-- KamalBenslama - 20 Aug 2005

Electron ID Using Multivariate Techniques

Likelihood Method

Introduction

We present a likelihood function to discriminate between clusters in the electromagnetic calorimeter originating from electrons and those from other processes. The performance of the method is evaluated using release 14.2.20 of the ATLAS reconstruction software. The reference figures and tables for efficiencies and rejections against jets are described, based on the MC08 simulated data samples.

Discriminating variables

The variables used as input to the likelihood method are described below and have been evaluated for both signal electrons from $ Z\rightarrow ee$ decay and fake electrons selected from a QCD di-jets sample.

  • $ F^{0}$ Energy fraction deposited in the presampler.
  • $ F^{1}$ Energy fraction deposited in the first sampling of EM.
  • $ F^{2} :$ Energy fraction deposited in the second sampling of EM.
  • $ F^{3} :$ Energy fraction deposited in the third sampling of EM.

  • $\frac{E_{t}Cone40}{E_{T}} :$ Ratio of transverse energy in a cone of size $\Delta $ R = 0.4 to the total cluster transverse energy.

  • $\frac{E237}{E277} :$ Ratio in $\eta$ of cell energies in 3X7 versus 7X7 in the second sampling.

  • $\frac{E233}{E277} :$ Ratio in $\phi$ of cell energies in 3X7 versus 7X7 in the second sampling.

  • $\frac{E_{T}}{E_{T}+E_{T}^{had1}} :$ transverse electromagnetic fraction.

  • $\frac{E_{T}}{P_{T}} :$ Ratio of the cluster's measured transverse energy to the track's measured transverse momentum.

  • $\Delta \eta :$ Distance in $ \eta $ between the cluster and its extrapolated track.
  • $\Delta \phi :$ Distance in $ \phi $ between the cluster and its extrapolated track.
  • $\frac{Z_{vertex}}{\sigma Z} :$ Ratio of Z position of the vertex reconstructed from the cluster to its standard deviation.
  • $W_{\eta 1} :$ Shower width using three strips around the one with the maximal energy deposit.
  • $hTRT:$ Number of TRT high threshold hits
  • $W_{\eta 2} :$ Corrected width using three strips around the one with the maximal energy deposit.
  • $\Delta E_{s 1} :$ difference between the energy of the cell corresponding to second energy maximum in the first sampling and energy reconstructed in the strip with the minimal value between the first and second maximum.
  • $\sum P_{T}^{Smallcone} :$ sum $P_{T}$ of tracks in a small cone of size 0.05.
  • $\sum P_{T}^{Largecone} :$ sum $P_{T}$ of tracks in a large cone of size 0.5.

Formulation of the Likelihood

Each of the variables described above is obtained from the signal and background samples in several eta bins. Only one $ E_{T}$ bin has been used so far (ET > 17 GeV). These distributions have been normalized to unit area to produce the probability distributions for each variable. Then these distributions are used to assign a probability for a given EM object to be signal or background:

\[ P_{sig}(x),P_{bak}(x) \]

Where x is a vector of likelihood variables. That is, each likelihood variable for the object is given a probability to be signal or background from the probability distributions. Then by neglecting correlation between the variables, these individual probabilities are multiplied together to give an overall probability for the event:

\[ P(x)=\prod\limits_{i}P(i_{x}) \]

Finally, to distinguish electrons from background objects, the following discriminant is used:

\[ L(x)=\log_{10}\frac{P_{sig}(x)}{p_{bkg}(x)}\]

Reference plots

In this section, we show the likelihood output for signal electrons (from Z boson) and for fake electrons (from QCD jets), in several ${\eta}$ bins and in the full ${\eta}$ range

${\eta}$ range likelihood ${\eta}$ range likelihood
${\mid\eta\mid<2.47}$ e_lval ${\mid\eta\mid<0.8}$ e_lval
${0.8< \mid\eta\mid <1.35}$ e_lval ${1.35< \mid\eta\mid <1.5}$ e_lval
${1.5< \mid\eta\mid <1.8}$ e_lval ${1.8< \mid\eta\mid <2.0}$ e_lval
${2.0< \mid\eta\mid <2.3}$ e_lval ${2.3< \mid\eta\mid <2.47}$ e_lval

Performance Studies using $ Z\rightarrow ee$ events and QCD dijets events (JF17)

