2$ & $16 \pm 2$ \\
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\hline
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\end{tabular}}
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\caption{ \ttdl\ predictions for alternative MC samples. The uncertainties are statistical only.
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\label{tab:ttdlalt}}
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\end{center}
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\end{table}
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\begin{table}[!h]
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\begin{center}
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{\footnotesize
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\begin{tabular}{l||c|c|c|c|c|c|c}
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\hline
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$\Delta/N$ [\%] & Madgraph & Mass Up & Mass Down & Scale Up & Scale Down &
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Match Up & Match Down \\
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\hline
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\hline
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SRA & $2$ & $2$ & $5$ & $12$ & $7$ & $0$ & $2$ \\
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\hline
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SRB & $6$ & $0$ & $6$ & $5$ & $12$ & $5$ & $6$ \\
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\hline
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SRC & $10$ & $3$ & $2$ & $12$ & $14$ & $16$ & $4$ \\
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\hline
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SRD & $10$ & $6$ & $6$ & $21$ & $15$ & $19$ & $0$ \\
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\hline
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SRE & $6$ & $17$ & $15$ & $2$ & $12$ & $17$ & $8$ \\
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\hline
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\end{tabular}}
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\caption{ Relative difference in \ttdl\ predictions for alternative MC samples.
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\label{tab:fracdiff}}
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\end{center}
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\end{table}
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\begin{table}[!h]
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\begin{center}
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{\footnotesize
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\begin{tabular}{l||c|c|c|c|c|c|c}
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\hline
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$N \sigma$ & Madgraph & Mass Up & Mass Down & Scale Up & Scale Down &
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Match Up & Match Down \\
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\hline
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\hline
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SRA & $0.38$ & $0.42$ & $1.02$ & $2.34$ & $1.58$ & $0.01$ & $0.33$ \\
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\hline
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SRB & $1.17$ & $0.07$ & $0.98$ & $0.76$ & $2.29$ & $0.78$ & $1.11$ \\
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\hline
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SRC & $1.33$ & $0.37$ & $0.26$ & $1.24$ & $1.82$ & $1.97$ & $0.54$ \\
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\hline
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SRD & $0.82$ & $0.46$ & $0.38$ & $1.32$ & $1.27$ & $1.47$ & $0.00$ \\
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\hline
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SRE & $0.32$ & $0.75$ & $0.66$ & $0.07$ & $0.66$ & $0.83$ & $0.38$ \\
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\hline
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\end{tabular}}
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\caption{ N $\sigma$ difference in \ttdl\ predictions for alternative MC samples.
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\label{tab:nsig}}
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\end{center}
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\end{table}
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\begin{table}[!h]
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\begin{center}
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\begin{tabular}{l||c|c|c|c}
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\hline
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Av. $\Delta$ Evt. & Alt. Gen. & $\Delta$ Mass & $\Delta$ Scale
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& $\Delta$ Match \\
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\hline
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\hline
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SRA & $5.0$ ($1\%$) & $9.6$ ($2\%$) & $56.8$ ($10\%$) & $4.4$ ($1\%$) \\
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\hline
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SRB & $10.4$ ($3\%$) & $9.6$ ($3\%$) & $28.2$ ($9\%$) & $2.8$ ($1\%$) \\
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\hline
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SRC & $5.7$ ($5\%$) & $3.1$ ($3\%$) & $14.5$ ($13\%$) & $6.4$ ($6\%$) \\
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\hline
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SRD & $1.9$ ($5\%$) & $0.1$ ($0\%$) & $6.9$ ($18\%$) & $3.6$ ($9\%$) \\
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\hline
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SRE & $0.5$ ($3\%$) & $2.3$ ($16\%$) & $1.0$ ($7\%$) & $1.8$ ($12\%$) \\
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\hline
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\end{tabular}
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\caption{ Av. difference in \ttdl\ events for alternative sample pairs.
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\label{tab:devt}}
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\end{center}
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\end{table}
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|
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\begin{figure}[hbt]
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\begin{center}
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\includegraphics[width=0.5\linewidth]{plots/n_dl_comp_SRA.pdf}%
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| 242 |
\includegraphics[width=0.5\linewidth]{plots/n_dl_comp_SRB.pdf}
|
| 243 |
\includegraphics[width=0.5\linewidth]{plots/n_dl_comp_SRC.pdf}%
|
| 244 |
\includegraphics[width=0.5\linewidth]{plots/n_dl_comp_SRD.pdf}
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| 245 |
\includegraphics[width=0.5\linewidth]{plots/n_dl_comp_SRE.pdf}
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\caption{
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| 247 |
\label{fig:ttllsyst}\protect
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Comparison of the \ttll\ central prediction with those using
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alternative MC samples. The blue band corresponds to the
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total statistical error for all data and MC samples. The
|
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alternative sample predictions are indicated by the
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datapoints. The uncertainties on the alternative predictions
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correspond to the uncorrelated statistical uncertainty from
|
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the size of the alternative sample only.
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[TO BE UPDATED WITH THE LATEST SELECTION AND SFS]}
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\end{center}
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\end{figure}
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\clearpage
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%
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%
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%The methodology for determining the systematics on the background
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%predictions has not changed with respect to the nominal analysis.
