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\section{Overview and Analysis Strategy} |
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\section{Overview and Strategy for Background Determination} |
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\label{sec:overview} |
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[REVISE --- MAKE SURE EVERYTHING IS CORRECT] |
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We are searching for a $t\bar{t}\chi^0\chi^0$ or $W b W \bar{b} \chi^0 \chi^0$ final state |
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(after top decay in the first mode, the final states are actually the same). So to first order |
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this is ``$t\bar{t} +$ extra \met''. |
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We work in the $\ell +$ jets final state, where the main background is $t\bar{t}$. We look for |
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\met\ inconsistent with $W \to \ell \nu$. We do this by concentrating on the $\ell \nu$ transverse |
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mass ($M_T$), since except for resolution effects, $M_T < M_W$ for $W \to \ell \nu$. Thus, the |
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mass ($M_T$), since except for resolution and W-off-shell effects, $M_T < M_W$ for $W \to \ell \nu$. Thus, the |
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initial analysis is simply a counting experiment in the tail of the $M_T$ distribution. |
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The event selection is one-and-only-one high \pt\ isolated lepton, four or more jets, and |
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some moderate \met\ cut. At least one of the jets has to be btagged to reduce $W+$ jets. |
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an \met\ cut. At least one of the jets has to be b tagged to reduce $W+$ jets. |
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The event sample is then dominated by $t\bar{t}$, but there are also contributions from $W+$ jets, |
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single top, dibosons, etc. |
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single top, dibosons, as well as rare SM processes such as $ttW$. |
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In order to be sensitive to $\widetilde{t}\widetilde{t}$ production, the background in the $M_T$ |
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tail has to be controlled at the level of 10\% or better. So this is (almost) a precision measurement. |
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% In order to be sensitive to $\widetilde{t}\widetilde{t}$ production, the background in the $M_T$ |
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% tail has to be controlled at the level of 10\% or better. So this is (almost) a precision measurement. |
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The $t\bar{t}$ events in the $M_T$ tail can be broken up into two categories: |
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(i) $t\bar{t} \to \ell $+ jets and (ii) $t\bar{t} \to \ell^+ \ell^-$ where one of the two |
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(i) $t\bar{t} \to \ell $+ jets, and (ii) $t\bar{t} \to \ell^+ \ell^-$ where one of the two |
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leptons is not found by the second-lepton-veto (here the second lepton can be a hadronically |
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decaying $\tau$). |
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For a reasonable $M_T$ cut, say $M_T >$ 150 GeV, the dilepton background is of order 80\% of |
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For a reasonable $M_T$ cut, say $M_T >$ 150 GeV, the dilepton background is approximately 70\% of |
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the total. This is because in dileptons there are two neutrinos from $W$ decay, thus $M_T$ |
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is not bounded by $M_W$. This is a very important point: while it is true that we are looking in |
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the tail of $M_T$, the bulk of the background events end up there not because of some exotic |
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\met\ reconstruction failure, but because of well understood physics processes. This means that |
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the background estimate can be taken from Monte Carlo (MC), after carefully accounting for possible |
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data/MC differences. Sophisticated fully ``data driven'' techniques are not really needed. |
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the background estimate can be taken from Monte Carlo (MC) |
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after carefully accounting for possible |
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data/MC differences. |
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The search is performed in a number of Signal Regions (SRs) defined |
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by minimum requirements on \met\ and $M_T$. The SRs |
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are defined in Section~\ref{sec:SR}. |
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In Section~\ref{sec:CR} we will describe the analysis of various Control Regions |
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(CRs) that are used to test the Monte Carlo model and, if necessary, |
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to extract data/MC scale factors. In this section we give a |
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general description of the procedure. The details of how the |
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final background prediction is assembled are given in Section~\ref{sec:bkg_pred}. |
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Another important point is that in order to minimize systematic uncertainties, the MC background |
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predictions are always normalized to the bulk of the $t\bar{t}$ data, ie, events passing all of the |
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% Sophisticated fully ``data driven'' techniques are not really needed. |
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One general point is that in order to minimize systematic uncertainties, the MC background |
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predictions are whenever possible normalized to the bulk of the $t\bar{t}$ data, i.e., events passing all of the |
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requirements but with $M_T \approx 80$ GeV. |
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This removes uncertainties |
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This (mostly) removes uncertainties |
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due to $\sigma(t\bar{t})$, lepton ID, trigger efficiency, luminosity, etc. |
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The $\ell +$ jets background, which is dominated by |
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$t\bar{t} \to \ell $+ jets, but also includes some $W +$ jets as well as single top, |
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is estimated as follows: |
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\begin{enumerate} |
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\item We select a control sample of events passing all cuts, but anti-btagged, i.e. b-vetoed. This |
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sample is now dominated by $W +$ jets. The sample is used to understand the |
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$M_T$ tail in $\ell +$ jets processes. |
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\item In MC we measure the ratio of the number of $\ell +$ jets events in the $M_T$ tail to |
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the number of events with $M_T \approx$ 80 GeV. This ratio turns out to be pretty much the |