These plots show the rejection versus efficiency obtained using the likelihood method, compared to the results obtained using the two set of cuts (tight and tight (NoIsol))

${\eta}$ range rejection vs efficiency ${\eta}$ range rejection vs efficiency
${\mid\eta\mid <2.47}$ e_lval ${\mid\eta\mid <0.8}$ e_lval
${0.8< \mid\eta\mid <1.35}$ e_lval ${1.35<\mid\eta\mid<1.5}$ e_lval
${1.5<\mid\eta\mid<1.8}$ e_lval ${1.8<\mid\eta\mid<2.0}$ e_lval
${2.0<\mid\eta\mid<2.3}$ e_lval ${2.3<\mid\eta\mid<2.47}$ e_lval

Performance Studies in $ Z\rightarrow ee$, $ W\rightarrow e\nu$, Top, $ Z'\rightarrow ee$, $ W'\rightarrow e/\mu/\tau \nu$, and SU1

name reference name reference
SU1 e_lval T1 e_lval
Wenu e_lval W' e_lval
Zee e_lval Z' e_lval

Likelihood Thresholds and their corresponding efficiencies and fake rates

${{\footnotesize \begin{singlespace} \begin{longtable} \hline Cut             &amp; Efficiency (\%)        &amp; Rejection \\ \hline \caption{$0 <\mid \eta \mid < 0.8$.} \hline\hline \multicolumn{3}{$0 <\mid \eta \mid < 0.8$} \\ \hline . \\ -0.8 &amp; $ 91.0 \pm 0.1 $ &amp; $ \E{( 206.5 \pm 6.4 )}\times 10^{ 2 }$ \\ 1.2 &amp; $ 90.0 \pm 0.1 $ &amp; $ \E{( 38.7 \pm 1.7 )}\times 10^{ 3 }$ \\ 2.2 &amp; $ 89.0 \pm 0.1 $ &amp; $ \E{( 54.8 \pm 2.8 )}\times 10^{ 3 }$ \\ 2.8 &amp; $ 88.1 \pm 0.1 $ &amp; $ \E{( 70.0 \pm 4.0 )}\times 10^{ 3 }$ \\ 3.4 &amp; $ 87.0 \pm 0.1 $ &amp; $ \E{( 90.9 \pm 5.9 )}\times 10^{ 3 }$ \\ 3.8 &amp; $ 86.0 \pm 0.1 $ &amp; $ \E{( 111.4 \pm 8.1 )}\times 10^{ 3 }$ \\ 4.0 &amp; $ 85.4 \pm 0.1 $ &amp; $ \E{( 120.2 \pm 9.0 )}\times 10^{ 3 }$ \\ 4.2 &amp; $ 84.7 \pm 0.1 $ &amp; $ \E{( 13.0 \pm 1.0 )}\times 10^{ 4 }$ \\ 4.4 &amp; $ 84.1 \pm 0.1 $ &amp; $ \E{( 14.2 \pm 1.2 )}\times 10^{ 4 }$ \\ 4.6 &amp; $ 83.4 \pm 0.1 $ &amp; $ \E{( 16.5 \pm 1.5 )}\times 10^{ 4 }$ \\ 4.8 &amp; $ 82.6 \pm 0.1 $ &amp; $ \E{( 18.7 \pm 1.8 )}\times 10^{ 4 }$ \\ 5.0 &amp; $ 81.7 \pm 0.1 $ &amp; $ \E{( 21.5 \pm 2.2 )}\times 10^{ 4 }$ \\ 5.2 &amp; $ 80.7 \pm 0.1 $ &amp; $ \E{( 25.0 \pm 2.7 )}\times 10^{ 4 }$ \\ 5.4 &amp; $ 79.6 \pm 0.1 $ &amp; $ \E{( 28.0 \pm 3.2 )}\times 10^{ 4 }$ \\ 5.6 &amp; $ 78.5 \pm 0.1 $ &amp; $ \E{( 32.7 \pm 4.1 )}\times 10^{ 4 }$ \\ 5.8 &amp; $ 77.3 \pm 0.2 $ &amp; $ \E{( 36.7 \pm 4.8 )}\times 10^{ 4 }$ \\ 6.0 &amp; $ 76.1 \pm 0.2 $ &amp; $ \E{( 43.4 \pm 6.2 )}\times 10^{ 4 }$ \\ 6.2 &amp; $ 74.7 \pm 0.2 $ &amp; $ \E{( 54.5 \pm 8.7 )}\times 10^{ 4 }$ \\ 6.4 &amp; $ 73.2 \pm 0.2 $ &amp; $ \E{( 6.3 \pm 1.1 )}\times 10^{ 5 }$ \\ 6.6 &amp; $ 71.7 \pm 0.2 $ &amp; $ \E{( 7.3 \pm 1.4 )}\times 10^{ 5 }$ \\ 6.8 &amp; $ 70.1 \pm 0.2 $ &amp; $ \E{( 8.5 \pm 1.7 )}\times 10^{ 5 }$ \\ 7.0 &amp; $ 68.4 \pm 0.2 $ &amp; $ \E{( 8.5 \pm 1.7 )}\times 10^{ 5 }$ \\ \hline \end{longtable} \end{singlespace} } % end footnotesize}$ ${{\footnotesize \begin{singlespace} \begin{longtable} \hline Cut             &amp; Efficiency (\%)        &amp; Rejection \\ \hline \caption{$0.8< \mid \eta \mid < 1.35$} \hline \multicolumn{3}{$0.8 < \mid \eta \mid < 1.35$} \\ \hline . \\ -2.8 &amp; $ 86.0 \pm 0.2 $ &amp; $ \E{( 76.2 \pm 1.8 )}\times 10^{ 2 }$ \\ 0.8 &amp; $ 85.1 \pm 0.2 $ &amp; $ \E{( 219.1 \pm 8.8 )}\times 10^{ 2 }$ \\ 2.0 &amp; $ 84.1 \pm 0.2 $ &amp; $ \E{( 30.8 \pm 1.5 )}\times 10^{ 3 }$ \\ 2.8 &amp; $ 83.1 \pm 0.2 $ &amp; $ \E{( 41.3 \pm 2.3 )}\times 10^{ 3 }$ \\ 3.2 &amp; $ 82.4 \pm 0.2 $ &amp; $ \E{( 47.4 \pm 2.8 )}\times 10^{ 3 }$ \\ 4.0 &amp; $ 80.5 \pm 0.2 $ &amp; $ \E{( 66.9 \pm 4.7 )}\times 10^{ 3 }$ \\ 4.4 &amp; $ 79.1 \pm 0.2 $ &amp; $ \E{( 83.5 \pm 6.6 )}\times 10^{ 3 }$ \\ 4.6 &amp; $ 78.4 \pm 0.2 $ &amp; $ \E{( 94.7 \pm 8.0 )}\times 10^{ 3 }$ \\ 4.8 &amp; $ 77.5 \pm 0.2 $ &amp; $ \E{( 104.3 \pm 9.2 )}\times 10^{ 3 }$ \\ 5.0 &amp; $ 76.4 \pm 0.2 $ &amp; $ \E{( 11.6 \pm 1.1 )}\times 10^{ 4 }$ \\ 5.2 &amp; $ 75.4 \pm 0.2 $ &amp; $ \E{( 13.1 \pm 1.3 )}\times 10^{ 4 }$ \\ 5.4 &amp; $ 74.2 \pm 0.2 $ &amp; $ \E{( 14.3 \pm 1.5 )}\times 10^{ 4 }$ \\ 5.6 &amp; $ 73.0 \pm 0.2 $ &amp; $ \E{( 16.4 \pm 1.8 )}\times 10^{ 4 }$ \\ 5.8 &amp; $ 71.7 \pm 0.2 $ &amp; $ \E{( 18.7 \pm 2.2 )}\times 10^{ 4 }$ \\ 6.0 &amp; $ 70.2 \pm 0.2 $ &amp; $ \E{( 21.0 \pm 2.6 )}\times 10^{ 4 }$ \\ 6.2 &amp; $ 68.5 \pm 0.2 $ &amp; $ \E{( 23.6 \pm 3.1 )}\times 10^{ 4 }$ \\ 6.4 &amp; $ 66.6 \pm 0.2 $ &amp; $ \E{( 28.6 \pm 4.2 )}\times 10^{ 4 }$ \\ 6.6 &amp; $ 64.7 \pm 0.2 $ &amp; $ \E{( 32.0 \pm 4.9 )}\times 10^{ 4 }$ \\ 6.8 &amp; $ 62.6 \pm 0.2 $ &amp; $ \E{( 37.4 \pm 6.2 )}\times 10^{ 4 }$ \\ 7.0 &amp; $ 60.4 \pm 0.2 $ &amp; $ \E{( 40.8 \pm 7.1 )}\times 10^{ 4 }$ \\ \hline \end{longtable} \end{singlespace} } % end footnotesize}$