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%Because the template method has not changed, the same
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| 266 |
%systematic uncertainty is assessed on this prediction (32\%).
|
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%The 50\% uncertainty on the WZ and ZZ background is also unchanged.
|
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%The systematic uncertainty in the OF background prediction based on
|
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%e$\mu$ events has changed, due to the different composition of this
|
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%sample after vetoing events containing b-tagged jets.
|
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%
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%As in the nominal analysis, we do not require the e$\mu$ events
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%to satisfy the dilepton mass requirement and apply a scaling factor K,
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%extracted from MC, to account for the fraction of e$\mu$ events
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%which satisfy the dilepton mass requirement. This procedure is used
|
| 276 |
%in order to improve the statistical precision of the OF background estimate.
|
| 277 |
%
|
| 278 |
%For the selection used in the nominal analysis,
|
| 279 |
%the e$\mu$ sample is completely dominated by $t\bar{t}$
|
| 280 |
%events, and we observe that K is statistically consistent with constant with
|
| 281 |
%respect to the \MET\ requirement. However, in this analysis, the $t\bar{t}$
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| 282 |
%background is strongly suppressed by the b-veto, and hence the non-$t\bar{t}$
|
| 283 |
%backgrounds (specifically, $Z\to\tau\tau$ and VV) become more relevant.
|
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%At low \MET, the $Z\to\tau\tau$ background is pronounced, while $t\bar{t}$
|
| 285 |
%and VV dominate at high \MET\ (see App.~\ref{app:kinemu}).
|
| 286 |
%Therefore, the sample composition changes
|
| 287 |
%as the \MET\ requirement is varied, and as a result K depends
|
| 288 |
%on the \MET\ requirement.
|
| 289 |
%
|
| 290 |
%We thus measure K in MC separately for each
|
| 291 |
%\MET\ requirement, as displayed in Fig.~\ref{fig:kvmet} (left).
|
| 292 |
%%The systematic uncertainty on K is determined separately for each \MET\
|
| 293 |
%%requirement by comparing the relative difference in K in data vs. MC.
|
| 294 |
%The values of K used are the MC predictions
|
| 295 |
%%and the total systematic uncertainty on the OF prediction
|
| 296 |
%%as shown in
|
| 297 |
%(Table \ref{fig:kvmettable}).
|
| 298 |
%The contribution to the total OF prediction systematic uncertainty
|
| 299 |
%from K is assessed from the ratio of K in data and MC,
|
| 300 |
%shown in Fig.~\ref{fig:kvmet} (right).
|
| 301 |
%The ratio is consistent with unity to roughly 17\%,
|
| 302 |
%so we take this value as the systematic from K.
|
| 303 |
%17\% added in quadrature with 7\% from
|
| 304 |
%the electron to muon efficieny ratio
|
| 305 |
%(as assessed in the inclusive analysis)
|
| 306 |
%yields a total systematic of $\sim$18\%
|
| 307 |
%which we round up to 20\%.
|
| 308 |
%For \MET\ $>$ 150, there are no OF events in data inside the Z mass window
|
| 309 |
%so we take a systematic based on the statistical uncertainty
|
| 310 |
%of the MC prediction for K.
|
| 311 |
%This value is 25\% for \MET\ $>$ 150 GeV and 60\% for \MET\ $>$ 200 GeV.
|
| 312 |
%%Although we cannot check the value of K in data for \MET\ $>$ 150
|
| 313 |
%%because we find no OF events inside the Z mass window for this \MET\
|
| 314 |
%%cut, the overall OF yields with no dilepton mass requirement
|
| 315 |
%%agree to roughly 20\% (9 data vs 7.0 $\pm$ 1.1 MC).
|
| 316 |
%
|
| 317 |
%
|
| 318 |
%%Below Old
|
| 319 |
%
|
| 320 |
%%In reevaluating the systematics on the OF prediction, however,
|
| 321 |
%%we observed a different behavior of K as a function of \MET\
|
| 322 |
%%as was seen in the inclusive analysis.
|
| 323 |
%
|
| 324 |
%%Recall that K is the ratio of the number of \emu\ events
|
| 325 |
%%inside the Z window to the total number of \emu\ events.
|
| 326 |
%%In the inclusive analysis, it is taken from \ttbar\ MC
|
| 327 |
%%and used to scale the inclusive \emu\ yield in data.
|
| 328 |
%%The yield scaled by K is then corrected for
|
| 329 |
%%the $e$ vs $\mu$ efficiency difference to obtain the
|
| 330 |
%%final OF prediction.
|
| 331 |
%
|
| 332 |
%%Based on the plot in figure \ref{fig:kvmet},
|
| 333 |
%%we choose to use a different
|
| 334 |
%%K for each \MET\ cut and assess a systematic uncertainty
|
| 335 |
%%on the OF prediction based on the difference between
|
| 336 |
%%K in data and MC.
|
| 337 |
%%The variation of K as a function of \MET\ is caused
|
| 338 |
%%by a change in sample composition with increasing \MET.
|
| 339 |
%%At \MET\ $<$ 60 GeV, the contribution of Z plus jets is
|
| 340 |
%%not negligible (as it was in the inclusive analysis)
|
| 341 |
%%because of the b veto. (See appendix \ref{app:kinemu}.)
|
| 342 |
%%At higher \MET, \ttbar\ and diboson backgrounds dominate.
|
| 343 |
%
|
| 344 |
%
|
| 345 |
%
|
| 346 |
%
|
| 347 |
%\begin{figure}[hbt]
|
| 348 |
% \begin{center}
|
| 349 |
% \includegraphics[width=0.48\linewidth]{plots/kvmet_data_ttbm.pdf}
|
| 350 |
% \includegraphics[width=0.48\linewidth]{plots/kvmet_ratio.pdf}
|
| 351 |
% \caption{
|
| 352 |
% \label{fig:kvmet}\protect
|
| 353 |
% The left plot shows
|
| 354 |
% K as a function of \MET\ in MC (red) and data (black).
