| 11 |
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initial analysis is simply a counting experiment in the tail of the $M_T$ distribution. |
| 12 |
|
|
| 13 |
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The event selection is one-and-only-one high \pt\ isolated lepton, four or more jets, and |
| 14 |
< |
an \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 b tagged to reduce $W+$ jets. |
| 15 |
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The event sample is then dominated by $t\bar{t}$, but there are also contributions from $W+$ jets, |
| 16 |
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single top, dibosons, as well as rare SM processes such as $ttW$. |
| 17 |
|
|
| 19 |
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% tail has to be controlled at the level of 10\% or better. So this is (almost) a precision measurement. |
| 20 |
|
|
| 21 |
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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 |
| 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 approximately 80\% of |
| 25 |
> |
For a reasonable $M_T$ cut, say $M_T >$ 150 GeV, the dilepton background is approximately 70\% 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 |
| 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 |
| 49 |
> |
predictions are whenever possible normalized to the bulk of the $t\bar{t}$ data, i.e. events passing all of the |
| 50 |
|
requirements but with $M_T \approx 80$ GeV. |
| 51 |
|
This (mostly) removes uncertainties |
| 52 |
|
due to $\sigma(t\bar{t})$, lepton ID, trigger efficiency, luminosity, etc. |
| 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 |
< |
$W$. |
| 68 |
> |
$W$s. |
| 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 |
| 70 |
> |
cannot exceed $M_{top}-M_b$. 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 |
|
|
| 74 |
|
|
| 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 |
| 77 |
> |
($R_{wjet}$) is validated 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 |
| 79 |
> |
The equivalent ratio for top events ($R_{top}$) is tested in a sample of well |
| 80 |
|
identified $Z \to \ell \ell$ with one lepton added to the \met\ |
| 81 |
< |
calculation. |
| 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. |
| 84 |
> |
requirement. However, this test is unfortunately statistically |
| 85 |
> |
limited and its usefulness is limited to |
| 86 |
> |
event selections with modest \met\ |
| 87 |
> |
requirements. |
| 88 |
|
|
| 89 |
|
Note that the fact that the ratios are different for |
| 90 |
|
$t\bar{t}$/single top and $W +$ jets introduces a systematic |
| 91 |
|
uncertainty in the background calculation because one needs |
| 92 |
|
to know the relative fractions of these two components in |
| 93 |
< |
$M_T \approx 80$ GeV lepton $+$ jets sample. |
| 93 |
> |
the $M_T \approx 80$ GeV lepton $+$ jets sample. |
| 94 |
|
|
| 95 |
|
|
| 96 |
|
\subsection{Dilepton background} |
| 97 |
|
\label{sec:dil-general} |
| 98 |
|
|
| 99 |
< |
To suppress dilepton backgrounds, we veto events with an isolated track of \pt $>$ 10 GeV (see Sec.~\ref{sec:tkveto} for details). |
| 99 |
> |
To suppress dilepton backgrounds, we veto events with an isolated track of \pt\ $>$ 10 GeV (see Sec.~\ref{sec:tkveto} for details). |
| 100 |
|
Being the common feature for electron, muon, and one-prong |
| 101 |
|
tau decays, this veto is highly efficient for rejecting |
| 102 |
|
$t\bar{t}$ to dilepton events. The remaining dilepton background can be classified into the following categories: |
| 108 |
|
%\item 1-prong hadronic tau decay |
| 109 |
|
%\item $e$ or $\mu$ possibly from $\tau$ decay |
| 110 |
|
%\end{itemize} |
| 111 |
< |
%We have currently no veto against 3-prong taus. For the other two categories, we explicitely |
| 111 |
> |
%We have currently no veto against 3-prong taus. For the other two categories, we explicitly |
| 112 |
|
%veto events %with additional electrons and muons above 10 GeV , and we veto events |
| 113 |
|
%with an isolated track of \pt\ $>$ 10 GeV. This rejects electrons and muons (either from $W\to e/\mu$ or |
| 114 |
|
%$W\to \tau\to e/\mu$) and 1-prong tau decays. |
| 115 |
|
%(it turns out that the explicit $e$ or $\mu$ veto is redundant with the isolated track veto). |
