| 1 |
< |
\section{Overview and Analysis Strategy} |
| 1 |
> |
\section{Overview and Strategy for Background Determination} |
| 2 |
|
\label{sec:overview} |
| 3 |
|
|
| 4 |
– |
[REVISE --- MAKE SURE EVERYTHING IS CORRECT] |
| 5 |
– |
|
| 4 |
|
We are searching for a $t\bar{t}\chi^0\chi^0$ or $W b W \bar{b} \chi^0 \chi^0$ final state |
| 5 |
|
(after top decay in the first mode, the final states are actually the same). So to first order |
| 6 |
|
this is ``$t\bar{t} +$ extra \met''. |
| 7 |
|
|
| 8 |
|
We work in the $\ell +$ jets final state, where the main background is $t\bar{t}$. We look for |
| 9 |
|
\met\ inconsistent with $W \to \ell \nu$. We do this by concentrating on the $\ell \nu$ transverse |
| 10 |
< |
mass ($M_T$), since except for resolution effects, $M_T < M_W$ for $W \to \ell \nu$. Thus, the |
| 10 |
> |
mass ($M_T$), since except for resolution and W-off-shell effects, $M_T < M_W$ for $W \to \ell \nu$. Thus, the |
| 11 |
|
initial analysis is simply a counting experiment in the tail of the $M_T$ distribution. |
| 12 |
|
|
| 13 |
|
The event selection is one-and-only-one high \pt\ isolated lepton, four or more jets, and |
| 14 |
< |
some moderate \met\ cut. At least one of the jets has to be btagged to reduce $W+$ jets. |
| 14 |
> |
an \met\ cut. At least one of the jets has to be btagged to reduce $W+$ jets. |
| 15 |
|
The event sample is then dominated by $t\bar{t}$, but there are also contributions from $W+$ jets, |
| 16 |
< |
single top, dibosons, etc. |
| 16 |
> |
single top, dibosons, as well as rare SM processes such as $ttW$. |
| 17 |
|
|
| 18 |
< |
In order to be sensitive to $\widetilde{t}\widetilde{t}$ production, the background in the $M_T$ |
| 19 |
< |
tail has to be controlled at the level of 10\% or better. So this is (almost) a precision measurement. |
| 18 |
> |
% In order to be sensitive to $\widetilde{t}\widetilde{t}$ production, the background in the $M_T$ |
| 19 |
> |
% tail has to be controlled at the level of 10\% or better. So this is (almost) a precision measurement. |
| 20 |
|
|
| 21 |
|
The $t\bar{t}$ events in the $M_T$ tail can be broken up into two categories: |
| 22 |
|
(i) $t\bar{t} \to \ell $+ jets and (ii) $t\bar{t} \to \ell^+ \ell^-$ where one of the two |
| 23 |
|
leptons is not found by the second-lepton-veto (here the second lepton can be a hadronically |
| 24 |
|
decaying $\tau$). |
| 25 |
< |
For a reasonable $M_T$ cut, say $M_T >$ 150 GeV, the dilepton background is of order 80\% of |
| 25 |
> |
For a reasonable $M_T$ cut, say $M_T >$ 150 GeV, the dilepton background is approximately 80\% of |
| 26 |
|
the total. This is because in dileptons there are two neutrinos from $W$ decay, thus $M_T$ |
| 27 |
|
is not bounded by $M_W$. This is a very important point: while it is true that we are looking in |
| 28 |
|
the tail of $M_T$, the bulk of the background events end up there not because of some exotic |
| 29 |
|
\met\ reconstruction failure, but because of well understood physics processes. This means that |
| 30 |
< |
the background estimate can be taken from Monte Carlo (MC), after carefully accounting for possible |
| 31 |
< |
data/MC differences. Sophisticated fully ``data driven'' techniques are not really needed. |
| 30 |
> |
the background estimate can be taken from Monte Carlo (MC) |
| 31 |
> |
after carefully accounting for possible |
| 32 |
> |
data/MC differences. |
| 33 |
> |
|
| 34 |
> |
The search is performed in a number of Signal Regions (SRs) defined |
| 35 |
> |
by minimum requirements on \met\ and $M_T$. The SRs |
| 36 |
> |
are defined in Section~\ref{sec:SR}. |
| 37 |
> |
|
| 38 |
> |
In Section~\ref{sec:CR} we will describe the analysis of various Control Regions |
| 39 |
> |
(CRs) that are used to test the Monte Carlo model and, if necessary, |
| 40 |
> |
to extract data/MC scale factors. In this section we give a |
| 41 |
> |
general description of the procedure. The details of how the |
| 42 |
> |
final background prediction is assembled are given in Section~\ref{sec:bkg_pred}. |
| 43 |
> |
|
| 44 |
|
|
| 45 |
< |
Another important point is that in order to minimize systematic uncertainties, the MC background |
| 46 |
< |
predictions are always normalized to the bulk of the $t\bar{t}$ data, ie, events passing all of the |
| 45 |
> |
|
| 46 |
> |
% Sophisticated fully ``data driven'' techniques are not really needed. |
| 47 |
> |
|
| 48 |
> |
