| 1 |
|
\section{Overview and Analysis Strategy} |
| 2 |
|
\label{sec:overview} |
| 3 |
|
|
| 4 |
< |
We are searching for a $t\bar{t}\chi^0\chi^0$ or $W \ell b W \ell \bar{b} \chi^0 \chi^0$ final state |
| 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 |
| 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 |
| 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 $P_T$ 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. |
| 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. |
| 15 |
|
The event sample is then dominated by $t\bar{t}$, but there are also contributions from $W+$ jets, |
| 16 |
|
single top, dibosons, etc. |
| 17 |
|
|
| 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 |
| 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. |
| 32 |
|
|
| 40 |
|
$t\bar{t} \to \ell $+ jets, but also includes some $W +$ jets as well as single top, |
| 41 |
|
is estimated as follows: |
| 42 |
|
\begin{enumerate} |
| 43 |
< |
\item We select a control sample of events passing all cuts, but anti-btagged. This is |
| 43 |
> |
\item We select a control sample of events passing all cuts, but anti-btagged, i.e. b-vetoed. This |
| 44 |
|
sample is now dominated by $W +$ jets. The sample is used to understand the |
| 45 |
|
$M_T$ tail in $\ell +$ jets processes. |
| 46 |
|
\item In MC we measure the ratio of the number of $\ell +$ jets events in the $M_T$ tail to |
| 51 |
|
the correction described below. |
| 52 |
|
\item We compare the two ratios, as well as the shapes of the data and MC $M_T$ distributions. |
| 53 |
|
If they do not agree, we try to figure out why and fix it. If they agree well enough, we define a |
| 54 |
< |
data MC scale factor (SF) which is the ratio of the ratios defined in step 2 and 3, keeping track of the |
| 54 |
> |
data-to-MC scale factor (SF) which is the ratio of the ratios defined in step 2 and 3, keeping track of the |
| 55 |
|
uncertainty. |
| 56 |
|
\item We next perform the full selection in $t\bar{t} \to \ell +$ jets MC, and measure this ratio |
| 57 |
|
again (which should be the same as that in step 2). |
| 58 |
< |
\item We perform the full selection in data. We count the events with $M_T \approx 80$ GeV, we |
| 59 |
< |
subtract off the dilepton contribution, we multiply the subtracted event count by the ratio from step 5 (or from |
| 60 |
< |
step 2), and also by the data/MC SF from step 4. The result is the prediction for the $\ell +$ jets BG in |
| 61 |
< |
the $M_T$ tail. |
| 58 |
> |
\item |
| 59 |
> |
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, |
| 60 |
> |
and multiply this count by the ratio from step 5 times the data/MC scale factor from step 4. |
| 61 |
> |
%We count the events with $M_T \approx 80$ GeV, we |
| 62 |
> |
%subtract off the dilepton contribution, we multiply the subtracted event count by the ratio from step 5 (or from |
| 63 |
> |
%step 2), and also by the data/MC SF from step 4. |
| 64 |
> |
The result is the prediction for the $\ell +$ jets BG in the $M_T$ tail. |
| 65 |
|
\end{enumerate} |
| 66 |
|
|
| 67 |
< |
The dilepton background can be broken up into many components depending |
| 68 |
< |
on the characteristics of the 2nd (undetected) lepton |
| 69 |
< |
\begin{itemize} |
| 70 |
< |
\item 3-prong hadronic tau decay |
| 71 |
< |
\item 1-prong hadronic tau decay |
| 72 |
< |
\item $e$ or $\mu$ possibly from $\tau$ decay |
| 73 |
< |
\end{itemize} |
| 74 |
< |
We have currently no veto against 3-prong taus. For the other two categories, we explicitely |
| 75 |
< |
veto events with additional electrons and muons above 10 GeV , and |
| 76 |
< |
we veto events with an isolated track of $P_T > 10$ GeV. This also rejects 1-prong taus |
| 77 |
< |
(it turns out that the explicit $e$ or $\mu$ veto is redundant with the isolated track veto). |
| 78 |
< |
Therefore the latter two categories can be broken into |
| 67 |
> |
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. |
| 68 |
> |
|
| 69 |
> |
To suppress dilepton backgrounds, we veto events with an isolated track of \pt $>$ 10 GeV. |