${{\footnotesize \begin{singlespace} \begin{longtable} \hline Cut             &amp; Efficiency (\%)        &amp; Rejection \\ \hline \caption{$1.35 < \mid \eta \mid < 1.5$.} \hline\hline \multicolumn{3}{$1.35 < \mid \eta \mid < 1.5$} \\ \hline . \\ -1.0 &amp; $ 81.0 \pm 0.3 $ &amp; $ \E{( 48.7 \pm 1.8 )}\times 10^{ 2 }$ \\ -0.2 &amp; $ 80.3 \pm 0.3 $ &amp; $ \E{( 69.7 \pm 3.1 )}\times 10^{ 2 }$ \\ 0.4 &amp; $ 79.3 \pm 0.3 $ &amp; $ \E{( 92.5 \pm 4.8 )}\times 10^{ 2 }$ \\ 0.8 &amp; $ 78.5 \pm 0.3 $ &amp; $ \E{( 114.7 \pm 6.6 )}\times 10^{ 2 }$ \\ 1.2 &amp; $ 77.2 \pm 0.4 $ &amp; $ \E{( 147.7 \pm 9.7 )}\times 10^{ 2 }$ \\ 1.4 &amp; $ 76.5 \pm 0.4 $ &amp; $ \E{( 16.8 \pm 1.2 )}\times 10^{ 3 }$ \\ 1.6 &amp; $ 75.6 \pm 0.4 $ &amp; $ \E{( 19.1 \pm 1.4 )}\times 10^{ 3 }$ \\ 1.8 &amp; $ 74.5 \pm 0.4 $ &amp; $ \E{( 21.0 \pm 1.6 )}\times 10^{ 3 }$ \\ 2.0 &amp; $ 73.4 \pm 0.4 $ &amp; $ \E{( 23.1 \pm 1.9 )}\times 10^{ 3 }$ \\ 2.2 &amp; $ 72.0 \pm 0.4 $ &amp; $ \E{( 24.6 \pm 2.1 )}\times 10^{ 3 }$ \\ 2.4 &amp; $ 70.7 \pm 0.4 $ &amp; $ \E{( 29.7 \pm 2.8 )}\times 10^{ 3 }$ \\ 2.6 &amp; $ 69.2 \pm 0.4 $ &amp; $ \E{( 35.5 \pm 3.6 )}\times 10^{ 3 }$ \\ 2.8 &amp; $ 67.3 \pm 0.4 $ &amp; $ \E{( 42.0 \pm 4.6 )}\times 10^{ 3 }$ \\ 3.0 &amp; $ 65.5 \pm 0.4 $ &amp; $ \E{( 46.5 \pm 5.4 )}\times 10^{ 3 }$ \\ 3.2 &amp; $ 63.4 \pm 0.4 $ &amp; $ \E{( 52.9 \pm 6.6 )}\times 10^{ 3 }$ \\ 3.4 &amp; $ 61.1 \pm 0.4 $ &amp; $ \E{( 7.0 \pm 1.0 )}\times 10^{ 4 }$ \\ 3.6 &amp; $ 58.7 \pm 0.4 $ &amp; $ \E{( 8.0 \pm 1.2 )}\times 10^{ 4 }$ \\ 3.8 &amp; $ 56.1 \pm 0.4 $ &amp; $ \E{( 11.1 \pm 2.0 )}\times 10^{ 4 }$ \\ 4.0 &amp; $ 53.4 \pm 0.4 $ &amp; $ \E{( 14.3 \pm 2.9 )}\times 10^{ 4 }$ \\ 4.2 &amp; $ 50.5 \pm 0.4 $ &amp; $ \E{( 18.1 \pm 4.2 )}\times 10^{ 4 }$ \\ 4.4 &amp; $ 47.3 \pm 0.4 $ &amp; $ \E{( 21.5 \pm 5.4 )}\times 10^{ 4 }$ \\ \hline \end{longtable} \end{singlespace} } % end footnotesize}$ ${{\footnotesize \begin{singlespace} \begin{longtable} \hline Cut             &amp; Efficiency (\%)        &amp; Rejection \\ \hline \caption{$1.5 < \mid \eta \mid < 1.8$} \hline\hline \multicolumn{3}{$1.5 < \mid \eta \mid < 1.8$} \\ \hline . \\ -0.4 &amp; $ 73.0 \pm 0.3 $ &amp; $ \E{( 130.6 \pm 5.8 )}\times 10^{ 2 }$ \\ 1.0 &amp; $ 72.1 \pm 0.3 $ &amp; $ \E{( 22.0 \pm 1.3 )}\times 10^{ 3 }$ \\ 1.8 &amp; $ 71.1 \pm 0.3 $ &amp; $ \E{( 28.4 \pm 1.9 )}\times 10^{ 3 }$ \\ 2.4 &amp; $ 70.2 \pm 0.3 $ &amp; $ \E{( 37.5 \pm 2.8 )}\times 10^{ 3 }$ \\ 2.8 &amp; $ 69.2 \pm 0.3 $ &amp; $ \E{( 42.4 \pm 3.4 )}\times 10^{ 3 }$ \\ 3.2 &amp; $ 68.1 \pm 0.3 $ &amp; $ \E{( 50.5 \pm 4.4 )}\times 10^{ 3 }$ \\ 3.4 &amp; $ 67.6 \pm 0.3 $ &amp; $ \E{( 54.3 \pm 4.9 )}\times 10^{ 3 }$ \\ 3.8 &amp; $ 66.3 \pm 0.3 $ &amp; $ \E{( 63.8 \pm 6.3 )}\times 10^{ 3 }$ \\ 4.0 &amp; $ 65.6 \pm 0.3 $ &amp; $ \E{( 69.1 \pm 7.1 )}\times 10^{ 3 }$ \\ 4.4 &amp; $ 64.0 \pm 0.3 $ &amp; $ \E{( 83.1 \pm 9.4 )}\times 10^{ 3 }$ \\ 4.6 &amp; $ 63.0 \pm 0.3 $ &amp; $ \E{( 9.1 \pm 1.1 )}\times 10^{ 4 }$ \\ 4.8 &amp; $ 62.0 \pm 0.3 $ &amp; $ \E{( 10.9 \pm 1.4 )}\times 10^{ 4 }$ \\ 5.0 &amp; $ 60.9 \pm 0.3 $ &amp; $ \E{( 10.9 \pm 1.4 )}\times 10^{ 4 }$ \\ 5.2 &amp; $ 59.7 \pm 0.3 $ &amp; $ \E{( 12.4 \pm 1.7 )}\times 10^{ 4 }$ \\ 5.4 &amp; $ 58.3 \pm 0.3 $ &amp; $ \E{( 14.6 \pm 2.2 )}\times 10^{ 4 }$ \\ 5.6 &amp; $ 56.9 \pm 0.3 $ &amp; $ \E{( 16.8 \pm 2.7 )}\times 10^{ 4 }$ \\ 5.8 &amp; $ 55.4 \pm 0.3 $ &amp; $ \E{( 19.9 \pm 3.5 )}\times 10^{ 4 }$ \\ 6.0 &amp; $ 53.6 \pm 0.3 $ &amp; $ \E{( 21.9 \pm 4.0 )}\times 10^{ 4 }$ \\ 6.2 &amp; $ 51.8 \pm 0.3 $ &amp; $ \E{( 26.3 \pm 5.3 )}\times 10^{ 4 }$ \\ 6.4 &amp; $ 49.9 \pm 0.3 $ &amp; $ \E{( 31.3 \pm 6.8 )}\times 10^{ 4 }$ \\ 6.6 &amp; $ 47.8 \pm 0.3 $ &amp; $ \E{( 36.5 \pm 8.6 )}\times 10^{ 4 }$ \\ 6.8 &amp; $ 45.4 \pm 0.3 $ &amp; $ \E{( 4.1 \pm 1.0 )}\times 10^{ 5 }$ \\ 7.0 &amp; $ 43.0 \pm 0.3 $ &amp; $ \E{( 4.4 \pm 1.1 )}\times 10^{ 5 }$ \\ \hline \end{longtable} \end{singlespace} } % end footnotesize}$
${{\footnotesize \begin{singlespace} \begin{longtable} \hline Cut             &amp; Efficiency (\%)        &amp; Rejection \\ \hline \caption{$1.8 < \mid \eta \mid < 2$}  \hline\hline \multicolumn{3}{$1.8 < \mid \eta \mid < 2$} \\ \hline \\ . \\ 0.4 &amp; $ 68.0 \pm 0.3 $ &amp; $ \E{( 105.1 \pm 5.3 )}\times 10^{ 2 }$ \\ 2.0 &amp; $ 67.1 \pm 0.4 $ &amp; $ \E{( 17.8 \pm 1.2 )}\times 10^{ 3 }$ \\ 3.0 &amp; $ 66.1 \pm 0.4 $ &amp; $ \E{( 24.1 \pm 1.9 )}\times 10^{ 3 }$ \\ 3.6 &amp; $ 65.3 \pm 0.4 $ &amp; $ \E{( 31.8 \pm 2.8 )}\times 10^{ 3 }$ \\ 4.2 &amp; $ 64.2 \pm 0.4 $ &amp; $ \E{( 39.9 \pm 4.0 )}\times 10^{ 3 }$ \\ 4.6 &amp; $ 63.2 \pm 0.4 $ &amp; $ \E{( 49.6 \pm 5.5 )}\times 10^{ 3 }$ \\ 5.0 &amp; $ 62.1 \pm 0.4 $ &amp; $ \E{( 60.7 \pm 7.4 )}\times 10^{ 3 }$ \\ 5.2 &amp; $ 61.4 \pm 0.4 $ &amp; $ \E{( 67.8 \pm 8.8 )}\times 10^{ 3 }$ \\ 5.4 &amp; $ 60.6 \pm 0.4 $ &amp; $ \E{( 7.8 \pm 1.1 )}\times 10^{ 4 }$ \\ 5.8 &amp; $ 58.8 \pm 0.4 $ &amp; $ \E{( 9.2 \pm 1.4 )}\times 10^{ 4 }$ \\ 6.0 &amp; $ 57.8 \pm 0.4 $ &amp; $ \E{( 10.4 \pm 1.7 )}\times 10^{ 4 }$ \\ 6.2 &amp; $ 56.8 \pm 0.4 $ &amp; $ \E{( 12.3 \pm 2.2 )}\times 10^{ 4 }$ \\ 6.4 &amp; $ 55.7 \pm 0.4 $ &amp; $ \E{( 14.0 \pm 2.6 )}\times 10^{ 4 }$ \\ 6.6 &amp; $ 54.4 \pm 0.4 $ &amp; $ \E{( 15.6 \pm 3.1 )}\times 10^{ 4 }$ \\ 6.8 &amp; $ 53.1 \pm 0.4 $ &amp; $ \E{( 16.9 \pm 3.5 )}\times 10^{ 4 }$ \\ 7.0 &amp; $ 51.6 \pm 0.4 $ &amp; $ \E{( 18.5 \pm 3.9 )}\times 10^{ 4 }$ \\ \hline \end{longtable} \end{singlespace} } % end footnotesize}$ ${{\footnotesize \begin{singlespace} \begin{longtable} \hline Cut             &amp; Efficiency (\%)        &amp; Rejection \\ \hline \caption{$2 <  \mid \eta \mid < 2.35$} \hline\hline \multicolumn{3}{$2 < \eta < 2.35$} \\ \hline . \\ -0.4 &amp; $ 73.0 \pm 0.3 $ &amp; $ \E{( 85.9 \pm 3.1 )}\times 10^{ 2 }$ \\ 2.4 &amp; $ 72.0 \pm 0.3 $ &amp; $ \E{( 20.9 \pm 1.2 )}\times 10^{ 3 }$ \\ 3.4 &amp; $ 71.1 \pm 0.3 $ &amp; $ \E{( 30.5 \pm 2.1 )}\times 10^{ 3 }$ \\ 4.0 &amp; $ 70.2 \pm 0.3 $ &amp; $ \E{( 39.6 \pm 3.1 )}\times 10^{ 3 }$ \\ 4.6 &amp; $ 69.1 \pm 0.3 $ &amp; $ \E{( 49.6 \pm 4.3 )}\times 10^{ 3 }$ \\ 5.0 &amp; $ 68.2 \pm 0.3 $ &amp; $ \E{( 63.3 \pm 6.2 )}\times 10^{ 3 }$ \\ 5.4 &amp; $ 67.0 \pm 0.3 $ &amp; $ \E{( 76.4 \pm 8.2 )}\times 10^{ 3 }$ \\ 5.6 &amp; $ 66.4 \pm 0.3 $ &amp; $ \E{( 85.2 \pm 9.7 )}\times 10^{ 3 }$ \\ 5.8 &amp; $ 65.6 \pm 0.3 $ &amp; $ \E{( 9.8 \pm 1.2 )}\times 10^{ 4 }$ \\ 6.0 &amp; $ 64.8 \pm 0.3 $ &amp; $ \E{( 10.7 \pm 1.4 )}\times 10^{ 4 }$ \\ 6.2 &amp; $ 63.9 \pm 0.3 $ &amp; $ \E{( 12.3 \pm 1.7 )}\times 10^{ 4 }$ \\ 6.4 &amp; $ 62.9 \pm 0.3 $ &amp; $ \E{( 13.3 \pm 1.9 )}\times 10^{ 4 }$ \\ 6.6 &amp; $ 61.8 \pm 0.3 $ &amp; $ \E{( 14.1 \pm 2.1 )}\times 10^{ 4 }$ \\ 6.8 &amp; $ 60.7 \pm 0.3 $ &amp; $ \E{( 16.6 \pm 2.6 )}\times 10^{ 4 }$ \\ 7.0 &amp; $ 59.3 \pm 0.3 $ &amp; $ \E{( 18.5 \pm 3.1 )}\times 10^{ 4 }$ \\ \hline \end{longtable} \end{singlespace} } % end footnotesize}$