One general point is that in order to minimize systematic uncertainties, the MC background |
| 49 |
> |
predictions are whenever possible normalized to the bulk of the $t\bar{t}$ data, ie, events passing all of the |
| 50 |
|
requirements but with $M_T \approx 80$ GeV. |
| 51 |
< |
This removes uncertainties |
| 51 |
> |
This (mostly) removes uncertainties |
| 52 |
|
due to $\sigma(t\bar{t})$, lepton ID, trigger efficiency, luminosity, etc. |
| 53 |
|
|
| 54 |
< |
The $\ell +$ jets background, which is dominated by |
| 55 |
< |
$t\bar{t} \to \ell $+ jets, but also includes some $W +$ jets as well as single top, |
| 56 |
< |
is estimated as follows: |
| 57 |
< |
\begin{enumerate} |
| 58 |
< |
\item We select a control sample of events passing all cuts, but anti-btagged, i.e. b-vetoed. This |
| 59 |
< |
sample is now dominated by $W +$ jets. The sample is used to understand the |
| 60 |
< |
$M_T$ tail in $\ell +$ jets processes. |
| 61 |
< |
\item In MC we measure the ratio of the number of $\ell +$ jets events in the $M_T$ tail to |
| 62 |
< |
the number of events with $M_T \approx$ 80 GeV. This ratio turns out to be pretty much the |
| 63 |
< |
same for all sources of $\ell +$ jets. |
| 64 |
< |
\item In data we measure the same ratio but after correcting for the $t\bar{t} \to$ dilepton |
| 65 |
< |
contribution, as well as dibosons etc. The dilepton contribution is taken from MC after |
| 66 |
< |
the correction described below. |
| 67 |
< |
\item We compare the two ratios, as well as the shapes of the data and MC $M_T$ distributions. |
| 68 |
< |
If they do not agree, we try to figure out why and fix it. If they agree well enough, we define a |
| 69 |
< |
data-to-MC scale factor (SF) which is the ratio of the ratios defined in step 2 and 3, keeping track of the |
| 70 |
< |
uncertainty. |
| 71 |
< |
\item We next perform the full selection in $t\bar{t} \to \ell +$ jets MC, and measure this ratio |
| 72 |
< |
again (which should be the same as that in step 2). |
| 60 |
< |
\item |
| 61 |
< |
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, |
| 62 |
< |
and multiply this count by the ratio from step 5 times the data/MC scale factor from step 4. |
| 63 |
< |
%We count the events with $M_T \approx 80$ GeV, we |
| 64 |
< |
%subtract off the dilepton contribution, we multiply the subtracted event count by the ratio from step 5 (or from |
| 65 |
< |
%step 2), and also by the data/MC SF from step 4. |
| 66 |
< |
The result is the prediction for the $\ell +$ jets BG in the $M_T$ tail. |
| 67 |
< |
\end{enumerate} |
| 54 |
> |
\subsection{$\ell +$ jets background} |
| 55 |
> |
\label{sec:ljbg-general} |
| 56 |
> |
|
| 57 |
> |
The $\ell +$ jets background is dominated by |
| 58 |
> |
$t\bar{t} \to \ell $+ jets, but also includes some $W +$ jets as well as single top. |
| 59 |
> |
The MC input used in the background estimation |
| 60 |
> |
is the ratio of the number of events with $M_T$ in the signal region |
| 61 |
> |
to the number of events with $M_T \approx 80$ GeV. |
| 62 |
> |
This ratio is (possibly) corrected by a data/MC scale factor obtained |
| 63 |
> |
from a study of CRs, as outlined below. |
| 64 |
> |
|
| 65 |
> |
Note that the ratio described above is actually different for |
| 66 |
> |
$t\bar{t}$/single top and $W +$ jets. This is because in $W$ events |
| 67 |
> |
there is a significant contribution to the $M_T$ tail from very off-shell |
| 68 |
> |
$W$. |
| 69 |
> |
This contribution is much smaller in top events because $M(\ell \nu)$ |
| 70 |
> |
cannot excees $M_{top}-M_b$. Therefore the large \mt\ tail in |
| 71 |
> |
$t\bar{t}$/single top is dominated by jet resolution effects, |
| 72 |
> |
while for \wjets\ events the large \mt\ tail is dominated by off-shell W production. |
| 73 |
|
|
| 69 |
– |
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. |
| 74 |
|
|
| 75 |
< |
To suppress dilepton backgrounds, we veto events with an isolated track of \pt $>$ 10 GeV. |
| 75 |
> |
|
| 76 |
> |
For $W +$ jets the ability of the Monte Carlo to model this ratio |
| 77 |
> |
($R_{wjet}$) is tested in a sample of $\ell +$ jets enriched in |
| 78 |
> |
$W +$ jets by the application of a b-veto. |
| 79 |
> |
The equivalent ratio for top events ($R_{top}$) is validated in a sample of well |
| 80 |
> |
identified $Z \to \ell \ell$ with one lepton added to the \met\ |
| 81 |
> |
calculation. |
| 82 |
> |
This sample is well suited to testing the resolution effects on |
| 83 |
> |