| 70 |
> |
Being the common feature for electron, muon, and one-prong |
| 71 |
> |
tau decays, this veto is highly efficient for rejecting |
| 72 |
> |
$t\bar{t}$ to dilepton events. The remaining dilepton background can be classified into the following categories: |
| 73 |
> |
|
| 74 |
> |
%The dilepton background can be broken up into many components depending |
| 75 |
> |
%on the characteristics of the 2nd (undetected) lepton |
| 76 |
> |
%\begin{itemize} |
| 77 |
> |
%\item 3-prong hadronic tau decay |
| 78 |
> |
%\item 1-prong hadronic tau decay |
| 79 |
> |
%\item $e$ or $\mu$ possibly from $\tau$ decay |
| 80 |
> |
%\end{itemize} |
| 81 |
> |
%We have currently no veto against 3-prong taus. For the other two categories, we explicitely |
| 82 |
> |
%veto events %with additional electrons and muons above 10 GeV , and we veto events |
| 83 |
> |
%with an isolated track of \pt\ $>$ 10 GeV. This rejects electrons and muons (either from $W\to e/\mu$ or |
| 84 |
> |
%$W\to \tau\to e/\mu$) and 1-prong tau decays. |
| 85 |
> |
%(it turns out that the explicit $e$ or $\mu$ veto is redundant with the isolated track veto). |
| 86 |
> |
%Therefore the latter two categories can be broken into |
| 87 |
|
\begin{itemize} |
| 88 |
< |
\item out of acceptance $(|\eta| > 2.50)$ |
| 89 |
< |
\item $P_T < 10$ GeV |
| 90 |
< |
\item $P_T > 10$ GeV, but survives the additional lepton/track isolation veto |
| 88 |
> |
\item lepton is out of acceptance $(|\eta| > 2.50)$ |
| 89 |
> |
\item lepton has \pt\ $<$ 10 GeV, and is inside the acceptance |
| 90 |
> |
\item lepton has \pt\ $>$ 10 GeV, is inside the acceptance, but survives the additional isolated track veto |
| 91 |
|
\end{itemize} |
| 92 |
< |
Monte Carlo studies indicate that there is no dominant contribution: it is ``a little bit of this, |
| 93 |
< |
and a little bit of that''. |
| 92 |
> |
|
| 93 |
> |
%Monte Carlo studies indicate that there is no dominant contribution: it is ``a little bit of this, |
| 94 |
> |
%and a little bit of that''. |
| 95 |
> |
|
| 96 |
> |
The last category includes 3-prong tau decays as well as electrons and muons from W decay that fail the isolation requirement. |
| 97 |
> |
Monte Carlo studies indicate that these three components populate the $M_T$ tail in the proportions of roughly 6\%, 47\%, 47\%. |
| 98 |
> |
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. |
| 99 |
|
|
| 100 |
|
The high $M_T$ dilepton backgrounds come from MC, but their rate is normalized to the |
| 101 |
< |
$M_T \approx 80$ GeV peak. In other to perform this normalization in data, the $W +$ jets |
| 101 |
> |
$M_T \approx 80$ GeV peak. In order to perform this normalization in data, the $W +$ jets |
| 102 |
|
events in the $M_T$ peak have to be subtracted off. This introduces a systematic uncertainty. |
| 103 |
|
|
| 104 |
|
There are two types of effects that can influence the MC dilepton prediction: physics effects |
| 106 |
|
|
| 107 |
|
First of all, many of our $t\bar{t}$ MC samples (eg: MadGraph) have |
| 108 |
|
BR$(W \to \ell \nu)=\frac{1}{9} = 0.1111$. |
| 109 |
< |
PDG says BR$(W \to \ell \nu) = 0.1080 \pm 0.0009$. This difference matter, so the $t\bar{t}$ MC |
| 109 |
> |
PDG says BR$(W \to \ell \nu) = 0.1080 \pm 0.0009$. This difference matters, so the $t\bar{t}$ MC |
| 110 |
|
must be corrected to account for this. |
| 111 |
|
|
| 112 |
|
Second, our selection is $\ell +$ 4 or more jets. A dilepton event passes the selection only if there are |
| 113 |
< |
two additional jet from ISR, or one jet from ISR and one jet which is reconstructed from the |
| 113 |
> |
two additional jets from ISR, or one jet from ISR and one jet which is reconstructed from the |
| 114 |
|
unidentified lepton, {\it e.g.}, a three-prong tau. Therefore, all MC dilepton $t\bar{t}$ samples used |
| 115 |
|
in the analysis must have their jet multiplicity corrected (if necessary) to agree with what is |
| 116 |
|
seen in $t\bar{t}$ data. We use a data control sample of well identified dilepton events with |
| 117 |