|
| 355 |
% The bin low edge corresponds to the \MET\ cut, and the
|
| 356 |
% bins are inclusive.
|
| 357 |
% The MC used is a sum of all SM MC used in the yield table of
|
| 358 |
% section \ref{sec:yields}.
|
| 359 |
% The right plot is the ratio of K in data to MC.
|
| 360 |
% The ratio is fit to a line whose slope is consistent with zero
|
| 361 |
% (the fit parameters are
|
| 362 |
% 0.9 $\pm$ 0.4 for the intercept and
|
| 363 |
% 0.001 $\pm$ 0.005 for the slope).
|
| 364 |
% }
|
| 365 |
% \end{center}
|
| 366 |
%\end{figure}
|
| 367 |
%
|
| 368 |
%
|
| 369 |
%
|
| 370 |
%\begin{table}[htb]
|
| 371 |
%\begin{center}
|
| 372 |
%\caption{\label{fig:kvmettable} The values of K used in the OF background prediction.
|
| 373 |
%The uncertainties shown are the total relative systematic used for the OF prediction,
|
| 374 |
%which is the systematic uncertainty from K added in quadrature with
|
| 375 |
%a 7\% uncertainty from the electron to muon efficieny ratio as assessed in the
|
| 376 |
%inclusive analysis.
|
| 377 |
%}
|
| 378 |
%\begin{tabular}{lcc}
|
| 379 |
%\hline
|
| 380 |
%\MET\ Cut & K & Relative Systematic \\
|
| 381 |
%\hline
|
| 382 |
%%the met zero row is used only for normalization of the money plot.
|
| 383 |
%%0 & 0.1 & \\
|
| 384 |
%30 & 0.12 & 20\% \\
|
| 385 |
%60 & 0.13 & 20\% \\
|
| 386 |
%80 & 0.12 & 20\% \\
|
| 387 |
%100 & 0.12 & 20\% \\
|
| 388 |
%150 & 0.09 & 25\% \\
|
| 389 |
%200 & 0.06 & 60\% \\
|
| 390 |
%\hline
|
| 391 |
%\end{tabular}
|
| 392 |
%\end{center}
|
| 393 |
%\end{table}
|
| 394 |
|
| 395 |
\subsection{Uncertainty from the isolated track veto}
|
| 396 |
This is the uncertainty associated with how well the isolated track
|
| 397 |
veto performance is modeled by the Monte Carlo. This uncertainty
|
| 398 |
only applies to the fraction of dilepton BG events that have
|
| 399 |
a second e/$\mu$ or a one prong $\tau \to h$, with
|
| 400 |
$P_T > 10$ GeV in $|\eta| < 2.4$. This fraction is 1/3 (THIS WAS THE
|
| 401 |
7 TEV NUMBER, CHECK). The uncertainty for these events
|
| 402 |
is XX\% and is obtained from Tag and Probe studies of Section~\ref{sec:trkveto}
|
| 403 |
|
| 404 |
\subsubsection{Isolated Track Veto: Tag and Probe Studies}
|
| 405 |
\label{sec:trkveto}
|
| 406 |
|
| 407 |
[EVERYTHING IS 7TEV HERE, UPDATE WITH NEW RESULTS \\
|
| 408 |
ADD TABLE WITH FRACTION OF EVENTS THAT HAVE A TRUE ISOLATED TRACK]
|
| 409 |
|
| 410 |
\begin{table}[!h]
|
| 411 |
\begin{center}
|
| 412 |
{\footnotesize
|
| 413 |
\begin{tabular}{l||c|c|c|c|c|c|c}
|
| 414 |
\hline
|
| 415 |
Sample & SRA & SRB & SRC & SRD & SRE & SRF & SRG \\
|
| 416 |
\hline
|
| 417 |
\hline
|
| 418 |
$\mu$ Frac. \ttdl\ with true iso. trk. & $0.32 \pm 0.03$ & $0.30 \pm 0.03$ & $0.32 \pm 0.06$ & $0.34 \pm 0.10$ & $0.35 \pm 0.16$ & $0.40 \pm 0.24$ & $0.50 \pm 0.32$ \\
|
| 419 |
\hline
|
| 420 |
\hline
|
| 421 |
e Frac. \ttdl\ with true iso. trk. & $0.32 \pm 0.03$ & $0.31 \pm 0.04$ & $0.33 \pm 0.06$ & $0.38 \pm 0.11$ & $0.38 \pm 0.19$ & $0.60 \pm 0.31$ & $0.61 \pm 0.45$ \\
|
| 422 |
\hline
|
| 423 |
\end{tabular}}
|
| 424 |
\caption{ Fraction of \ttdl\ events with a true isolated track.
|
| 425 |
\label{tab:trueisotrk}}
|
| 426 |
\end{center}
|
| 427 |
\end{table}
|
| 428 |
|
| 429 |
|
| 430 |
In this section we compare the performance of the isolated track veto in data and MC using tag-and-probe studies
|
| 431 |
with samples of Z$\to$ee and Z$\to\mu\mu$. The purpose of these studies is to demonstrate that the efficiency
|
| 432 |
to satisfy the isolated track veto requirements is well-reproduced in the MC, since if this were not the case
|
| 433 |
we would need to apply a data-to-MC scale factor in order to correctly predict the \ttll\ background. This study
|
| 434 |
addresses possible data vs. MC discrepancies for the {\bf efficiency} to identify (and reject) events with a
|
| 435 |
second {\bf genuine} lepton (e, $\mu$, or $\tau\to$1-prong). It does not address possible data vs. MC discrepancies
|
| 436 |
in the fake rate for rejecting events without a second genuine lepton; this is handled separately in the top normalization
|
| 437 |
procedure by scaling the \ttlj\ contribution to match the data in the \mt\ peak after applying the isolated track veto.
