| 1 |
Electron is identified by combining information from the CMS
|
| 2 |
tracker and ECAL. Our initial (preselection) requirement is that
|
| 3 |
the electron candidate in addition to the kinematics criteria
|
| 4 |
described in the Section above, is also identified as a GSF electron,
|
| 5 |
{\it i.e.}, it has a GSF track matched with the ECAL Super Cluster (SC).
|
| 6 |
The efficiency of the selection criteria is measured with respect
|
| 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.
|
| 11 |
This can be achieved by optimizing the thresholds, optimizing the
|
| 12 |
discriminants that have more background rejection power, and selecting
|
| 13 |
the variables that are not highly correlated with each other.
|
| 14 |
The latter allows keeping the number of variables in the criteria to a
|
| 15 |
minimum, which results in a simpler set of requirements with smaller
|
| 16 |
systematic uncertainties, and thus more robust in the startup conditions.
|
| 17 |
|
| 18 |
Variables that allow discriminating electrons from em-jets can be roughly
|
| 19 |
divided into two classes: matching/shower-shape and isolation
|
| 20 |
discriminants. In the following we treat these two classes separately to
|
| 21 |
follow the existing egamma POG identification scheme. The variables are
|
| 22 |
described in the next two subsections.
|
| 23 |
|
| 24 |
\subsection{Identification variables}
|
| 25 |
\label{ss:matching}
|
| 26 |
\subsubsection{Track-ECAL matching}
|
| 27 |
An electron GSF track should be well-matched to the ECAL Super Cluster (SC), while
|
| 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.
|
| 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
|
| 41 |
\begin{equation}
|
| 42 |
\label{eq:etawidth}
|
| 43 |
\sigma_\eta = \frac{1}{E_{SC}} \sqrt{\sum_{ECAL~SC~RecHits} E_i(\eta_i - \eta_{SC})^2}.
|
| 44 |
\end{equation}
|
| 45 |
|
| 46 |
\subsubsection{E/p-based variables}
|
| 47 |
Electrons should deposit all of their energy in the ECAL detector, thus the track momentum
|
| 48 |
at the outer edge of tracker $p_{out}$ should be of the same order as an energy of the seed EM
|
| 49 |
cluster $E_{seed}$ of the electron's SC. The em-content of a jet is carried mostly by neutral
|
| 50 |
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.
|
| 54 |
|
| 55 |
\subsubsection{H/E variables}
|
| 56 |
One can form a powerful discriminant by using the HCAL and ECAL energies associated
|
| 57 |
with an electron candidate, as electrons tend to deposit very little or no energy in HCAL,
|
| 58 |
while jets produce a wide energy deposition in the HCAL. An official variable used in
|
| 59 |
``Robust" criteria is the ratio of HCAL and ECAL energies: $H/E$. It peaks around 0 for
|
| 60 |
electrons and can be quite large for em-jets. We also form a variable that also takes into
|
| 61 |
account the width of the HCAL energy deposition by making a ratio of the energy deposited
|
| 62 |
in HCAL and ECAL in the cone of $\Delta R < 0.3$ which is not included in the SC, normalized
|
| 63 |
to the SC energy as follows
|
| 64 |
|
| 65 |
\begin{equation}
|
| 66 |
\label{eq:emhad}
|
| 67 |
EMHAD =\frac{1}{E_{SC}}\left(\sum_{\Delta R=0.3}E^{ecal}_{RecHit} +
|
| 68 |
\sum_{\Delta R=0.3}E^{hcal}_{RecHit} - E_{SC}\right).
|
| 69 |
\end{equation}
|
| 70 |
|
| 71 |
\subsubsection{Track isolation requirements}
|
| 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:
|
| 76 |
|
| 77 |
\begin{equation}
|
| 78 |
\label{eq:trkIsoN}
|
| 79 |
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 |
\end{equation}
|
| 81 |
|
| 82 |
and non-normalized version of the above:
|
| 83 |
|
| 84 |
\begin{equation}
|
| 85 |
\label{eq:trkIso}
|
| 86 |
Iso_{trk} = \sum_{\Delta R=0.3} p_T(trk) - \sum_{\Delta R=0.05} p_T(trk).
|
| 87 |
\end{equation}
|
| 88 |
|
| 89 |
We also test the track isolation discriminant defined within electroweak group:
|
| 90 |
\begin{equation}
|
| 91 |
\label{eq:trkIsoEWK}
|
| 92 |
Iso_{trk}(EWK) = \sum_{\Delta R = 0.6} p_T(trk) - \sum_{\Delta R = 0.02} p_T(trk).
|
| 93 |
\end{equation}
|
| 94 |
|
| 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.
|
| 104 |
|
| 105 |
|
| 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.
|
| 120 |
|
| 121 |
\subsection{Tuning ``Loose" criteria}
|
| 122 |
\subsection{Tuning ``Tight" criteria}
|
| 123 |
|
| 124 |
|