< |
\met and at least two jets as a template to ``adjust'' the $N_{jet}$ distribution of the $t\bar{t} \to$ |
| 117 |
> |
\met\ and at least two jets as a template to ``adjust'' the $N_{jet}$ distribution of the $t\bar{t} \to$ |
| 118 |
|
dileptons MC samples. |
| 119 |
|
|
| 120 |
|
The final physics effect has to do with the modeling of $t\bar{t}$ production and decay. Different |
| 121 |
|
MC models could in principle result in different BG predictions. Therefore we use several different |
| 122 |
< |
$t\bar{t}$ MC samples using different generators and dfferent parameters, to test the stability |
| 123 |
< |
of the dilepton BG prediction. All these predictions {\bf after} corrections for branching ratio |
| 122 |
> |
$t\bar{t}$ MC samples using different generators and different parameters, to test the stability |
| 123 |
> |
of the dilepton BG prediction. All these predictions, {\bf after} corrections for branching ratio |
| 124 |
|
and $N_{jet}$ dependence, are compared to each other. The spread is a measure of the systematic |
| 125 |
|
uncertainty associated with the $t\bar{t}$ generator modeling. |
| 126 |
|
|
| 127 |
< |
The main instrumental effect is associated with the underefficiency of the 2nd lepton veto. |
| 127 |
> |
The main instrumental effect is associated with the efficiency of the isolated track veto. |
| 128 |
|
We use tag-and-probe to compare the isolated track veto performance in $Z + 4$ jet data and |
| 129 |
|
MC, and we extract corrections if necessary. Note that the performance of the isolated track veto |
| 130 |
|
is not exactly the same on $e/\mu$ and on one prong hadronic tau decays. This is because |
| 131 |
|
the pions from one-prong taus are often accompanied by $\pi^0$'s that can then result in extra |
| 132 |
< |
tracks due to phton conversions. We let the simulation take care of that. Similarly, at the moment |
| 133 |
< |
we also let the simulation take care of the possibility of a hadronic tau ``disappearing'' in the |
| 118 |
< |
detector due to nuclear interaction of the pion. |
| 132 |
> |
tracks due to phton conversions. We let the simulation take care of that. |
| 133 |
> |
Note that JES uncertainties are effectively ``calibrated away'' by the $N_{jet}$ rescaling described above. |
| 134 |
|
|
| 135 |
< |
The sample of events failing the last isolated track veto is an important control sample to |
| 136 |
< |
check that we are doing the right thing. |
| 135 |
> |
%Similarly, at the moment |
| 136 |
> |
%we also let the simulation take care of the possibility of a hadronic tau ``disappearing'' in the |
| 137 |
> |
%detector due to nuclear interaction of the pion. |
| 138 |
|
|
| 139 |
< |
Note that JES uncertainties are effectively ``calibrated away'' by the $N_{jet}$ rescaling described |
| 140 |
< |
above. |
| 139 |
> |
%The sample of events failing the last isolated track veto is an important control sample to |
| 140 |
> |
%check that we are doing the right thing. |
| 141 |
|
|
| 142 |
|
Finally, there are possible improvements to this basic analysis strategy that can be added in the future: |
| 143 |
|
\begin{itemize} |
| 145 |
|
experiment under control. |
| 146 |
|
\item Add an explicit three prong tau veto |
| 147 |
|
\item Do something to require that three of the jets in the event be consistent with $t \to Wb, W \to q\bar{q}$. |
| 148 |
< |
This could help rejecting some of the dilepton BG; however, it would also loose efficiency for |
| 149 |
< |
the $\widetilde{t} \to b \chi^+$ mode |
| 148 |
> |
%This could help rejecting some of the dilepton BG; however, it would also loose efficiency for |
| 149 |
> |
%the $\widetilde{t} \to b \chi^+$ mode |
| 150 |
> |
This could help reject some of the dilepton BG in the search for $\widetilde{t} \to t \chi^0$, |
| 151 |
> |
but is not applicable to the $\widetilde{t} \to b \chi^+$ search. |
| 152 |
|
\item Consider the $M(\ell b)$ variable, which is not bounded by $M_{top}$ in $\widetilde{t} \to b \chi^+$ |
| 153 |
< |
\end{itemize} |
| 153 |
> |
\end{itemize} |
