| 28 |
|
a $\pi^0$ energy deposit in ECAL is not necessarily matched well with a GSF track, which |
| 29 |
|
is usually belong to a charged pion. Thus, a spatial match between a track and a SC can be a good |
| 30 |
|
discriminant. This match is described in azimuthal and pseudorapidity planes and denoted as |
| 31 |
< |
$\Delta_\phi$ and $\Delta_\eta$, respectively. |
| 31 |
> |
$\Delta\phi$ and $\Delta\eta$, respectively. |
| 32 |
|
|
| 33 |
|
\subsubsection{ECAL energy width} |
| 34 |
|
An electron brems extensively in CMS tracker, which results in a rather wide shower in azimuthal |
| 35 |
|
plane due to a strong CMS magnetic field. However, the width of a shower in pseudorapidity |
| 36 |
< |
plane remains very narrow and can discriminate against jets, which tend to have rather large |
| 37 |
< |
$\eta$ and $\phi$ energy widths. We consider two parameterization of the shower width: |
| 38 |
< |
the official one $\sigma_{\eta\eta} = \sqrt{CovEtaEta}$ which describes the width of the highest-energy |
| 39 |
< |
basic cluster of the SC, further referred to as a seed cluster, and an energy-weighted $\eta$-width of |
| 40 |
< |
the SC, defined as |
| 36 |
> |
plane remains very narrow and can discriminate against jets, which tend to create rather large |
| 37 |
> |
clusters in both $\eta$ and $\phi$ directions. We consider two parameterization of the shower width: |
| 38 |
> |
the one, used in official electron identification developed by egamma POG, $\sigma_{\eta\eta} = \sqrt{CovEtaEta}$ which describes the width of the highest-energy basic cluster of the SC, further referred |
| 39 |
> |
to as a seed cluster, and an energy-weighted width of SC in $\eta$ direction, defined as |
| 40 |
|
\begin{equation} |
| 41 |
|
\label{eq:etawidth} |
| 42 |
|
\sigma_\eta = \frac{1}{E_{SC}} \sqrt{\sum_{ECAL~SC~RecHits} E_i(\eta_i - \eta_{SC})^2}. |
| 43 |
|
\end{equation} |
| 44 |
|
|
| 45 |
|
\subsubsection{E/p-based variables} |
| 46 |
< |
Electrons should deposit all of their energy in the ECAL detector, thus the track momentum |
| 46 |
> |
Electron should deposit all of its energy in the ECAL detector, thus the track momentum |
| 47 |
|
at the outer edge of tracker $p_{out}$ should be of the same order as an energy of the seed EM |
| 48 |
< |
cluster $E_{seed}$ of the electron's SC. The em-content of a jet is carried mostly by neutral |
| 49 |
< |
pions which do not have much correlation to the momentum of charged particles in the vicinity. |
| 51 |
< |
Thus, a ratio $E_{seed}/p_{out}$ can be a good discriminant. We also considered an official |
| 52 |
< |
version of this discriminant $E_{SC}/p_{in}$, where $E_{SC}$ is a SC energy, and $p_{in}$ |
| 53 |
< |
is the initial momentum of a charged particle. |
| 48 |
> |
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. |
| 49 |
> |
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. |
| 50 |
|
|
| 51 |
|
\subsubsection{H/E variables} |
| 52 |
|
One can form a powerful discriminant by using the HCAL and ECAL energies associated |
| 53 |
|
with an electron candidate, as electrons tend to deposit very little or no energy in HCAL, |
| 54 |
< |
while jets produce a wide energy deposition in the HCAL. An official variable used in |
| 55 |
< |
``Robust" criteria is the ratio of HCAL and ECAL energies: $H/E$. It peaks around 0 for |
| 56 |
< |
electrons and can be quite large for em-jets. We also form a variable that also takes into |
| 57 |
< |