| 116 |
|
%Therefore the latter two categories can be broken into |
| 117 |
|
\begin{itemize} |
| 118 |
< |
\item lepton is out of acceptance $(|\eta| > 2.50)$ |
| 118 |
> |
\item lepton is out of acceptance $(|\eta| > 2.5)$ |
| 119 |
|
\item lepton has \pt\ $<$ 10 GeV, and is inside the acceptance |
| 120 |
|
\item lepton has \pt\ $>$ 10 GeV, is inside the acceptance, but survives the additional isolated track veto |
| 121 |
|
\end{itemize} |
| 127 |
|
that fail the isolation requirement. |
| 128 |
|
% HOOBERMAN: commenting out for now |
| 129 |
|
%Monte Carlo studies indicate that these three components populate the $M_T$ tail in the proportions of roughly 6\%, 47\%, 47\%. |
| 130 |
< |
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. |
| 130 |
> |
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. |
| 131 |
|
|
| 132 |
< |
The high $M_T$ dilepton backgrounds come from MC, but their rate is normalized to the |
| 132 |
> |
The high $M_T$ dilepton background predictions come from MC, but their rate is normalized to the |
| 133 |
|
$M_T \approx 80$ GeV peak. In order to perform this normalization in |
| 134 |
< |
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. |
| 134 |
> |
data, the rare background events in the $M_T$ peak are subtracted off. This also introduces a systematic uncertainty. |
| 135 |
|
|
| 136 |
|
There are two types of effects that can influence the MC dilepton prediction: physics effects |
| 137 |
|
and instrumental effects. We discuss these next, starting from physics. |
| 138 |
|
|
| 139 |
< |
First of all, many of our $t\bar{t}$ MC samples (eg: MadGraph) have |
| 139 |
> |
First of all, many of our $t\bar{t}$ MC samples (e.g. MadGraph) have |
| 140 |
|
BR$(W \to \ell \nu)=\frac{1}{9} = 0.1111$. |
| 141 |
|
PDG says BR$(W \to \ell \nu) = 0.1080 \pm 0.0009$. This difference matters, so the $t\bar{t}$ MC |
| 142 |
|
must be corrected to account for this. |
| 143 |
|
|
| 144 |
< |
Second, our selection is $\ell +$ 4 or more jets. A dilepton event passes the selection only if there are |
| 144 |
> |
Second, our selection is $\ell +4$ or more jets. A dilepton event passes the selection only if there are |
| 145 |
|
two additional jets from ISR, or one jet from ISR and one jet which is reconstructed from the |
| 146 |
|
unidentified lepton, {\it e.g.}, a three-prong tau. Therefore, all MC dilepton $t\bar{t}$ samples used |
| 147 |
|
in the analysis must have their jet multiplicity corrected (if necessary) to agree with what is |
| 148 |
|
seen in $t\bar{t}$ data. We use a data control sample of well identified dilepton events with |
| 149 |
< |
\met\ and at least two jets as a template to ``adjust'' the $N_{jet}$ distribution of the $t\bar{t} \to$ |
| 149 |
> |
\met\ and at least one jet (including at least one b-tag) as a template to ``adjust'' the $N_{jet}$ distribution of the $t\bar{t} \to$ |
| 150 |
|
dileptons MC samples. |
| 151 |
|
|
| 152 |
|
The final physics effect has to do with the modeling of $t\bar{t}$ production and decay. Different |
| 157 |
|
uncertainty associated with the $t\bar{t}$ generator modeling. |
| 158 |
|
|
| 159 |
|
The main instrumental effect is associated with the efficiency of the isolated track veto. |
| 160 |
< |
We use tag-and-probe to compare the isolated track veto performance in $Z + 4$ jet data and |
| 160 |
> |
We use tag-and-probe to compare the isolated track veto performance in $Z + 4$ jets data and |
| 161 |
|
MC. Note that the performance of the isolated track veto |
| 162 |
|
is not exactly the same on $e/\mu$ and on one prong hadronic tau decays. This is because |
| 163 |
|
the pions from one-prong taus are often accompanied by $\pi^0$'s that can then result in extra |
| 173 |
|
|
| 174 |
|
\subsection{Other backgrounds} |
| 175 |
|
\label{sec:other-general} |
| 176 |
< |
Other backgrounds are $tW$, $ttV$, dibosons, tribosons, Drell Yan. |
| 176 |
> |
Other backgrounds are $tW$, $ttV$, dibosons, tribosons, and Drell Yan. |
| 177 |
|
These are small. They are taken from MC with appropriate scale |
| 178 |
|
factors for trigger efficiency, and reweighting to match the distribution of reconstructed primary vertices in data. |
| 179 |
|
|
