| 7 |
|
to these initial requirements. |
| 8 |
|
|
| 9 |
|
The focus of this note is to optimize official loose and tight identification |
| 10 |
< |
criteria to identify electrons from $Z$ and $W$ decays, respectively. |
| 10 |
> |
criteria defined in Appendix~\ref{a:OfficialCriteria} |
| 11 |
> |
to identify electrons from $Z$ and $W$ decays, respectively. |
| 12 |
|
This can be achieved by optimizing the thresholds, optimizing the |
| 13 |
|
discriminants that have more background rejection power, and selecting |
| 14 |
|
the variables that are not highly correlated with each other. |
| 27 |
|
\subsubsection{Track-ECAL matching} |
| 28 |
|
An electron GSF track should be well-matched to the ECAL Super Cluster (SC), while |
| 29 |
|
a $\pi^0$ energy deposit in ECAL is not necessarily matched well with a GSF track, which |
| 30 |
< |
is usually belong to a charged pion. Thus, a spatial match between a track and a SC can be a good |
| 30 |
> |
is usually produced by a charged pion. Thus, a spatial match between a track and a SC can be a good |
| 31 |
|
discriminant. This match is described in azimuthal and pseudorapidity planes and denoted as |
| 32 |
|
$\Delta\phi$ and $\Delta\eta$, respectively. |
| 33 |
|
|
| 33 |
– |
\subsubsection{E/p-based variables} |
| 34 |
– |
Electron should deposit all of its energy in the ECAL detector, thus the track momentum |
| 35 |
– |
at the outer edge of tracker $p_{out}$ should be of the same order as an energy of the seed EM |
| 36 |
– |
cluster $E_{seed}$. Jet is reconstructed combining information from CMS tracker and hadronic calomitere (HCAL). It interact with ECAL much less intensively and most of its energy, carried after tracker, is deposited in HCAL. Hence, $p_{out}$ and $E_{seed}$ differ significantly for the jets and can be used to discriminate them from electrons. |
| 37 |
– |
We also considered an official version of this discriminant $E_{SC}/p_{in}$, where $E_{SC}$ is a SC energy, and $p_{in}$ is the initial momentum of a charged particle. |
| 38 |
– |
|
| 34 |
|
\subsubsection{ECAL energy width} |
| 35 |
+ |
\label{ss:etawidth} |
| 36 |
|
An electron brems extensively in CMS tracker, which results in a rather wide shower in azimuthal |
| 37 |
|
plane due to a strong CMS magnetic field. However, the width of a shower in pseudorapidity |
| 38 |
|
plane remains very narrow and can discriminate against jets, which tend to create rather large |
| 44 |
|
\sigma_\eta = \frac{1}{E_{SC}} \sqrt{\sum_{ECAL~SC~RecHits} E_i(\eta_i - \eta_{SC})^2}. |
| 45 |
|
\end{equation} |
| 46 |
|
|
| 47 |
+ |
\subsubsection{E/p-based variables} |
| 48 |
+ |
\label{ss:ep} |
| 49 |
+ |
Electron should deposit all of its energy in the ECAL detector, thus the track momentum |
| 50 |
+ |
at the outer edge of tracker $p_{out}$ should be of the same order as an energy of the seed EM |
| 51 |
+ |
cluster $E_{seed}$. Jet is reconstructed combining information from CMS tracker and hadronic calomitere (HCAL). It interact with ECAL much less intensively and most of its energy, carried after tracker, is deposited in HCAL. Hence, $p_{out}$ and $E_{seed}$ differ significantly for the jets and can be used to discriminate them from electrons. |
| 52 |
+ |
We also considered an official version of this discriminant $E_{SC}/p_{in}$, where $E_{SC}$ is a SC energy, and $p_{in}$ is the initial momentum of a charged particle. |
| 53 |
+ |
|
| 54 |
|
\subsubsection{H/E variables} |
| 55 |
|
One can form a powerful discriminant by using the HCAL and ECAL energies associated |
| 56 |
|
with an electron candidate, as electrons tend to deposit very little or no energy in HCAL, |
| 57 |
< |
while jets produce a wide energy deposition in the HCAL. An variable used in official |
| 57 |
> |
while jets produce a wide energy deposition in the HCAL. A variable used in official |
| 58 |
|
``Robust" as well as ``Loose" and ``Tight" criteria is the ratio of HCAL and ECAL energies: $H/E$. |
| 59 |
|
It peaks around 0 for electrons and can be quite large for em-jets. We form a variable that also |
| 60 |
|
takes into account the width of the ECAL energy deposition by making a ratio of the energy deposited |