|
| 438 |
Furthermore, we test the data and MC
|
| 439 |
isolated track veto efficiencies for electrons and muons since we are using a Z tag-and-probe technique, but we do not
|
| 440 |
directly test the performance for hadronic tracks from $\tau$ decays. The performance for hadronic $\tau$ decay products
|
| 441 |
may differ from that of electrons and muons for two reasons. First, the $\tau$ may decay to a hadronic track plus one
|
| 442 |
or two $\pi^0$'s, which may decay to $\gamma\gamma$ followed by a photon conversion. As shown in Figure~\ref{fig:absiso},
|
| 443 |
the isolation distribution for charged tracks from $\tau$ decays that are not produced in association with $\pi^0$s are
|
| 444 |
consistent with that from $\E$s and $\M$s. Since events from single prong $\tau$ decays produced in association with
|
| 445 |
$\pi^0$s comprise a small fraction of the total sample, and since the kinematics of $\tau$, $\pi^0$ and $\gamma\to e^+e^-$
|
| 446 |
decays are well-understood, we currently demonstrate that the isolation is well-reproduced for electrons and muons only.
|
| 447 |
Second, hadronic tracks may undergo nuclear interactions and hence their tracks may not be reconstructed.
|
| 448 |
As discussed above, independent studies show that the MC reproduces the hadronic tracking efficiency within 4\%,
|
| 449 |
leading to a total background uncertainty of less than 0.5\% (after taking into account the fraction of the total background
|
| 450 |
due to hadronic $\tau$ decays with \pt\ $>$ 10 GeV tracks), and we hence regard this effect as neglgigible.
|
| 451 |
|
| 452 |
The tag-and-probe studies are performed in the full 2011 data sample, and compared with the DYJets madgraph sample.
|
| 453 |
All events must contain a tag-probe pair (details below) with opposite-sign and satisfying the Z mass requirement 76--106 GeV.
|
| 454 |
We compare the distributions of absolute track isolation for probe electrons/muons in data vs. MC. The contributions to
|
| 455 |
this isolation sum are from ambient energy in the event from underlying event, pile-up and jet activitiy, and hence do
|
| 456 |
not depend on the \pt\ of the probe lepton. We therefore restrict the probe \pt\ to be $>$ 30 GeV in order to suppress
|
| 457 |
fake backgrounds with steeply-falling \pt\ spectra. To suppress non-Z backgrounds (in particular \ttbar) we require
|
| 458 |
\met\ $<$ 30 GeV and 0 b-tagged events.
|
| 459 |
The specific criteria for tags and probes for electrons and muons are:
|
| 460 |
|
| 461 |
%We study the isolated track veto efficiency in bins of \njets.
|
| 462 |
%We are interested in events with at least 4 jets to emulate the hadronic activity in our signal sample. However since
|
| 463 |
%there are limited statistics for Z + $\geq$4 jet events, we study the isolated track performance in events with
|
| 464 |
|
| 465 |
|
| 466 |
\begin{itemize}
|
| 467 |
\item{Electrons}
|
| 468 |
|
| 469 |
\begin{itemize}
|
| 470 |
\item{Tag criteria}
|
| 471 |
|
| 472 |
\begin{itemize}
|
| 473 |
\item Electron passes full analysis ID/iso selection
|
| 474 |
\item \pt\ $>$ 30 GeV, $|\eta|<2.1$
|
| 475 |
\item Matched to the single electron trigger \verb=HLT_Ele27_WP80_v*=
|
| 476 |
\end{itemize}
|
| 477 |
|
| 478 |
\item{Probe criteria}
|
| 479 |
\begin{itemize}
|
| 480 |
\item Electron passes full analysis ID selection
|
| 481 |
\item \pt\ $>$ 30 GeV
|
| 482 |
\end{itemize}
|
| 483 |
\end{itemize}
|
| 484 |
\item{Muons}
|
| 485 |
\begin{itemize}
|
| 486 |
\item{Tag criteria}
|
| 487 |
\begin{itemize}
|
| 488 |
\item Muon passes full analysis ID/iso selection
|
| 489 |
\item \pt\ $>$ 30 GeV, $|\eta|<2.1$
|
| 490 |
\item Matched to 1 of the 2 single muon triggers
|
| 491 |
\begin{itemize}
|
| 492 |
\item \verb=HLT_IsoMu30_v*=
|
| 493 |
\item \verb=HLT_IsoMu30_eta2p1_v*=
|
| 494 |
\end{itemize}
|
| 495 |
\end{itemize}
|
| 496 |
\item{Probe criteria}
|
| 497 |
\begin{itemize}
|
| 498 |
\item Muon passes full analysis ID selection
|
| 499 |
\item \pt\ $>$ 30 GeV
|
| 500 |
\end{itemize}
|
| 501 |
\end{itemize}
|
| 502 |
\end{itemize}
|
| 503 |
|
| 504 |
The absolute track isolation distributions for passing probes are displayed in Fig.~\ref{fig:tnp}. In general we observe
|
| 505 |
good agreement between data and MC. To be more quantitative, we compare the data vs. MC efficiencies to satisfy
|
| 506 |
absolute track isolation requirements varying from $>$ 1 GeV to $>$ 5 GeV, as summarized in Table~\ref{tab:isotrk}.