account the width of the HCAL energy deposition by making a ratio of the energy deposited |
| 54 |
> |
while jets produce a wide energy deposition in the HCAL. An variable used in official |
| 55 |
> |
``Robust" as well as ``Loose" and ``Tight" criteria is the ratio of HCAL and ECAL energies: $H/E$. |
| 56 |
> |
It peaks around 0 for electrons and can be quite large for em-jets. We form a variable that also |
| 57 |
> |
takes into account the width of the HCAL energy deposition by making a ratio of the energy deposited |
| 58 |
|
in HCAL and ECAL in the cone of $\Delta R < 0.3$ which is not included in the SC, normalized |
| 59 |
|
to the SC energy as follows |
| 60 |
|
|
| 61 |
|
\begin{equation} |
| 62 |
|
\label{eq:emhad} |
| 63 |
< |
EMHAD =\frac{1}{E_{SC}}\left(\sum_{\Delta R=0.3}E^{ecal}_{RecHit} + |
| 63 |
> |
Iso_{EmHad} =\frac{1}{E_{SC}}\left(\sum_{\Delta R=0.3}E^{ecal}_{RecHit} + |
| 64 |
|
\sum_{\Delta R=0.3}E^{hcal}_{RecHit} - E_{SC}\right). |
| 65 |
|
\end{equation} |
| 66 |
|
|
| 82 |
|
Iso_{trk} = \sum_{\Delta R=0.3} p_T(trk) - \sum_{\Delta R=0.05} p_T(trk). |
| 83 |
|
\end{equation} |
| 84 |
|
|
| 85 |
< |
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} |
| 85 |
> |
%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 |
| 100 |
|
|
| 101 |
|
|
| 102 |
|
\subsection{Optimization method and strategy} |
| 103 |
< |
We start building the ``Loose" electron criteria based on the discriminants utilized in the official |
| 103 |
> |
We start building the ``Simple Loose" electron criteria based on the discriminants utilized in the official |
| 104 |
|
``Robust'' and adding more variables from the ``Loose" criteria (or their more powerful variants described |
| 105 |
|
above), and tuning the threshold to keep the efficiency of each criterion to be |
| 106 |
< |
above 99\%. A similar optimization is done for the ``Tight" requirements, although, the efficiency |
| 107 |
< |
was not required to exceed 99\% for the a given criterion. Instead, we vary the thresholds and plot |
| 108 |
< |
signal efficiency $v.s.$ background efficiency and find a region in the plot that is closest to the |
| 109 |
< |
``perfect" performance corner that has 100\% signal and 0\% background efficiencies. |
| 106 |
> |
above 99\%. ``Simple Tight'' selection is developed for selection electrons coming from $W$ boson. In order |
| 107 |
> |
to keep the whole selection robust and avoid many different thresholds and reduce source of systematic |
| 108 |
> |
uncertainties we define ``Simple Tight'' based on ``Simple Loose'' with one addition discriminator. |
| 109 |
> |
%A similar optimization is done for the ``Simple Tight" requirements, although, the efficiency |
| 110 |
> |
%was not required to exceed 99\% for the a given criterion. Instead, |
| 111 |
> |
To pick up the threshold for the tight criterion we plot signal efficiency $v.s.$ background efficiency |
| 112 |
> |
and find a region in the plot that is closest to the ``perfect" performance corner that has 100\% signal |
| 113 |
> |
and 0\% background efficiencies. |
| 114 |
|
|
| 115 |
|
We study the performance of the requirements by applying them in sequential order, starting |
| 116 |
|
with the most simple and robust, and continuing to more complex |
| 117 |
|
ones. We also study the correlation between variables by changing the order they are |
| 118 |
|
applied to see if some of the variables are completely correlated with the others and can |