| 63 |
|
|
| 64 |
|
\begin{equation} |
| 65 |
|
\label{eq:emhad} |
| 66 |
< |
Iso_{EmHad} =\frac{1}{E_{SC}}\left(\sum_{\Delta R=0.3}E^{ecal}_{RecHit} + |
| 66 |
> |
EmHad =\frac{1}{E_{SC}}\left(\sum_{\Delta R=0.3}E^{ecal}_{RecHit} + |
| 67 |
|
\sum_{\Delta R=0.3}E^{hcal}_{RecHit} - E_{SC}\right). |
| 68 |
|
\end{equation} |
| 69 |
|
|
| 70 |
|
\subsubsection{Track isolation requirements} |
| 71 |
+ |
\label{ss:trackIso} |
| 72 |
|
As electrons from $W$ and $Z$ boson decays are isolated, requiring electron isolated from tracking |
| 73 |
|
activity can significantly suppress em-jets that usually have a large number of soft tracks around the |
| 74 |
|
leading $\pi^0$. It also can suppress real electrons from semi-leptonic decays of $b$ quarks which |
| 75 |
< |
tend to be non-isolated as well. We consider several versions of the track isolation requirements: |
| 75 |
> |
tend to be non-isolated as well. We consider several versions of the track isolation requirements |
| 76 |
> |
using CTF tracks around the electron candidates. |
| 77 |
|
|
| 78 |
|
\begin{equation} |
| 79 |
|
\label{eq:trkIsoN} |
| 80 |
< |
IsoN_{trk} = \frac{1}{p_T(e)}\left(\sum_{\Delta R=0.3} p_T(trk) - \sum_{\Delta R=0.05} p_T(trk)\right), |
| 80 |
> |
Iso^{trk}_{Norm.} = \frac{1}{p_T(e)}\left(\sum_{\Delta R=0.3} p_T(trk) - \sum_{\Delta R=0.05} p_T(trk)\right), |
| 81 |
|
\end{equation} |
| 82 |
|
|
| 83 |
|
and non-normalized version of the above: |
| 84 |
|
|
| 85 |
|
\begin{equation} |
| 86 |
|
\label{eq:trkIso} |
| 87 |
< |
Iso_{trk} = \sum_{\Delta R=0.3} p_T(trk) - \sum_{\Delta R=0.05} p_T(trk). |
| 87 |
> |
Iso^{trk} = \sum_{\Delta R=0.3} p_T(trk) - \sum_{\Delta R=0.05} p_T(trk). |
| 88 |
> |
\end{equation} |
| 89 |
> |
|
| 90 |
> |
We also test the track isolation discriminant with the larger outer cone, similar to that defined by electroweak group:~\footnote{Our analysis trees do not store information that would allow us to test |
| 91 |
> |
the isolation variable with an annulus of $0.02 < \Delta R < 0.6$. However, the performance |
| 92 |
> |
of a track isolation in an annulus of $0.05 < \Delta R < 0.5$ is similar.} |
| 93 |
> |
\begin{equation} |
| 94 |
> |
\label{eq:trkIsoEWK} |
| 95 |
> |
Iso^{trk}_{EWK} = \sum_{\Delta R = 0.6} p_T(trk) - \sum_{\Delta R = 0.02} p_T(trk). |
| 96 |
|
\end{equation} |
| 97 |
|
|
| 98 |
< |
%We also test the track isolation discriminant defined within electroweak group: |
| 86 |
< |
%\begin{equation} |
| 87 |
< |
%\label{eq:trkIsoEWK} |
| 88 |
< |
%Iso_{trk}(EWK) = \sum_{\Delta R = 0.6} p_T(trk) - \sum_{\Delta R = 0.02} p_T(trk). |
| 89 |
< |
%\end{equation} |
| 90 |
< |
|
| 91 |
< |
%\subsubsection{ECAL and HCAL isolation requirements} |
| 92 |
< |
%We also consider a few ECAL |
| 93 |
< |
% |
| 94 |
< |
%In order to discriminate electron from em-jet isolation variable defined using both ECAL and HCAL is used. |
| 95 |
< |
%Jet deposit high fraction of its energy in HCAL and much less in ECAL. While electron deposits all its energy in ECAL |
| 96 |
< |
%with very small hadronic fraction, unless it is very energetic when longitudinal energy leakage appears. |
| 97 |
< |
%Isolation variable, defined as Eq.~\ref{eq:3}, is very similar by the content to the variable $H/E$, |
| 98 |
< |
%ratio of energy deposited HCAL behind the SC over the SC energy, which is used in official egamma POG |
| 99 |
< |
%electron identification criteria. |
| 98 |
> |
|
| 99 |
|
|
| 100 |
|
|
| 101 |
|
\subsection{Optimization method and strategy} |
| 102 |
< |
We start building the ``Simple Loose" electron criteria based on the discriminants utilized in the official |
| 103 |
< |
``Robust'' and adding more variables from the ``Loose" criteria (or their more powerful variants described |
| 104 |
< |
above), and tuning the threshold to keep the efficiency of each criterion to be |
| 105 |
< |
above 99\%. ``Simple Tight'' selection is developed for selection electrons coming from $W$ boson. In order |
| 106 |
< |
to keep the whole selection robust and avoid many different thresholds and reduce source of systematic |