the $M_T$ tail, since off-shell effects are eliminated by the $Z$-mass |
| 84 |
> |
requirement. |
| 85 |
> |
|
| 86 |
> |
Note that the fact that the ratios are different for |
| 87 |
> |
$t\bar{t}$/single top and $W +$ jets introduces a systematic |
| 88 |
> |
uncertainty in the background calculation because one needs |
| 89 |
> |
to know the relative fractions of these two components in |
| 90 |
> |
$M_T \approx 80$ GeV lepton $+$ jets sample. |
| 91 |
> |
|
| 92 |
> |
|
| 93 |
> |
\subsection{Dilepton background} |
| 94 |
> |
\label{sec:dil-general} |
| 95 |
> |
|
| 96 |
> |
To suppress dilepton backgrounds, we veto events with an isolated track of \pt $>$ 10 GeV (see Sec.~\ref{sec:tkveto} for details). |
| 97 |
|
Being the common feature for electron, muon, and one-prong |
| 98 |
|
tau decays, this veto is highly efficient for rejecting |
| 99 |
|
$t\bar{t}$ to dilepton events. The remaining dilepton background can be classified into the following categories: |
| 120 |
|
%Monte Carlo studies indicate that there is no dominant contribution: it is ``a little bit of this, |
| 121 |
|
%and a little bit of that''. |
| 122 |
|
|
| 123 |
< |
The last category includes 3-prong tau decays as well as electrons and muons from W decay that fail the isolation requirement. |
| 124 |
< |
Monte Carlo studies indicate that these three components populate the $M_T$ tail in the proportions of roughly 6\%, 47\%, 47\%. |
| 123 |
> |
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 |
| 124 |
> |
that fail the isolation requirement. |
| 125 |
> |
% HOOBERMAN: commenting out for now |
| 126 |
> |
%Monte Carlo studies indicate that these three components populate the $M_T$ tail in the proportions of roughly 6\%, 47\%, 47\%. |
| 127 |
|
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. |
| 128 |
|
|
| 129 |
|
The high $M_T$ dilepton backgrounds come from MC, but their rate is normalized to the |
| 130 |
< |
$M_T \approx 80$ GeV peak. In order to perform this normalization in data, the $W +$ jets |
| 131 |
< |
events in the $M_T$ peak have to be subtracted off. This introduces a systematic uncertainty. |
| 130 |
> |
$M_T \approx 80$ GeV peak. In order to perform this normalization in |
| 131 |
> |
data, the non-$t\bar{t}$ (eg, $W +$ jets) |
| 132 |
> |
events in the $M_T$ peak have to be subtracted off. This also introduces a systematic uncertainty. |
| 133 |
|
|
| 134 |
|
There are two types of effects that can influence the MC dilepton prediction: physics effects |
| 135 |
|
and instrumental effects. We discuss these next, starting from physics. |
| 156 |
|
|
| 157 |
|
The main instrumental effect is associated with the efficiency of the isolated track veto. |
| 158 |
|
We use tag-and-probe to compare the isolated track veto performance in $Z + 4$ jet data and |
| 159 |
< |
MC, and we extract corrections if necessary. Note that the performance of the isolated track veto |
| 159 |
> |
MC. Note that the performance of the isolated track veto |
| 160 |
|
is not exactly the same on $e/\mu$ and on one prong hadronic tau decays. This is because |
| 161 |
|
the pions from one-prong taus are often accompanied by $\pi^0$'s that can then result in extra |
| 162 |
< |
tracks due to phton conversions. We let the simulation take care of that. |
| 162 |
> |
tracks due to photon conversions. We let the simulation take care of that. |
| 163 |
|
Note that JES uncertainties are effectively ``calibrated away'' by the $N_{jet}$ rescaling described above. |
| 164 |
|
|
| 165 |
|
%Similarly, at the moment |
| 169 |
|
%The sample of events failing the last isolated track veto is an important control sample to |
| 170 |
|
%check that we are doing the right thing. |
| 171 |
|
|
| 172 |
+ |
\subsection{Other backgrounds} |
| 173 |
+ |
\label{sec:other-general} |
| 174 |
+ |
Other backgrounds are $tW$, $ttV$, dibosons, tribosons, Drell Yan. |
| 175 |
+ |
These are small. They are taken from MC with appropriate scale |
| 176 |
+ |
factors for trigger efficiency, and reweighting to match the distribution of reconstructed primary vertices in data. |
| 177 |
+ |
|
| 178 |
+ |
|
| 179 |
+ |
\subsection{Future improvements} |
| 180 |
+ |
\label{sec:improvements-general} |
| 181 |
|
Finally, there are possible improvements to this basic analysis strategy that can be added in the future: |
| 182 |
|
\begin{itemize} |
| 183 |
|
\item Move from counting experiment to shape analysis. But first, we need to get the counting |