| 119 |
|
be omitted. |
| 120 |
+ |
Electrons reconstructed in barrel and endcap of electronmagnetic calorimeter are considered seperately. |
| 121 |
+ |
WZ signal samples are used as a source of real electrons and multijet samples from ``Gumbo soup'' are used as |
| 122 |
+ |
a source of em-jets. |
| 123 |
+ |
|
| 124 |
+ |
\subsection{Tuning ``Simple Loose" criteria} |
| 125 |
+ |
Tunning of ``WZ Loose'' critaria is described below. |
| 126 |
+ |
As mentioned above, we start from the variables used within ``Robust'' selection and studying their performance |
| 127 |
+ |
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. |
| 130 |
+ |
|
| 131 |
+ |
\begin{figure}[tb] |
| 132 |
+ |
\begin{center} |
| 133 |
+ |
\includegraphics[width=16cm]{Figs/deltaEta.eps} |
| 134 |
+ |
\vspace{-10mm} |
| 135 |
+ |
\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). |
| 136 |
+ |
\label{fig:DeltaEta}} |
| 137 |
+ |
\end{center} |
| 138 |
+ |
\end{figure} |
| 139 |
+ |
|
| 140 |
+ |
|
| 141 |
+ |
\begin{figure}[tb] |
| 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). |
| 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}. |
| 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. |
| 160 |
+ |
\label{fig:SigmaEE_vs_EtaWidth}} |
| 161 |
+ |
\end{center} |
| 162 |
+ |
\end{figure} |
| 163 |
+ |
|
| 164 |
+ |
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}. |
| 165 |
+ |
|
| 166 |
+ |
\begin{figure}[tb] |
| 167 |
+ |
\begin{center} |
| 168 |
+ |
\includegraphics[width=16cm]{Figs/Eff_EtaWidth_SigmaEtaEta.eps} |
| 169 |
+ |
\vspace{-10mm} |
| 170 |
+ |
\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). |
| 171 |
+ |
\label{fig:SigmaEtaEta}} |
| 172 |
+ |
\end{center} |
| 173 |
+ |
\end{figure} |
| 174 |
+ |
|
| 175 |
+ |
|
| 176 |
+ |
These three discriminants are the same as used in official ``Robust'', ``Loose'' or ``Tight'' selections. |
| 177 |
+ |
For utilizing matching of energy/momentum from ECAL and tracker two variables are studied: $E_{seed}/p_{out}$ and $E/p$, |
| 178 |
+ |
where the latter one is used in official ``Loose'' and ``Tight'' selection to categorize electons on $E/p$ $v.s.$ $fbrem$ |
| 179 |
+ |
plane. Here $fbrem$ is defined as $(p_{in}-p_{out})/p_{in}$, where $p_{in}$ and $p_{out}$ are momenta measured at the |
| 180 |
+ |
inner and outer edge of tracker respectively. Comparison the signal $v.s.$ background efficiency for these two options |
| 181 |
+ |
is shown in figure ~\ref{fig:EseedOPout_vs_EoP}. |
| 182 |
+ |
|
| 183 |
+ |
|
| 184 |
+ |
\begin{figure}[tb] |
| 185 |
+ |
\begin{center} |
| 186 |
+ |
\includegraphics[width=16cm]{Figs/Eff_EoP_EseedoPout.eps} |
| 187 |
+ |
\vspace{-10mm} |
| 188 |
+ |
\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. |
| 189 |
+ |
\label{fig:EseedOPout_vs_EoP}} |
| 190 |
+ |
\end{center} |
| 191 |
+ |
\end{figure} |
| 192 |
+ |
|
| 193 |
+ |
|
| 194 |
+ |
$E_{seed}/p_{out}$ is included as another criterion in ``Simple Loose'' selection. Its distribution both in barrel |
| 195 |
+ |
and endcap is shown on figure ~\ref{fig:EseedOPout} |
| 196 |
+ |
|
| 197 |
+ |
\begin{figure}[tb] |
| 198 |
+ |
\begin{center} |
| 199 |
+ |
\includegraphics[width=16cm]{Figs/EseedPout.eps} |
| 200 |
+ |
\vspace{-10mm} |
| 201 |
+ |
\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). |
| 202 |
+ |
\label{fig:EseedOPout}} |
| 203 |
+ |
\end{center} |
| 204 |
+ |
\end{figure} |
| 205 |
+ |
|
| 206 |
+ |
|
| 207 |