| 107 |
< |
uncertainties we define ``Simple Tight'' based on ``Simple Loose'' with one addition discriminator. |
| 108 |
< |
%A similar optimization is done for the ``Simple Tight" requirements, although, the efficiency |
| 109 |
< |
%was not required to exceed 99\% for the a given criterion. Instead, |
| 110 |
< |
To pick up the threshold for the tight criterion we plot signal efficiency $v.s.$ background efficiency |
| 111 |
< |
and find a region in the plot that is closest to the ``perfect" performance corner that has 100\% signal |
| 112 |
< |
and 0\% background efficiencies. |
| 113 |
< |
|
| 114 |
< |
We study the performance of the requirements by applying them in sequential order, starting |
| 115 |
< |
with the most simple and robust, and continuing to more complex |
| 116 |
< |
ones. We also study the correlation between variables by changing the order they are |
| 117 |
< |
applied to see if some of the variables are completely correlated with the others and can |
| 118 |
< |
be omitted. |
| 119 |
< |
Electrons reconstructed in barrel and endcap of electronmagnetic calorimeter are considered seperately. |
| 120 |
< |
WZ signal samples are used as a source of real electrons and multijet samples from ``Gumbo soup'' are used as |
| 121 |
< |
a source of em-jets. |
| 122 |
< |
|
| 123 |
< |
\subsection{Tuning ``Simple Loose" criteria} |
| 124 |
< |
Tunning of ``WZ Loose'' critaria is described below. |
| 125 |
< |
As mentioned above, we start from the variables used within ``Robust'' selection and studying their performance |
| 126 |
< |
on the our samples and optimizing thresholds. Spatial track matching variables, $\Delta\eta$ and $\Delta\phi$, |
| 128 |
< |
are used at the first dictriminants. The disctribution of these variables are shown on figures ~\ref{fig:DeltaEta} |
| 129 |
< |
and ~\ref{fig:DeltaPhi} respectively. |
| 102 |
> |
The focus of this work is to define two simple selection criteria: ``Simple Loose" and ``Simple Tight" |
| 103 |
> |
to select electrons from $Z \to ee$ and $W \to e\nu_e$ processes, respectively. We start building |
| 104 |
> |
the ``Simple Loose" electron criteria based on the discriminants utilized in the official ``Robust'' |
| 105 |
> |
and adding more variables from the ``Loose" criteria (or their more powerful equivalents described |
| 106 |
> |
above), and tuning the thresholds to keep the efficiency of each criterion high. We change the order |
| 107 |
> |
of how the requirements are applied to assess the level of correlation between different criteria. |
| 108 |
> |
We try to retain only the variables that are as less correlated as possible to keep the number |
| 109 |
> |
of criteria to a minimum. |
| 110 |
> |
|
| 111 |
> |
We design the ``Simple Tight'' requirements by applying additional criteria on top of the |
| 112 |
> |
unchanged ``Simple Loose''. We chose not to modify thresholds of ``Simple Loose'' criteria |
| 113 |
> |
to reduce possible systematic uncertainties and to make the process of extracting the |
| 114 |
> |
efficiency from data easier. |
| 115 |
> |
|
| 116 |
> |
Both ``Simple Tight'' and ``Simple Loose'' criteria are designed separately for ECAL |
| 117 |
> |
barrel and endcap. We consider electron candidates with $p_T > 10$ GeV. The signal |
| 118 |
> |
electron sample was obtained from the $WZ$ Monte Carlo simulation, and the misidentified |
| 119 |
> |
jets are obtained from the "Gumbo" soup where we exclude $\gamma+X$ processes. |
| 120 |
> |
|
| 121 |
> |
\subsection{Tuning the ``Simple Loose" criteria} |
| 122 |
> |
The first two criteria of ``Robust'' requirements are $\Delta \eta$ and $\Delta \phi$. |
| 123 |
> |
The distributions of these variables for signal and background together with the |
| 124 |
> |
em-jet separation power are given in Figs.~\ref{fig:DeltaEta}~and~\ref{fig:DeltaPhi}. |
| 125 |
> |
We apply both requirements with the thresholds of 0.009(0.007) and 0.05(0.05) for |
| 126 |
> |
$\Delta \eta$ and $\Delta \phi$ for barrel(endcap), respectively. |
| 127 |
|
|
| 128 |
|
\begin{figure}[!tb] |
| 129 |
|
\begin{center} |
| 130 |
|