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same for all sources of $\ell +$ jets. |
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\item In data we measure the same ratio but after correcting for the $t\bar{t} \to$ dilepton |
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contribution, as well as dibosons etc. The dilepton contribution is taken from MC after |
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the correction described below. |
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\item We compare the two ratios, as well as the shapes of the data and MC $M_T$ distributions. |
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If they do not agree, we try to figure out why and fix it. If they agree well enough, we define a |
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data-to-MC scale factor (SF) which is the ratio of the ratios defined in step 2 and 3, keeping track of the |
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uncertainty. |
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\item We next perform the full selection in $t\bar{t} \to \ell +$ jets MC, and measure this ratio |
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again (which should be the same as that in step 2). |
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\item |
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We perform the full selection in data. We count the number of events with $M_T \approx 80$ GeV, after subtracting off the dilepton contribution, |
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and multiply this count by the ratio from step 5 times the data/MC scale factor from step 4. |
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%We count the events with $M_T \approx 80$ GeV, we |
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%subtract off the dilepton contribution, we multiply the subtracted event count by the ratio from step 5 (or from |
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%step 2), and also by the data/MC SF from step 4. |
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The result is the prediction for the $\ell +$ jets BG in the $M_T$ tail. |
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\end{enumerate} |
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\subsection{$\ell +$ jets background} |
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\label{sec:ljbg-general} |
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The $\ell +$ jets background is dominated by |
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$t\bar{t} \to \ell $+ jets, but also includes some $W +$ jets as well as single top. |
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The MC input used in the background estimation |
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is the ratio of the number of events with $M_T$ in the signal region |
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to the number of events with $M_T \approx 80$ GeV. |
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This ratio is (possibly) corrected by a data/MC scale factor obtained |
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from a study of CRs, as outlined below. |
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Note that the ratio described above is actually different for |
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$t\bar{t}$/single top and $W +$ jets. This is because in $W$ events |
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there is a significant contribution to the $M_T$ tail from very off-shell |
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$W$s. |
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This contribution is much smaller in top events because $M(\ell \nu)$ |
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cannot exceed $M_{top}-M_b$. Therefore the large \mt\ tail in |
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$t\bar{t}$/single top is dominated by jet resolution effects, |
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while for \wjets\ events the large \mt\ tail is dominated by off-shell W production. |
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Steps 1-4 above are all measurements on the b-vetoed samples in data and/or MC. Steps 5 and 6 are performed on the b-tagged sample. |
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To suppress dilepton backgrounds, we veto events with an isolated track of \pt $>$ 10 GeV. |
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For $W +$ jets the ability of the Monte Carlo to model this ratio |
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($R_{wjet}$) is validated in a sample of $\ell +$ jets enriched in |
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$W +$ jets by the application of a b-veto. |
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The equivalent ratio for top events ($R_{top}$) is tested in a sample of well |
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identified $Z \to \ell \ell$ with one lepton added to the \met\ |
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calculation. |
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This sample is well suited to testing the resolution effects on |
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the $M_T$ tail, since off-shell effects are eliminated by the $Z$-mass |
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requirement. |
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Note that the fact that the ratios are different for |
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$t\bar{t}$/single top and $W +$ jets introduces a systematic |
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uncertainty in the background calculation because one needs |
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to know the relative fractions of these two components in |
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the $M_T \approx 80$ GeV lepton $+$ jets sample. |
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\subsection{Dilepton background} |
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\label{sec:dil-general} |
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To suppress dilepton backgrounds, we veto events with an isolated track of \pt\ $>$ 10 GeV (see Sec.~\ref{sec:tkveto} for details). |
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Being the common feature for electron, muon, and one-prong |
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tau decays, this veto is highly efficient for rejecting |
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$t\bar{t}$ to dilepton events. The remaining dilepton background can be classified into the following categories: |
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%\item 1-prong hadronic tau decay |
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%\item $e$ or $\mu$ possibly from $\tau$ decay |
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%\end{itemize} |
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%We have currently no veto against 3-prong taus. For the other two categories, we explicitely |
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%We have currently no veto against 3-prong taus. For the other two categories, we explicitly |
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%veto events %with additional electrons and muons above 10 GeV , and we veto events |
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%with an isolated track of \pt\ $>$ 10 GeV. This rejects electrons and muons (either from $W\to e/\mu$ or |
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%$W\to \tau\to e/\mu$) and 1-prong tau decays. |
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%(it turns out that the explicit $e$ or $\mu$ veto is redundant with the isolated track veto). |
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%Therefore the latter two categories can be broken into |
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\begin{itemize} |
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\item lepton is out of acceptance $(|\eta| > 2.50)$ |
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\item lepton is out of acceptance $(|\eta| > 2.5)$ |