|
| 507 |
In the $\geq$0 and $\geq$1 jet bins where the efficiencies can be tested with statistical precision, the data and MC
|
| 508 |
efficiencies agree within 6\%, and we apply this as a systematic uncertainty on the isolated track veto efficiency.
|
| 509 |
For the higher jet multiplicity bins the statistical precision decreases, but we do not observe any evidence for
|
| 510 |
a data vs. MC discrepancy in the isolated track veto efficiency.
|
| 511 |
|
| 512 |
|
| 513 |
%This is because our analysis requirement is relative track isolation $<$ 0.1, and m
|
| 514 |
%This requirement is chosen because most of the tracks rejected by the isolated
|
| 515 |
%track veto have a \pt\ near the 10 GeV threshold, and our analysis requirement is relative track isolation $<$ 1 GeV.
|
| 516 |
|
| 517 |
\begin{figure}[hbt]
|
| 518 |
\begin{center}
|
| 519 |
\includegraphics[width=0.3\linewidth]{plots/el_tkiso_0j.pdf}%
|
| 520 |
\includegraphics[width=0.3\linewidth]{plots/mu_tkiso_0j.pdf}
|
| 521 |
\includegraphics[width=0.3\linewidth]{plots/el_tkiso_1j.pdf}%
|
| 522 |
\includegraphics[width=0.3\linewidth]{plots/mu_tkiso_1j.pdf}
|
| 523 |
\includegraphics[width=0.3\linewidth]{plots/el_tkiso_2j.pdf}%
|
| 524 |
\includegraphics[width=0.3\linewidth]{plots/mu_tkiso_2j.pdf}
|
| 525 |
\includegraphics[width=0.3\linewidth]{plots/el_tkiso_3j.pdf}%
|
| 526 |
\includegraphics[width=0.3\linewidth]{plots/mu_tkiso_3j.pdf}
|
| 527 |
\includegraphics[width=0.3\linewidth]{plots/el_tkiso_4j.pdf}%
|
| 528 |
\includegraphics[width=0.3\linewidth]{plots/mu_tkiso_4j.pdf}
|
| 529 |
\caption{
|
| 530 |
\label{fig:tnp} Comparison of the absolute track isolation in data vs. MC for electrons (left) and muons (right)
|
| 531 |
for events with the \njets\ requirement varied from \njets\ $\geq$ 0 to \njets\ $\geq$ 4.
|
| 532 |
}
|
| 533 |
\end{center}
|
| 534 |
\end{figure}
|
| 535 |
|
| 536 |
\clearpage
|
| 537 |
|
| 538 |
\begin{table}[!ht]
|
| 539 |
\begin{center}
|
| 540 |
\caption{\label{tab:isotrk} Comparison of the data vs. MC efficiencies to satisfy the indicated requirements
|
| 541 |
on the absolute track isolation, and the ratio of these two efficiencies. Results are indicated separately for electrons and muons and for various
|
| 542 |
jet multiplicity requirements.}
|
| 543 |
\begin{tabular}{l|c|c|c|c|c}
|
| 544 |
|
| 545 |
%Electrons:
|
| 546 |
%Selection : ((((((((((abs(tagAndProbeMass-91)<15)&&(qProbe*qTag<0))&&((eventSelection&1)==1))&&(abs(tag->eta())<2.1))&&(tag->pt()>30.0))&&(HLT_Ele27_WP80_tag > 0))&&(met<30))&&(nbl==0))&&((leptonSelection&8)==8))&&(probe->pt()>30))&&(drprobe<0.05)
|
| 547 |
%Total MC yields : 2497277
|
| 548 |
%Total DATA yields : 2649453
|
| 549 |
%Muons:
|
| 550 |
%Selection : ((((((((((abs(tagAndProbeMass-91)<15)&&(qProbe*qTag<0))&&((eventSelection&2)==2))&&(abs(tag->eta())<2.1))&&(tag->pt()>30.0))&&(HLT_IsoMu24_tag > 0))&&(met<30))&&(nbl==0))&&((leptonSelection&65536)==65536))&&(probe->pt()>30))&&(drprobe<0.05)
|
| 551 |
%Total MC yields : 3749863
|
| 552 |
%Total DATA yields : 4210022
|
| 553 |