\includegraphics[width=16cm]{Figs/deltaEta.eps} |
| 131 |
|
\vspace{-10mm} |
| 132 |
< |
\caption{Upper plots represent the distribution of $\Delta\eta$ for electrons and mis-identified jets in Barrel(left) and Endcap(right). Lower plots represent background efficiency $v.s.$ signal efficiency for given criterion in Barrel(left) and Endcap(right). |
| 132 |
> |
\caption{Distributions of $\Delta \eta$ for electrons (blue solid line) and misidentified jets |
| 133 |
> |
(red dashed line) in barrel (top left) and endcap (top right). |
| 134 |
> |
The performance of these discriminants in terms of efficiencies to select |
| 135 |
> |
true electrons and misidentified jets are given below. |
| 136 |
|
\label{fig:DeltaEta}} |
| 137 |
|
\end{center} |
| 138 |
|
\end{figure} |
| 142 |
|
\begin{center} |
| 143 |
|
\includegraphics[width=16cm]{Figs/deltaPhi.eps} |
| 144 |
|
\vspace{-10mm} |
| 145 |
< |
\caption{Upper plots represent the distribution of $\Delta\phi$ for electrons and mis-identified jets in Barrel(left) and Endcap(right). Lower plots represent background efficiency $v.s.$ signal efficiency for given criteron in Barrel(left) and Endcap(right). |
| 145 |
> |
\caption{The same as Fig.~\ref{fig:DeltaEta}, but for $\Delta \phi$. |
| 146 |
|
\label{fig:DeltaPhi}} |
| 147 |
|
\end{center} |
| 148 |
|
\end{figure} |
| 149 |
|
|
| 150 |
< |
|
| 151 |
< |
Third disctriminating variable included in ``Simple Loose'' selection is based on shower shape in ECAL. We stady |
| 152 |
< |
two ways of parametrization described in section 4.1.2 and checked their power on rejecting em-jets lookeing |
| 153 |
< |
at background efficinecy $v.s.$ signal efficinecy.This comparison is presented figure ~\ref{fig:SigmaEE_vs_EtaWidth}. |
| 150 |
> |
The third discriminating variable included in the ``Robust'' criteria describes the width |
| 151 |
> |
of the EM shower. We study two different parameterizations of this variable |
| 152 |
> |
described in~\ref{ss:etawidth}. The performance of their discriminating power is given in |
| 153 |
> |
Fig.~\ref{fig:SigmaEE_vs_EtaWidth}. |
| 154 |
|
|
| 155 |
|
\begin{figure}[!tb] |
| 156 |
|
\begin{center} |
| 157 |
|
\includegraphics[width=16cm]{Figs/Eff_EtaWidth_SigmaEtaEta.eps} |
| 158 |
|
\vspace{-10mm} |
| 159 |
< |
\caption{Plot on the left represents background efficiency $v.s.$ signal efficiency in Barrel for $\eta$ width of SC (red) and $\sigma_{\eta\eta}$ (blue). Plot on the right represents the same for Endcap. |
| 159 |
> |
\caption{The background efficiency $v.s.$ signal efficiency in barrel (left) and endcap (right) |
| 160 |
> |
for $\eta$ width of SC (red) and $\sigma_{\eta\eta}$ (blue). |
| 161 |
|
\label{fig:SigmaEE_vs_EtaWidth}} |
| 162 |
|
\end{center} |
| 163 |
|
\end{figure} |
| 164 |
|
|
| 165 |
< |
As it can be seen $\sigma_{\eta\eta}$ variable is more powerfull in Barrel allowing to reject \~ 70\% of em-jet with only couple of \% loss of signal, while in endcap the performance of these two variables are more comparable. This result leads us to keep $\sigma_{\eta\eta}$ in our selection. Distribution of $\sigma_{\eta\eta}$ is presented on figure ~\ref{fig:SigmaEtaEta}. |
| 166 |
< |
|
| 165 |
> |
As it can be seen, the $\sigma_{\eta\eta}$ variable is more powerful in barrel that can reject $\sim 70\%$ |
| 166 |
> |
of em-jets while loosing only a couple of percents of signal. The performance in endcap is comparable |
| 167 |
> |
between the two. As $\sigma_{\eta\eta}$ is shown to be described very well by Monte |
| 168 |
> |
Carlo~\footnote{$\sigma_{\eta\eta}$ was studied using test beam data and was shown to be described |
| 169 |
> |
in simulation very well.} we chose to select $\sigma_{\eta\eta} < 0.012 (0.026)$ for barrel (endcap). |
| 170 |
> |
The plot with distributions of $\sigma_{\eta\eta}$ and the performance in barrel and endcap is given |
| 171 |
> |
in Fig.~\ref{fig:SigmaEtaEta}. |
| 172 |
|
\begin{figure}[!tb] |
| 173 |
|
\begin{center} |
| 174 |
< |
\includegraphics[width=16cm]{Figs/Eff_EtaWidth_SigmaEtaEta.eps} |
| 174 |
> |
\includegraphics[width=16cm]{Figs/sigmaEtaEta.eps} |
| 175 |
|
\vspace{-10mm} |
| 176 |
< |