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\item lepton has \pt\ $<$ 10 GeV, and is inside the acceptance |
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\item lepton has \pt\ $>$ 10 GeV, is inside the acceptance, but survives the additional isolated track veto |
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\end{itemize} |
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%Monte Carlo studies indicate that there is no dominant contribution: it is ``a little bit of this, |
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%and a little bit of that''. |
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The last category includes 3-prong tau decays as well as electrons and muons from W decay that fail the isolation requirement. |
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Monte Carlo studies indicate that these three components populate the $M_T$ tail in the proportions of roughly 6\%, 47\%, 47\%. |
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We note that at present we do not attempt to veto 3-prong tau decays as they are only 16\% of the total dilepton background according to the MC. |
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The high $M_T$ dilepton backgrounds come from MC, but their rate is normalized to the |
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$M_T \approx 80$ GeV peak. In order to perform this normalization in data, the $W +$ jets |
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events in the $M_T$ peak have to be subtracted off. This introduces a systematic uncertainty. |
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The last category includes 1-prong and 3-prong hadronic tau decays, as well as electrons and muons either from direct W decay or via W$\to\tau\to\ell$ decay |
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that fail the isolation requirement. |
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% HOOBERMAN: commenting out for now |
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%Monte Carlo studies indicate that these three components populate the $M_T$ tail in the proportions of roughly 6\%, 47\%, 47\%. |
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We note that at present we do not attempt to veto 3-prong tau decays as they are about 15\% of the total dilepton background according to the MC. |
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The high $M_T$ dilepton background predictions come from MC, but their rate is normalized to the |
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$M_T \approx 80$ GeV peak. In order to perform this normalization in |
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data, the rare background events in the $M_T$ peak are subtracted off. This also introduces a systematic uncertainty. |
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There are two types of effects that can influence the MC dilepton prediction: physics effects |
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and instrumental effects. We discuss these next, starting from physics. |
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First of all, many of our $t\bar{t}$ MC samples (eg: MadGraph) have |
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First of all, many of our $t\bar{t}$ MC samples (e.g. MadGraph) have |
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BR$(W \to \ell \nu)=\frac{1}{9} = 0.1111$. |
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PDG says BR$(W \to \ell \nu) = 0.1080 \pm 0.0009$. This difference matters, so the $t\bar{t}$ MC |
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must be corrected to account for this. |
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Second, our selection is $\ell +$ 4 or more jets. A dilepton event passes the selection only if there are |
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Second, our selection is $\ell +4$ or more jets. A dilepton event passes the selection only if there are |
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two additional jets from ISR, or one jet from ISR and one jet which is reconstructed from the |
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unidentified lepton, {\it e.g.}, a three-prong tau. Therefore, all MC dilepton $t\bar{t}$ samples used |
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in the analysis must have their jet multiplicity corrected (if necessary) to agree with what is |
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seen in $t\bar{t}$ data. We use a data control sample of well identified dilepton events with |
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\met\ and at least two jets as a template to ``adjust'' the $N_{jet}$ distribution of the $t\bar{t} \to$ |
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\met\ and at least one jet (including at least one b-tag) as a template to ``adjust'' the $N_{jet}$ distribution of the $t\bar{t} \to$ |
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dileptons MC samples. |
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The final physics effect has to do with the modeling of $t\bar{t}$ production and decay. Different |
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uncertainty associated with the $t\bar{t}$ generator modeling. |
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The main instrumental effect is associated with the efficiency of the isolated track veto. |
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We use tag-and-probe to compare the isolated track veto performance in $Z + 4$ jet data and |
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MC, and we extract corrections if necessary. Note that the performance of the isolated track veto |
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We use tag-and-probe to compare the isolated track veto performance in $Z + 4$ jets data and |
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MC. Note that the performance of the isolated track veto |
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is not exactly the same on $e/\mu$ and on one prong hadronic tau decays. This is because |
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the pions from one-prong taus are often accompanied by $\pi^0$'s that can then result in extra |
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tracks due to phton conversions. We let the simulation take care of that. |
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tracks due to photon conversions. We let the simulation take care of that. |
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Note that JES uncertainties are effectively ``calibrated away'' by the $N_{jet}$ rescaling described above. |
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%Similarly, at the moment |
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%The sample of events failing the last isolated track veto is an important control sample to |
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%check that we are doing the right thing. |
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\subsection{Other backgrounds} |
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\label{sec:other-general} |
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Other backgrounds are $tW$, $ttV$, dibosons, tribosons, and Drell Yan. |
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These are small. They are taken from MC with appropriate scale |
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factors for trigger efficiency, and reweighting to match the distribution of reconstructed primary vertices in data. |
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\subsection{Future improvements} |
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\label{sec:improvements-general} |
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Finally, there are possible improvements to this basic analysis strategy that can be added in the future: |
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\begin{itemize} |
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\item Move from counting experiment to shape analysis. But first, we need to get the counting |
