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#	Line 7 | Line 7 | The efficiency of the selection criteria
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.
#	Line 26 | Line 27 | described in the next two subsections.
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.
32	>	$\Delta\phi$ and $\Delta\eta$, respectively.
33
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 have rather large
39	<	$\eta$ and $\phi$ energy widths. We consider two parameterization of the shower width:
40	<	the official one $\sigma_{\eta\eta} = \sqrt{CovEtaEta}$ which describes the width of the highest-energy
41	<	basic cluster of the SC, further referred to as a seed cluster, and an energy-weighted $\eta$-width of
40	<	the SC, defined as
38	>	plane remains very narrow and can discriminate against jets, which tend to create rather large
39	>	clusters in both $\eta$ and $\phi$ directions. We consider two parameterization of the shower width:
40	>	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
41	>	to as a seed cluster, and an energy-weighted width of SC in $\eta$ direction, defined as
42		\begin{equation}
43		\label{eq:etawidth}
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	<	Electrons should deposit all of their energy in the ECAL detector, thus the track momentum
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 $E_{seed}$ of the electron's SC.  The em-content of a jet is carried mostly by neutral
52	<	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.
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 official variable used in
58	<	``Robust" criteria is the ratio of HCAL and ECAL energies: $H/E$. It peaks around 0 for
59	<	electrons and can be quite large for em-jets. We also form a variable that also takes into
60	<	account the width of the HCAL energy deposition by making a ratio of the energy deposited
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
61		in HCAL and ECAL in the cone of $\Delta R < 0.3$ which is not included in the SC, normalized
62		to the SC energy as follows
63
64		\begin{equation}
65		\label{eq:emhad}
66	<	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 defined within electroweak group:
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).
95	>	Iso^{trk}_{EWK} = \sum_{\Delta R = 0.6} p_T(trk) - \sum_{\Delta R = 0.02} p_T(trk).
96		\end{equation}
97
95	–	%\subsubsection{ECAL and HCAL isolation requirements}
96	–	%We also consider a few ECAL
97	–	%
98	–	%In order to discriminate electron from em-jet isolation variable defined using both ECAL and HCAL is used.
99	–	%Jet deposit high fraction of its energy in HCAL and much less in ECAL. While electron deposits all its energy in ECAL
100	–	%with very small hadronic fraction, unless it is very energetic when longitudinal energy leakage appears.
101	–	%Isolation variable, defined as Eq.~\ref{eq:3}, is very similar by the content to the variable $H/E$,
102	–	%ratio of energy deposited HCAL behind the SC over the SC energy, which is used in official egamma POG
103	–	%electron identification criteria.
98
99
106	–	\subsection{Optimization method and strategy}
107	–	We start building the ``Loose" electron criteria based on the discriminants utilized in the official
108	–	``Robust'' and adding more variables from the ``Loose" criteria (or their more powerful variants described
109	–	above), and tuning the threshold to keep the efficiency of each criterion to be
110	–	above 99\%. A similar optimization is done for the ``Tight" requirements, although, the efficiency
111	–	was not required to exceed 99\% for the a given criterion. Instead, we vary the thresholds and plot
112	–	signal efficiency $v.s.$ background efficiency and find a region in the plot that is closest to the
113	–	``perfect" performance corner that has 100\% signal 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.
100
101	<	\subsection{Tuning ``Loose" criteria}
102	<	\subsection{Tuning ``Tight" criteria}
101	>	\subsection{Optimization method and strategy}
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{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}
139	>
140	>
141	>	\begin{figure}[!tb]
142	>	\begin{center}
143	>	\includegraphics[width=16cm]{Figs/deltaPhi.eps}
144	>	\vspace{-10mm}
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	>	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{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, 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/sigmaEtaEta.eps}
175	>	\vspace{-10mm}
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	>	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{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	>	$E_{seed}/p_{out}$ 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{$E_{seed}/p_{out}$ 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	>	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_trkIsoEWK.eps}
245	>	\vspace{-10mm}
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	>	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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	>	\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{$EmHad$ 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	+	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	+
366

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