\caption{Upper plots represent the distribution of $\sigma_{\eta\eta}$ for electrons and mis-identified jets in Barrel(left) and Endcap(right). Lower plots represent background efficiency $v.s.$ signal efficiency for this discriminator in Barrel(left) and Endcap(right). |
| 176 |
> |
\caption{ |
| 177 |
> |
Distributions of $\sigma_{\eta\eta}$ for electrons (blue solid line) and misidentified jets |
| 178 |
> |
(red dashed line) in barrel (top left) and endcap (top right). |
| 179 |
> |
The performance of these discriminants in terms of efficiencies to select |
| 180 |
> |
true electrons and misidentified jets are given below. |
| 181 |
|
\label{fig:SigmaEtaEta}} |
| 182 |
|
\end{center} |
| 183 |
|
\end{figure} |
| 184 |
|
|
| 185 |
< |
|
| 186 |
< |
These three discriminants are the same as used in official ``Robust'', ``Loose'' or ``Tight'' selections. |
| 187 |
< |
For utilizing matching of energy/momentum from ECAL and tracker two variables are studied: $E_{seed}/p_{out}$ and $E/p$, |
| 188 |
< |
where the latter one is used in official ``Loose'' and ``Tight'' selection to categorize electons on $E/p$ $v.s.$ $fbrem$ |
| 189 |
< |
plane. Here $fbrem$ is defined as $(p_{in}-p_{out})/p_{in}$, where $p_{in}$ and $p_{out}$ are momenta measured at the |
| 190 |
< |
inner and outer edge of tracker respectively. Comparison the signal $v.s.$ background efficiency for these two options |
| 191 |
< |
is shown in figure ~\ref{fig:EseedOPout_vs_EoP}. |
| 192 |
< |
|
| 185 |
> |
The discriminants that we chose so far are used in official ``Robust'' criteria. |
| 186 |
> |
The last requirement from the official criteria is $H/E$ which we chose to keep |
| 187 |
> |
unchanged from the predefined GSF electron requirement ($H/E < 0.2$). |
| 188 |
> |
It will be shown that $H/E$ variable is highly correlated with isolation requirements |
| 189 |
> |
that we will apply later, and thus it does not need to be tightened. |
| 190 |
> |
|
| 191 |
> |
As all the discriminants from the ``Robust'' selection are considered, we start including |
| 192 |
> |
the variables utilized in the official ``Loose'' requirement. At first, we consider |
| 193 |
> |
$E_{seed}/p_{out}$ and $E/p$, described in Section~\ref{ss:ep}. |
| 194 |
> |
The latter is used in the official ``Loose'' and ``Tight'' selections to categorize |
| 195 |
> |
electrons in $E/p$ $v.s.$ $fbrem$ phase space, where $fbrem$ is defined as |
| 196 |
> |
\begin{equation} |
| 197 |
> |
\label{eq:fbrem} |
| 198 |
> |
fbrem = \frac{p_{in} - p_{out}}{p_{in}}, |
| 199 |
> |
\end{equation} |
| 200 |
> |
where $p_{in}$ and $p_{out}$ are momenta measured at the inner and outer edge of |
| 201 |
> |
the tracker, respectively. The performance of the $E_{seed}/p_{out}$ and $E/p$ |
| 202 |
> |
are given in Fig.~\ref{fig:EseedOPout_vs_EoP}. |
| 203 |
|
|
| 204 |
|
\begin{figure}[!tb] |
| 205 |
|
\begin{center} |
| 206 |
|
\includegraphics[width=16cm]{Figs/Eff_EoP_EseedoPout.eps} |
| 207 |
|
\vspace{-10mm} |
| 208 |
< |
\caption{Plot on the left represents background efficiency $v.s.$ signal efficiency in Barrel for $E/p$ (red) and $E_{seed}/p_{out}$ (blue). Plot on the right represents the same for Endcap. |
| 208 |
> |
\caption{Background $v.s.$ signal efficiency for barrel (left) and endcap (right) for $E/p$ (red) |
| 209 |
> |
and $E_{seed}/p_{out}$ (blue). |
| 210 |
|
\label{fig:EseedOPout_vs_EoP}} |
| 211 |
|
\end{center} |
| 212 |
|
\end{figure} |
| 213 |
|
|
| 214 |
< |
|
| 215 |
< |
$E_{seed}/p_{out}$ is included as another criterion in ``Simple Loose'' selection. Its distribution both in barrel |
| 216 |
< |
and endcap is shown on figure ~\ref{fig:EseedOPout} |
| 214 |
> |
$E_{seed}/p_{out}$ has a better performance and we include it to the ``Simple Loose'' |
| 215 |
> |
requirement to be more than 0.9 for both barrel and endcap. The distributions of this |
| 216 |
> |
variable and discriminating performance is given in Fig.~\ref{fig:EseedOPout}. |
| 217 |
|
|
| 218 |
|
\begin{figure}[!tb] |
| 219 |
|
\begin{center} |
| 220 |
|
\includegraphics[width=16cm]{Figs/EseedPout.eps} |
| 221 |
|
\vspace{-10mm} |
| 222 |
< |