%Info in <TCanvas::MakeDefCanvas>: created default TCanvas with name c1
|
| 554 |
%Info in <TCanvas::Print>: pdf file plots/nvtx.pdf has been created
|
| 555 |
|
| 556 |
\hline
|
| 557 |
\hline
|
| 558 |
e + $\geq$0 jets & $>$ 1 GeV & $>$ 2 GeV & $>$ 3 GeV & $>$ 4 GeV & $>$ 5 GeV \\
|
| 559 |
\hline
|
| 560 |
data & 0.098 $\pm$ 0.0002 & 0.036 $\pm$ 0.0001 & 0.016 $\pm$ 0.0001 & 0.009 $\pm$ 0.0001 & 0.006 $\pm$ 0.0000 \\
|
| 561 |
mc & 0.097 $\pm$ 0.0002 & 0.034 $\pm$ 0.0001 & 0.016 $\pm$ 0.0001 & 0.009 $\pm$ 0.0001 & 0.005 $\pm$ 0.0000 \\
|
| 562 |
data/mc & 1.00 $\pm$ 0.00 & 1.04 $\pm$ 0.00 & 1.04 $\pm$ 0.01 & 1.03 $\pm$ 0.01 & 1.02 $\pm$ 0.01 \\
|
| 563 |
|
| 564 |
\hline
|
| 565 |
\hline
|
| 566 |
$\mu$ + $\geq$0 jets & $>$ 1 GeV & $>$ 2 GeV & $>$ 3 GeV & $>$ 4 GeV & $>$ 5 GeV \\
|
| 567 |
\hline
|
| 568 |
data & 0.094 $\pm$ 0.0001 & 0.034 $\pm$ 0.0001 & 0.016 $\pm$ 0.0001 & 0.009 $\pm$ 0.0000 & 0.006 $\pm$ 0.0000 \\
|
| 569 |
mc & 0.093 $\pm$ 0.0001 & 0.033 $\pm$ 0.0001 & 0.015 $\pm$ 0.0001 & 0.009 $\pm$ 0.0000 & 0.006 $\pm$ 0.0000 \\
|
| 570 |
data/mc & 1.01 $\pm$ 0.00 & 1.03 $\pm$ 0.00 & 1.03 $\pm$ 0.01 & 1.03 $\pm$ 0.01 & 1.02 $\pm$ 0.01 \\
|
| 571 |
|
| 572 |
\hline
|
| 573 |
\hline
|
| 574 |
e + $\geq$1 jets & $>$ 1 GeV & $>$ 2 GeV & $>$ 3 GeV & $>$ 4 GeV & $>$ 5 GeV \\
|
| 575 |
\hline
|
| 576 |
data & 0.110 $\pm$ 0.0005 & 0.044 $\pm$ 0.0003 & 0.022 $\pm$ 0.0002 & 0.014 $\pm$ 0.0002 & 0.009 $\pm$ 0.0002 \\
|
| 577 |
mc & 0.110 $\pm$ 0.0005 & 0.042 $\pm$ 0.0003 & 0.021 $\pm$ 0.0002 & 0.013 $\pm$ 0.0002 & 0.009 $\pm$ 0.0001 \\
|
| 578 |
data/mc & 1.00 $\pm$ 0.01 & 1.04 $\pm$ 0.01 & 1.06 $\pm$ 0.02 & 1.08 $\pm$ 0.02 & 1.06 $\pm$ 0.03 \\
|
| 579 |
|
| 580 |
\hline
|
| 581 |
\hline
|
| 582 |
$\mu$ + $\geq$1 jets & $>$ 1 GeV & $>$ 2 GeV & $>$ 3 GeV & $>$ 4 GeV & $>$ 5 GeV \\
|
| 583 |
\hline
|
| 584 |
data & 0.106 $\pm$ 0.0004 & 0.043 $\pm$ 0.0003 & 0.023 $\pm$ 0.0002 & 0.014 $\pm$ 0.0002 & 0.010 $\pm$ 0.0001 \\
|
| 585 |
mc & 0.106 $\pm$ 0.0004 & 0.042 $\pm$ 0.0003 & 0.021 $\pm$ 0.0002 & 0.013 $\pm$ 0.0002 & 0.009 $\pm$ 0.0001 \\
|
| 586 |
data/mc & 1.00 $\pm$ 0.01 & 1.04 $\pm$ 0.01 & 1.06 $\pm$ 0.01 & 1.08 $\pm$ 0.02 & 1.07 $\pm$ 0.02 \\
|
| 587 |
|
| 588 |
\hline
|
| 589 |
\hline
|
| 590 |
e + $\geq$2 jets & $>$ 1 GeV & $>$ 2 GeV & $>$ 3 GeV & $>$ 4 GeV & $>$ 5 GeV \\
|
| 591 |
\hline
|
| 592 |
data & 0.117 $\pm$ 0.0012 & 0.050 $\pm$ 0.0008 & 0.026 $\pm$ 0.0006 & 0.017 $\pm$ 0.0005 & 0.012 $\pm$ 0.0004 \\
|
| 593 |
mc & 0.120 $\pm$ 0.0012 & 0.048 $\pm$ 0.0008 & 0.025 $\pm$ 0.0006 & 0.016 $\pm$ 0.0005 & 0.011 $\pm$ 0.0004 \\
|
| 594 |
data/mc & 0.97 $\pm$ 0.01 & 1.05 $\pm$ 0.02 & 1.05 $\pm$ 0.03 & 1.07 $\pm$ 0.04 & 1.07 $\pm$ 0.05 \\
|
| 595 |
|
| 596 |
\hline
|
| 597 |
\hline
|
| 598 |
$\mu$ + $\geq$2 jets & $>$ 1 GeV & $>$ 2 GeV & $>$ 3 GeV & $>$ 4 GeV & $>$ 5 GeV \\
|
| 599 |
\hline
|
| 600 |
data & 0.111 $\pm$ 0.0010 & 0.048 $\pm$ 0.0007 & 0.026 $\pm$ 0.0005 & 0.018 $\pm$ 0.0004 & 0.013 $\pm$ 0.0004 \\
|
| 601 |
mc & 0.115 $\pm$ 0.0010 & 0.048 $\pm$ 0.0006 & 0.025 $\pm$ 0.0005 & 0.016 $\pm$ 0.0004 & 0.012 $\pm$ 0.0003 \\