${{\footnotesize \begin{singlespace} \begin{longtable} \hline Cut             &amp; Efficiency (\%)        &amp; Rejection \\ \hline \caption{$2.35 < \mid \eta \mid < 2.47$} \hline\hline \multicolumn{3}{$2.35 < \eta < 2.47$} \\ \hline . \\ 0.8 &amp; $ 70.0 \pm 0.5 $ &amp; $ \E{( 19.2 \pm 1.8 )}\times 10^{ 3 }$ \\ 3.0 &amp; $ 69.0 \pm 0.5 $ &amp; $ \E{( 37.7 \pm 5.0 )}\times 10^{ 3 }$ \\ 4.0 &amp; $ 68.1 \pm 0.5 $ &amp; $ \E{( 48.0 \pm 7.2 )}\times 10^{ 3 }$ \\ 4.8 &amp; $ 66.9 \pm 0.5 $ &amp; $ \E{( 6.6 \pm 1.2 )}\times 10^{ 4 }$ \\ 5.0 &amp; $ 66.6 \pm 0.5 $ &amp; $ \E{( 6.8 \pm 1.2 )}\times 10^{ 4 }$ \\ 5.6 &amp; $ 65.2 \pm 0.5 $ &amp; $ \E{( 10.1 \pm 2.2 )}\times 10^{ 4 }$ \\ 5.8 &amp; $ 64.5 \pm 0.5 $ &amp; $ \E{( 11.7 \pm 2.8 )}\times 10^{ 4 }$ \\ 6.2 &amp; $ 63.2 \pm 0.5 $ &amp; $ \E{( 17.6 \pm 5.1 )}\times 10^{ 4 }$ \\ 6.4 &amp; $ 62.6 \pm 0.5 $ &amp; $ \E{( 21.1 \pm 6.7 )}\times 10^{ 4 }$ \\ 6.6 &amp; $ 61.5 \pm 0.5 $ &amp; $ \E{( 23.5 \pm 7.8 )}\times 10^{ 4 }$ \\ 6.8 &amp; $ 60.6 \pm 0.5 $ &amp; $ \E{( 23.5 \pm 7.8 )}\times 10^{ 4 }$ \\ 7.0 &amp; $ 59.6 \pm 0.5 $ &amp; $ \E{( 3.5 \pm 1.4 )}\times 10^{ 5 }$ \\ \hline \end{longtable} \end{singlespace} } % end footnotesize }$ ${{\footnotesize \begin{singlespace} \begin{longtable} \hline Cut             &amp; Efficiency (\%)        &amp; Rejection \\ \hline \caption{{$ \mid \eta \mid < 2.47$} } \hline\hline . \\ -0.6    &amp;       $82.0   \pm     0.1$    &amp;       $\E{(126.0      \pm     1.9)}\times 10^{2}$ \\ 1.2     &amp;       $81.0   \pm     0.1$    &amp;       $\E{(229.4      \pm     4.6)}\times 10^{2}$ \\ 2       &amp;       $80.1   \pm     0.1$    &amp;       $\E{(304.7      \pm     7.0)}\times 10^{2}$ \\ 2.6     &amp;       $79.2   \pm     0.1$    &amp;       $\E{(38.6       \pm     1.0)}\times 10^{3}$ \\ 3       &amp;       $78.4   \pm     0.1$    &amp;       $\E{(44.7       \pm     1.3)}\times 10^{3}$ \\ 3.4     &amp;       $77.4   \pm     0.1$    &amp;       $\E{(53.5       \pm     1.6)}\times 10^{3}$ \\ 3.8     &amp;       $76.2   \pm     0.1$    &amp;       $\E{(64.3       \pm     2.2)}\times 10^{3}$ \\ 4       &amp;       $75.6   \pm     0.1$    &amp;       $\E{(69.9       \pm     2.4)}\times 10^{3}$ \\ 4.4     &amp;       $74.1   \pm     0.1$    &amp;       $\E{(84.9       \pm     3.3)}\times 10^{3}$ \\ 4.6     &amp;       $73.2   \pm     0.1$    &amp;       $\E{(95.5       \pm     3.9)}\times 10^{3}$ \\ 4.8     &amp;       $72.3   \pm     0.1$    &amp;       $\E{(106.8      \pm     4.6)}\times 10^{3}$ \\ 5       &amp;       $71.3   \pm     0.1$    &amp;       $\E{(119.7      \pm     5.5)}\times 10^{3}$ \\ 5.2     &amp;       $70.2   \pm     0.1$    &amp;       $\E{(133.5      \pm     6.4)}\times 10^{3}$ \\ 5.4     &amp;       $69.0   \pm     0.1$    &amp;       $\E{(150.7      \pm     7.7)}\times 10^{3}$ \\ 5.6     &amp;       $67.7   \pm     0.1$    &amp;       $\E{(173.4      \pm     9.5)}\times 10^{3}$ \\ 5.8     &amp;       $66.4   \pm     0.1$    &amp;       $\E{(19.6       \pm     1.1)}\times 10^{4}$ \\ 6       &amp;       $65.0   \pm     0.1$    &amp;       $\E{(22.0       \pm     1.4)}\times 10^{4}$ \\ 6.2     &amp;       $63.5   \pm     0.1$    &amp;       $\E{(26.0       \pm     1.8)}\times 10^{4}$ \\ 6.4     &amp;       $61.9   \pm     0.1$    &amp;       $\E{(30.0       \pm     2.2)}\times 10^{4}$ \\ 6.6     &amp;       $60.3   \pm     0.1$    &amp;       $\E{(33.7       \pm     2.6)}\times 10^{4}$ \\ 6.8     &amp;       $58.5   \pm     0.1$    &amp;       $\E{(38.4       \pm     3.1)}\times 10^{4}$ \\ 7       &amp;       $56.7   \pm     0.1$    &amp;       $\E{(42.0       \pm     3.6)}\times 10^{4}$ \\ \hline \end{longtable} \end{singlespace} } % end footnotesize}$

How to use the electron Likelihood in your analysis

Starting release 15, in order to use the logarithmic likelihood ratio, one needs to access egammaPID::ElectronWeight and egammaPID::BgWeight, where ElectronWeight and BgWeight are already stored as:

\[ \log _{10}(P_{sig}(x))} \;and \;{ \log_{10}(P_{bak}(x))\]

Then use as a likelihood discriminant the variable Lval = (ElectronWeight - BgWeight )

Note: In release 14 and earlier, one has to use as discriminant the variable Lval defined as:

\[\log_{10} (\frac{ElectronWeight}{BgWeight })\]

because in these releases, ElectronWeight and BgWeight have been stored simply as:

\[ P_{sig}(x)} \;and {\;P_{bak}(x)\]

Documentation

ATLAS Note
Latex rendering error!! dvi file was not created.

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Topic revision: r23 - 2009-03-10 - KamalBenslama
 
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