\caption{Upper plots represent the distribution of $E_{seed}/p_{out}$ for electrons and mis-identified jets in Barrel(left) and Endcap(right). Lower plots represent background efficiency $v.s.$ signal efficiency for this discriminator in Barrel(left) and Endcap(right). |
| 222 |
> |
\caption{$E_{seed}/p_{out}$ for electrons(blue solid line) and mis-identified jets (red dashed line) |
| 223 |
> |
in barrel (left top) and endcap (right top). The performance of the criteria for different thresholds |
| 224 |
> |
is given in the bottom left plot for barrel, and bottom right plot for endcap. |
| 225 |
|
\label{fig:EseedOPout}} |
| 226 |
|
\end{center} |
| 227 |
|
\end{figure} |
| 228 |
|
|
| 229 |
< |
|
| 230 |
< |
In order to select isolated electron candidates we use track isolation. As mentioned in section 4.1.5 we |
| 231 |
< |
study both normalized and non-normalized definition of it. We compare which one of the two definitions allow |
| 232 |
< |
us better identify real electrons from em-jets, figure ~\ref{fig:TrkIso_no_vs_norm} |
| 233 |
< |
|
| 229 |
> |
Up to this point we utilized all of the variables of the ``Robust'' and ``Loose'' criteria with an exception |
| 230 |
> |
of a much looser $H/E$ requirement and substitution of $E/p$ with $E_{seed}/p_{out}$ variable. |
| 231 |
> |
As it is shown later in the note, the performance of this criteria with respect to the official ``Loose'' is |
| 232 |
> |
very comparable without complexity due to the categorization employed by the ``Loose'' criteria. |
| 233 |
> |
The improvement is mostly achieved by utilizing a more discriminating variables and tuned |
| 234 |
> |
thresholds. |
| 235 |
> |
|
| 236 |
> |
It is possible to further improve the performance of the ``Simple Loose'' identification by applying |
| 237 |
> |
track isolation requirements. We study the performance of three various track isolation requirements |
| 238 |
> |
described in Section~\ref{ss:trackIso} where we varied the cone sizes from 0.5 to 0.05 and select |
| 239 |
> |
the most optimal values. The results for the variables with optimized cone sizes are given |
| 240 |
> |
in Fig.~\ref{fig:TrkIso_no_vs_norm}. |
| 241 |
|
|
| 242 |
|
\begin{figure}[!tb] |
| 243 |
|
\begin{center} |
| 244 |
< |
\includegraphics[width=16cm]{Figs/Eff_trkISoNonNorm_trkIsoNorm.eps} |
| 244 |
> |
\includegraphics[width=16cm]{Figs/Eff_trkISoNonNorm_trkIsoNorm_trkIsoEWK.eps} |
| 245 |
|
\vspace{-10mm} |
| 246 |
< |
\caption{Plot on the left represents background efficiency $v.s.$ signal efficiency in Barrel for non-normalized (red) and normalized (blue) definition of track isolation. Plot on the right represents the same for Endcap. |
| 246 |
> |
\caption{Performance of three track isolation variables for barrel (left) and endcap (right). |
| 247 |
|
\label{fig:TrkIso_no_vs_norm}} |
| 248 |
|
\end{center} |
| 249 |
|
\end{figure} |
| 250 |
|
|
| 251 |
+ |
The normalized track isolation variable, $Iso^{trk}_{Norm}$, offers the best performance, |
| 252 |
+ |
with an expense of making the efficiency to depend on the electron candidate $p_T$. |
| 253 |
+ |
As it is described in the Section~\ref{Results}, the requirement results in a loss of efficiency |
| 254 |
+ |
at low $p_T$; however, the loss is small in the characteristic range of $p_T$ of electrons |
| 255 |
+ |
from $W$ and $Z$ boson decays. |
| 256 |
+ |
|
| 257 |
+ |
By introducing the isolation requirement, we also reject a significant background from |
| 258 |
+ |
non-isolated electrons from $Zb\bar{b}$ production, where $b$ quarks decay semileptonically. |
| 259 |
+ |
The distribution of $Iso^{trk}_{Norm}$ for signal electrons and misidentified |
| 260 |
+ |
light- and $b$-quark jets are given in Fig.~\ref{fig:TrackIsoChowd} |
| 261 |
+ |
|
| 262 |
+ |
\begin{figure}[!tb] |
| 263 |
+ |
\begin{center} |
| 264 |
+ |
\includegraphics[width=16cm]{Figs/TrackIsoChowd.eps} |
| 265 |
+ |
\vspace{-10mm} |
| 266 |
+ |
\caption{The distribution of the normalized track isolation defined in Eq.~\ref{eq:trkIsoN} for signal |
| 267 |
+ |
electrons (blue solid line), misidentified light-quark jets (red squares), and $b$-quark jets (black inverted |