|
| 602 |
data/mc & 0.97 $\pm$ 0.01 & 1.01 $\pm$ 0.02 & 1.04 $\pm$ 0.03 & 1.09 $\pm$ 0.04 & 1.09 $\pm$ 0.04 \\
|
| 603 |
|
| 604 |
\hline
|
| 605 |
\hline
|
| 606 |
e + $\geq$3 jets & $>$ 1 GeV & $>$ 2 GeV & $>$ 3 GeV & $>$ 4 GeV & $>$ 5 GeV \\
|
| 607 |
\hline
|
| 608 |
data & 0.123 $\pm$ 0.0031 & 0.058 $\pm$ 0.0022 & 0.034 $\pm$ 0.0017 & 0.023 $\pm$ 0.0014 & 0.017 $\pm$ 0.0012 \\
|
| 609 |
mc & 0.131 $\pm$ 0.0030 & 0.055 $\pm$ 0.0020 & 0.030 $\pm$ 0.0015 & 0.020 $\pm$ 0.0013 & 0.015 $\pm$ 0.0011 \\
|
| 610 |
data/mc & 0.94 $\pm$ 0.03 & 1.06 $\pm$ 0.06 & 1.14 $\pm$ 0.08 & 1.16 $\pm$ 0.10 & 1.17 $\pm$ 0.12 \\
|
| 611 |
|
| 612 |
\hline
|
| 613 |
\hline
|
| 614 |
$\mu$ + $\geq$3 jets & $>$ 1 GeV & $>$ 2 GeV & $>$ 3 GeV & $>$ 4 GeV & $>$ 5 GeV \\
|
| 615 |
\hline
|
| 616 |
data & 0.121 $\pm$ 0.0025 & 0.055 $\pm$ 0.0018 & 0.033 $\pm$ 0.0014 & 0.022 $\pm$ 0.0011 & 0.017 $\pm$ 0.0010 \\
|
| 617 |
mc & 0.120 $\pm$ 0.0024 & 0.052 $\pm$ 0.0016 & 0.029 $\pm$ 0.0012 & 0.019 $\pm$ 0.0010 & 0.014 $\pm$ 0.0009 \\
|
| 618 |
data/mc & 1.01 $\pm$ 0.03 & 1.06 $\pm$ 0.05 & 1.14 $\pm$ 0.07 & 1.14 $\pm$ 0.08 & 1.16 $\pm$ 0.10 \\
|
| 619 |
|
| 620 |
\hline
|
| 621 |
\hline
|
| 622 |
e + $\geq$4 jets & $>$ 1 GeV & $>$ 2 GeV & $>$ 3 GeV & $>$ 4 GeV & $>$ 5 GeV \\
|
| 623 |
\hline
|
| 624 |
data & 0.129 $\pm$ 0.0080 & 0.070 $\pm$ 0.0061 & 0.044 $\pm$ 0.0049 & 0.031 $\pm$ 0.0042 & 0.021 $\pm$ 0.0034 \\
|
| 625 |
mc & 0.132 $\pm$ 0.0075 & 0.059 $\pm$ 0.0053 & 0.035 $\pm$ 0.0041 & 0.025 $\pm$ 0.0035 & 0.017 $\pm$ 0.0029 \\
|
| 626 |
data/mc & 0.98 $\pm$ 0.08 & 1.18 $\pm$ 0.15 & 1.26 $\pm$ 0.20 & 1.24 $\pm$ 0.24 & 1.18 $\pm$ 0.28 \\
|
| 627 |
|
| 628 |
\hline
|
| 629 |
\hline
|
| 630 |
$\mu$ + $\geq$4 jets & $>$ 1 GeV & $>$ 2 GeV & $>$ 3 GeV & $>$ 4 GeV & $>$ 5 GeV \\
|
| 631 |
\hline
|
| 632 |
data & 0.136 $\pm$ 0.0067 & 0.064 $\pm$ 0.0048 & 0.041 $\pm$ 0.0039 & 0.029 $\pm$ 0.0033 & 0.024 $\pm$ 0.0030 \\
|
| 633 |
mc & 0.130 $\pm$ 0.0063 & 0.065 $\pm$ 0.0046 & 0.035 $\pm$ 0.0034 & 0.020 $\pm$ 0.0026 & 0.013 $\pm$ 0.0022 \\
|
| 634 |
data/mc & 1.04 $\pm$ 0.07 & 0.99 $\pm$ 0.10 & 1.19 $\pm$ 0.16 & 1.47 $\pm$ 0.25 & 1.81 $\pm$ 0.37 \\
|
| 635 |
|
| 636 |
\hline
|
| 637 |
\hline
|
| 638 |
|
| 639 |
\end{tabular}
|
| 640 |
\end{center}
|
| 641 |
\end{table}
|
| 642 |
|
| 643 |
|
| 644 |
%Figure.~\ref{fig:reliso} compares the relative track isolation
|
| 645 |
%for events with a track with $\pt > 10~\GeV$ in addition to a selected
|
| 646 |
%muon for $\Z+4$ jet events and various \ttll\ components. The
|
| 647 |
%isolation distributions show significant differences, particularly
|
| 648 |
%between the leptons from a \W\ or \Z\ decay and the tracks arising
|
| 649 |
%from $\tau$ decays. As can also be seen in the figure, the \pt\
|
| 650 |
%distribution for the various categories of tracks is different, where
|
| 651 |
%the decay products from $\tau$s are significantly softer. Since the
|
| 652 |
%\pt\ enters the denominator of the isolation definition and hence
|
| 653 |
%alters the isolation variable...