+ |
In order to select isolated electron candidates we use track isolation. As mentioned in section 4.1.5 we |
| 208 |
+ |
study both normalized and non-normalized definition of it. We compare which one of the two definitions allow |
| 209 |
+ |
us better identify real electrons from em-jets, figure ~\ref{fig:TrkIso_no_vs_norm} |
| 210 |
+ |
|
| 211 |
+ |
|
| 212 |
+ |
\begin{figure}[tb] |
| 213 |
+ |
\begin{center} |
| 214 |
+ |
\includegraphics[width=16cm]{Figs/Eff_trkISoNonNorm_trkIsoNorm.eps} |
| 215 |
+ |
\vspace{-10mm} |
| 216 |
+ |
\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. |
| 217 |
+ |
\label{fig:TrkIso_no_vs_norm}} |
| 218 |
+ |
\end{center} |
| 219 |
+ |
\end{figure} |
| 220 |
+ |
|
| 221 |
+ |
|
| 222 |
+ |
We keep isolation defined as ~\ref{eq:trkIsoN} in ``Simple Loose'' selection. |
| 223 |
+ |
|
| 224 |
+ |
|
| 225 |
+ |
\subsection{Tuning ``Simple Tight" criteria} |
| 226 |
+ |
As mentioned in section 4.2 we stydy another isolation variable, using the information from ECAL and HCAL, in order |
| 227 |
+ |
to reject higher fraction of em-jets which can easily mimic electron from $W$ boson decay. The comparison is done |
| 228 |
+ |
between $H/E$ and $Iso_{EmHad}$ ($Sec 4.1.4$) variables and their discrimination power. First obsetvarion is that there |
| 229 |
+ |
is clear correlation between them, once $Iso_{EmHad}$ discriminator is applied to select elctrons the efficiency of |
| 230 |
+ |
$H/E$ variable to reject em-jets is hardly a few \%. Also the study has shown that isoaltion variable is more effecient |
| 231 |
+ |
in selecting real electrons than $H/E$. Thus we keep $Iso_{EmHad}$ as the additional criterion for ``Simple Tight'' |
| 232 |
+ |
selection. Its istribution is presented on figure ~\ref{fig:EmHadIso} |
| 233 |
+ |
|
| 234 |
+ |
\begin{figure}[tb] |
| 235 |
+ |
\begin{center} |
| 236 |
+ |
\includegraphics[width=16cm]{Figs/EmHadIso.eps} |
| 237 |
+ |
\vspace{-10mm} |
| 238 |
+ |
\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). |
| 239 |
+ |
\label{fig:EmHadIso}} |
| 240 |
+ |
\end{center} |
| 241 |
+ |
\end{figure} |
| 242 |
+ |
|
| 243 |
+ |
|
| 244 |
+ |
|
| 245 |
+ |
%TABLE |
| 246 |
+ |
|
| 247 |
+ |
The table below table~\ref{tab:OurSelection} contains the threshold values and their corresponding efficiencies |
| 248 |
+ |
on signal and background for barrel and endcap. We select electrons if its discriminators are less than |
| 249 |
+ |
corresponding thresholds for all the cases except the criterion $E_{seed}/p_{out}$, when we require it to be more than |
| 250 |
+ |
threshold. |
| 251 |
+ |
|
| 252 |
+ |
|
| 253 |
+ |
|
| 254 |
+ |
%\begin{table}[htb] |
| 255 |
+ |
% \caption{Thresholds and efficinecy of the criteria.} |
| 256 |
+ |
% \label{tab:DeltaEtaDeltaPhi} |
| 257 |
+ |
% \begin{center} |
| 258 |
+ |
% \begin{tabular}{|c|c|c|c|} \hline |
| 259 |
+ |
% & Barrel & Endcap \\ \hline |
| 260 |
+ |
% & $Thr$ & $Eff_{sig}$ & $Bkg_{bkg}$ & $Thr$ & $Eff_{sig}$ & $Bkg_{bkg}$ \\ \hline |
| 261 |
+ |
%$\Delta\eta$ & 0.009 & ----- & ----- & 0.007 & ---- & ---- & \\ \hline |
| 262 |
+ |
%$\Delta\phi$ & 0.005 & ----- & ----- & 0.005 & ---- & ---- & \\ \hline |
| 263 |
+ |
% \end{tabular} |
| 264 |
+ |
% \end{center} |
| 265 |
+ |
% \end{table} |
| 266 |
+ |
|
| 267 |
+ |
|
| 268 |
+ |
|
| 269 |
|
|
| 121 |
– |
\subsection{Tuning ``Loose" criteria} |
| 122 |
– |
\subsection{Tuning ``Tight" criteria} |
| 270 |
|
|
| 271 |
|
|