| 268 |
+ |
triangles) in barrel (left) and endcap (right). |
| 269 |
+ |
\label{fig:TrackIsoChowd} |
| 270 |
+ |
} |
| 271 |
+ |
\end{center} |
| 272 |
+ |
\end{figure} |
| 273 |
+ |
|
| 274 |
+ |
We illustrate the performance of track isolation variable chosen for ``Simple Loose'' criteria |
| 275 |
+ |
in Fig.~\ref{fig:trkIso}, and we set the requirement of $Iso^{trk}_{Norm}$ to be less than |
| 276 |
+ |
0.1 (0.2) for barrel(endcap). |
| 277 |
+ |
\begin{figure}[!tb] |
| 278 |
+ |
\begin{center} |
| 279 |
+ |
\includegraphics[width=16cm]{Figs/TrkIso.eps} |
| 280 |
+ |
\vspace{-10mm} |
| 281 |
+ |
\caption{The $Iso^{trk}_{Norm}$ discriminant for electrons (blue soild line) and misidentified jets (red dashed line) for barrel (top left) and endcap (top right). The signal $v.s.$ background efficiencies |
| 282 |
+ |
obtained by varying the threshold are displayed in bottom left (barrel) and bottom right (endcap) plots. |
| 283 |
+ |
\label{fig:trkIso} |
| 284 |
+ |
} |
| 285 |
+ |
\end{center} |
| 286 |
+ |
\end{figure} |
| 287 |
|
|
| 288 |
< |
We keep isolation defined as ~\ref{eq:trkIsoN} in ``Simple Loose'' selection. |
| 288 |
> |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 289 |
|
|
| 290 |
+ |
\subsection{Tuning the ``Simple Tight" criteria} |
| 291 |
+ |
The ``Simple Loose'' criteria utilize variables that describe spatial- and energy-matching of a |
| 292 |
+ |
track to a SC, lateral energy deposition profile of a SC, and a track isolation requirement. |
| 293 |
+ |
Although, these requirements are sufficient to select a relatively clean sample of $Z\to ee$ events, |
| 294 |
+ |
the discriminating power is insufficient to suppress the background from misidentified jets |
| 295 |
+ |
from the $Z+jets$ processes. Therefore, we introduce a ``Simple Tight'' criteria that is based |
| 296 |
+ |
on the ``Simple Loose'' one with an addition of the variable that takes into account the energy |
| 297 |
+ |
deposition in the HCAL. |
| 298 |
+ |
|
| 299 |
+ |
The variable that is used by the official criteria is $H/E$. We also study $EmHad$ variable |
| 300 |
+ |
defined in Eq.~\ref{eq:emhad} which is a mix of $H/E$ and an HCAL+ECAL isolation in a |
| 301 |
+ |
relatively narrow cone of $\Delta R < 0.3$.~\footnote{Similarly to the track isolation variable, |
| 302 |
+ |
we varied the cone size to select the most optimal variable.} |
| 303 |
+ |
As expected, these two variables are found to be |
| 304 |
+ |
correlated, although the $EmHad$ has much stronger discriminating power |
| 305 |
+ |
(see Fig.~\ref{fig:Eff_hoE_IsoEmHad}, due to an additional requirement on the lateral energy |
| 306 |
+ |
profile in the 0.3 cone. |
| 307 |
|
|
| 308 |
< |
\subsection{Tuning ``Simple Tight" criteria} |
| 309 |
< |
As mentioned in section 4.2 we stydy another isolation variable, using the information from ECAL and HCAL, in order |
| 310 |
< |
to reject higher fraction of em-jets which can easily mimic electron from $W$ boson decay. The comparison is done |
| 311 |
< |
between $H/E$ and $Iso_{EmHad}$ ($Sec 4.1.4$) variables and their discrimination power. First obsetvarion is that there |
| 312 |
< |
is clear correlation between them, once $Iso_{EmHad}$ discriminator is applied to select elctrons the efficiency of |
| 313 |
< |
$H/E$ variable to reject em-jets is hardly a few \%. Also the study has shown that isoaltion variable is more effecient |
| 314 |
< |
in selecting real electrons than $H/E$. Thus we keep $Iso_{EmHad}$ as the additional criterion for ``Simple Tight'' |
| 315 |
< |
selection. Its istribution is presented on figure ~\ref{fig:EmHadIso} |
| 308 |
> |
\begin{figure}[!tb] |
| 309 |
> |
\begin{center} |
| 310 |
> |
\includegraphics[width=16cm]{Figs/Eff_HoE_IsoEmHad.eps} |
| 311 |
> |
\vspace{-10mm} |
| 312 |
> |
\caption{$H/E$ and $EmHad$ variables for barrel (left) and endcap (right). |
| 313 |
> |
\label{fig:Eff_hoE_IsoEmHad}} |
| 314 |
> |
\end{center} |
| 315 |
> |
\end{figure} |
| 316 |
> |
|
| 317 |
> |
We chose to apply the $EmHad < 0.18 (0.1)$ requirement for barrel (endcap) |
| 318 |
> |