|
| 654 |
|
| 655 |
%\begin{figure}[hbt]
|
| 656 |
% \begin{center}
|
| 657 |
% \includegraphics[width=0.5\linewidth]{plots/pfiso_njets4_log.png}%
|
| 658 |
% \includegraphics[width=0.5\linewidth]{plots/pfpt_njets4.png}
|
| 659 |
% \caption{
|
| 660 |
% \label{fig:reliso}%\protect
|
| 661 |
% Comparison of relative track isolation variable for PF cand probe in Z+jets and ttbar
|
| 662 |
% Z+Jets and ttbar dilepton have similar isolation distributions
|
| 663 |
% ttbar with leptonic and single prong taus tend to be less
|
| 664 |
% isolated. The difference in the isolation can be attributed
|
| 665 |
% to the different \pt\ distribution of the samples, since
|
| 666 |
% $\tau$ decay products tend to be softer than leptons arising
|
| 667 |
% from \W\ or \Z\ decays.}
|
| 668 |
% \end{center}
|
| 669 |
%\end{figure}
|
| 670 |
|
| 671 |
% \includegraphics[width=0.5\linewidth]{plots/pfabsiso_njets4_log.png}
|
| 672 |
|
| 673 |
|
| 674 |
%BEGIN SECTION TO WRITE OUT
|
| 675 |
%In detail, the procedure to correct the dilepton background is:
|
| 676 |
|
| 677 |
%\begin{itemize}
|
| 678 |
%\item Using tag-and-probe studies, we plot the distribution of {\bf absolute} track isolation for identified probe electrons
|
| 679 |
%and muons {\bf TODO: need to compare the e vs. $\mu$ track iso distributions, they might differ due to e$\to$e$\gamma$}.
|
| 680 |
%\item We verify that the distribution of absolute track isolation does not depend on the \pt\ of the probe lepton.
|
| 681 |
%This is due to the fact that this isolation is from ambient PU and jet activity in the event, which is uncorrelated with
|
| 682 |
%the lepton \pt {\bf TODO: verify this in data and MC.}.
|
| 683 |
%\item Our requirement is {\bf relative} track isolation $<$ 0.1. For a given \ttll\ MC event, we determine the \pt of the 2nd
|
| 684 |
%lepton and translate this to find the corresponding requirement on the {\bf absolute} track isolation, which is simply $0.1\times$\pt.
|
| 685 |
%\item We measure the efficiency to satisfy this requirement in data and MC, and define a scale-factor $SF_{\epsilon(trk)}$ which
|
| 686 |
%is the ratio of the data-to-MC efficiencies. This scale-factor is applied to the \ttll\ MC event.
|
| 687 |
%\item {\bf THING 2 we are unsure about: we can measure this SF for electrons and for muons, but we can't measure it for hadronic
|
| 688 |
%tracks from $\tau$ decays. Verena has showed that the absolute track isolation distribution in hadronic $\tau$ tracks is harder due
|
| 689 |
%to $\pi^0\to\gamma\gamma$ with $\gamma\to e^+e^-$.}
|
| 690 |
%\end{itemize}
|
| 691 |
%END SECTION TO WRITE OUT
|
| 692 |
|
| 693 |
|
| 694 |
{\bf fix me: What you have written in the next paragraph does not explain how $\epsilon_{fake}$ is measured.
|
| 695 |
Why not measure $\epsilon_{fake}$ in the b-veto region?}
|
| 696 |
|
| 697 |
%A measurement of the $\epsilon_{fake}$ in data is non-trivial. However, it is
|
| 698 |
%possible to correct for differences in the $\epsilon_{fake}$ between data and MC by
|
| 699 |
%applying an additional scale factor for the single lepton background
|
| 700 |
%alone, using the sample in the \mt\ peak region. This scale factor is determined after applying the isolated track
|
| 701 |
%veto and after subtracting the \ttll\ component, corrected for the
|
| 702 |
%isolation efficiency derived previously.
|
| 703 |
%As shown in Figure~\ref{fig:vetoeffcomp}, the efficiency for selecting an
|
| 704 |
%isolated track in single lepton events is independent of \mt\, so the use of
|
| 705 |
%an overall scale factor is justified to estimate the contribution in
|
| 706 |
%the \mt\ tail.
|
| 707 |
%
|
| 708 |
%\begin{figure}[hbt]
|
| 709 |
% \begin{center}
|
| 710 |
% \includegraphics[width=0.5\linewidth]{plots/vetoeff_comp.png}
|
| 711 |
% \caption{
|
| 712 |
% \label{fig:vetoeffcomp}%\protect
|
| 713 |
% Efficiency for selecting an isolated track comparing
|
| 714 |
% single lepton \ttlj\ and dilepton \ttll\ events in MC and
|
| 715 |
% data as a function of \mt. The
|
| 716 |
% efficiencies in \ttlj\ and \ttll\ exhibit no dependence on
|
| 717 |
% \mt\, while the data ranges between the two. This behavior
|
| 718 |
% is expected since the low \mt\ region is predominantly \ttlj, while the
|
| 719 |
% high \mt\ region contains mostly \ttll\ events.}
|
| 720 |
% \end{center}
|
| 721 |
%\end{figure}
|
| 722 |
|
| 723 |
\subsection{Summary of uncertainties}
|
| 724 |
\label{sec:bgunc-bottomline}.
|
| 725 |
|
| 726 |
THIS NEEDS TO BE WRITTEN
|