to the ``Simple Loose'' set (see Fig.~\ref{fig:EmHadIso}). The obtained selection |
| 319 |
> |
criteria is thus referred to as to ``Simple Tight''. Applying other ECAL or HCAL isolation |
| 320 |
> |
criteria on top of ``Simple Tight'' does not result in any substantial improvement |
| 321 |
> |
in performance. Thus, we believe that $EmHad$ and tracker isolation are sufficient |
| 322 |
> |
to identify the isolated electrons in the $p_T$ range of those from $W$ and $Z$ boson decays. |
| 323 |
|
|
| 324 |
|
\begin{figure}[!tb] |
| 325 |
|
\begin{center} |
| 326 |
|
\includegraphics[width=16cm]{Figs/EmHadIso.eps} |
| 327 |
|
\vspace{-10mm} |
| 328 |
< |
\caption{Upper plots represent the distribution of $Iso_{EmHad}$ for electrons and mis-identified jets in Barrel(left) and Endcap(right). Lower plots represent background efficiency $v.s.$ signal efficiency for this discriminator in Barrel(left) and Endcap(right). |
| 328 |
> |
\caption{$EmHad$ for electrons (solid blue line) and mis-identified jets (red dashed line) |
| 329 |
> |
in barrel (top left) and endcap (top right). The performance for the discriminator is given below |
| 330 |
> |
for barrel (bottom left) and endcap (bottom right). |
| 331 |
|
\label{fig:EmHadIso}} |
| 332 |
|
\end{center} |
| 333 |
|
\end{figure} |
| 334 |
|
|
| 335 |
|
|
| 336 |
+ |
\subsection{Summary of definitions of the ``Simple Loose'' and ``Simple Tight''} |
| 337 |
|
|
| 338 |
< |
%TABLE |
| 339 |
< |
|
| 340 |
< |
The table below table~\ref{tab:OurSelection} contains the threshold values and their corresponding efficiencies |
| 341 |
< |
on signal and background for barrel and endcap. We select electrons if its discriminators are less than |
| 342 |
< |
corresponding thresholds for all the cases except the criterion $E_{seed}/p_{out}$, when we require it to be more than |
| 343 |
< |
threshold. |
| 344 |
< |
|
| 345 |
< |
|
| 346 |
< |
|
| 347 |
< |
%\begin{table}[htb] |
| 348 |
< |
% \caption{Thresholds and efficinecy of the criteria.} |
| 349 |
< |
% \label{tab:DeltaEtaDeltaPhi} |
| 350 |
< |
% \begin{center} |
| 351 |
< |
% \begin{tabular}{|c|c|c|c|} \hline |
| 352 |
< |
% & Barrel & Endcap \\ \hline |
| 353 |
< |
% & $Thr$ & $Eff_{sig}$ & $Bkg_{bkg}$ & $Thr$ & $Eff_{sig}$ & $Bkg_{bkg}$ \\ \hline |
| 354 |
< |
%$\Delta\eta$ & 0.009 & ----- & ----- & 0.007 & ---- & ---- & \\ \hline |
| 355 |
< |
%$\Delta\phi$ & 0.005 & ----- & ----- & 0.005 & ---- & ---- & \\ \hline |
| 356 |
< |
% \end{tabular} |
| 357 |
< |
% \end{center} |
| 358 |
< |
% \end{table} |
| 359 |
< |
|
| 360 |
< |
|
| 361 |
< |
|
| 338 |
> |
To summarize the results, the ``Simple Loose'' criteria is a simple cut-based criteria |
| 339 |
> |
that utilize three discriminants from the official ``Robust'' ($\Delta\eta$, $\Delta\phi$, and |
| 340 |
> |
$\sigma_{\eta\eta}$), a modified variable from the ``Loose'' (a replacement of $E/p$ with |
| 341 |
> |
$E_{seed}/p_{out}$) and an additional track isolation requirement. The thresholds |
| 342 |
> |
have been also optimized to retain high signal efficiency. |
| 343 |
> |
|
| 344 |
> |
The ``Simple Tight'' requirement is ``Simple Loose'' with an addition of an effective |
| 345 |
> |
$H/E$ and ECAL+HCAL isolation requirement. |
| 346 |
> |
|
| 347 |
> |
We summarize the thresholds for barrel and endcap in Table~\ref{tab:OurSelection} |
| 348 |
> |
and proceed with detailed analysis of the performance in the next Section. |
| 349 |
> |
|
| 350 |
> |
\begin{table}[htb] |
| 351 |
> |
\caption{Thresholds and efficinecy of the criteria.} |
| 352 |
> |
\label{tab:OurSelection} |
| 353 |
> |
\begin{center} |
| 354 |
> |
\begin{tabular}{|c|c|c|} \hline |
| 355 |
> |
& Barrel threshold & Endcap \\ \hline |
| 356 |
> |
$\Delta\eta < $ & 0.009 & 0.007 \\ |
| 357 |
> |
$\Delta\phi < $ & 0.005 & 0.005 \\ |
| 358 |
> |
$\sigma_{\eta\eta} < $ & 0.012 & 0.026 \\ |
| 359 |
> |
$E_{seed}/p_{out} > $ & 0.9 & 0.9 \\ |
| 360 |
> |
$Iso^{trk}_{Norm} < $ & 0.1 & 0.2 \\ |
| 361 |
> |
$EmHad < $ & 0.18 & 0.1 \\ \hline |
| 362 |
> |
\end{tabular} |
| 363 |
> |
\end{center} |
| 364 |
> |
\end{table} |
| 365 |
|
|
| 270 |
– |
|
| 366 |
|
|
