Triggers

The triggers of interest are

  1. HLT_Ele15_LW_L1R
    • L1 Seed: hltL1sRelaxedSingleEgammaEt8
    • Last Filter: hltL1NonIsoHLTNonIsoSingleElectronLWEt15PixelMatchFilter
  2. HLT_Photon10_L1R
    • L1 Seed: hltL1sRelaxedSingleEgammaEt5
    • Last Filter: hltL1NonIsoHLTNonIsoSinglePhotonEt10HcalIsolFilter

Samples

Monte Carlo samples used in the study of electron trigger efficiencies are listed in Table 1.

TABLE 1 Sample Location of PAT Files
ttbar TTbarJets-madgraph-7TeV /castor/cern.ch/user/c/chadwick/TopAna/CMSSW_3_3_1/TTbarJets-madgraph-7TeV

More information about the sample is detailed here.

Cuts

Two separate sets of cuts were used.

  • Loose Cut
    • $p_{T}$ < 1.0 GeV
    • $|\eta|$ < 2.4
    • eidRobustLoose

  • Tight Cut (Analysis cuts taken from here, excluding $p_{T}$ cut, and with eidRobustTight)
    • $p_{T}$ < 1.0 GeV
    • $|\eta|$ < 1.4442 or 1.5660 < $|\eta|$ < 2.4
    • $d_{0}$ < 0.200 mm
    • ComRelIso < 0.1
    • eidRobustTight

Plots

The $p_{T}$ plot overflow has been transferred to the last bin in the histogram.

All efficiency plots were generated by defining a TGraphAsymmErrors in ROOT, and calling the member function BayesDivide(). This function takes two histograms (one the numerator and the other the denominator) and computes the efficiencies, while assigning suitable asymmetric errors using Bayesian statistics. Information about the TGraphAsymmErrors class can be found here, and a paper explaining the computation of the errors (which goes beyond normal binomial distribution errors) can be found here.

Each efficiency plot is fitted with the following function:

$y=\frac{A}{2}(1 + erf(\frac{x - x_{0}}{s\sqrt{x}}))$

In the plots below, p0 = A, p1 = $x_{0}$ and p2 = s. p0 corresponds to the high $p_{T}$ limit of the efficiency, $x_{0}$ the midpoint of the slope, and s the gradient of the slope at $x=x_{0}$.

HLT_Ele15_LW_L1R, Loose Cut

  • $p_{T}$ of all electrons.

  • $p_{T}$ Trigger efficiency plots.

The fit for $\epsilon^{HLT}_{L1}$ has been performed only on data points above 12, ignoring the "wiggle" at low $p_{T}$. Reading off the value of p0 from the fits, we have at high transverse momentum

TABLE 2 Efficiencies from fit
$\epsilon^{L1}_{ele}$ 0.9895
$\epsilon^{HLT}_{L1}$ 0.9796
$\epsilon^{HLT}_{ele}$ 0.9663

We should expect that $\epsilon^{HLT}_{ele}=\epsilon^{L1}_{ele}\cdot\epsilon^{HLT}_{L1}$. From Table 2, we obtain $\epsilon^{L1}_{ele}\cdot\epsilon^{HLT}_{L1}=0.9693$.

Comparing the plots shown above, we see that the slopes of the trigger efficiency for the L1 seed and the HLT begin at different transverse momenta: around 5 GeV for the former and 12 GeV for the latter. This accounts for the wiggle that we see in the plot of $\epsilon^{HLT}_{L1}$: at low transverse momentum, both the L1 seed and the HLT have similar efficiencies with respect to all PAT electrons. But between 5 and 12 GeV, the L1 seed is increasingly likely to pass electrons, while the HLT still has the same efficiency as before, leading to a dip in $\epsilon^{HLT}_{L1}$.

  • $\eta$ of all electrons.

  • $\eta$ Trigger efficiency plots.

In bin 6 and 35 out of 40 bins in the efficiency histograms, ROOT reports that $\epsilon_{ele}^{HLT}$ is greater than $\epsilon_{ele}^{L1}$, which is anomalous.

  • trackIso of all electrons.

  • trackIso Trigger efficiency plots.

HLT_Photon10_L1R, Loose Cut

See the HLT_Ele15_LW_L1R section for a discussion of the common features shared by the plots for both triggers.

  • $p_{T}$ Trigger efficiency plots.

Reading off the value of p0 from the fits, we have at high transverse momentum

TABLE 2 Efficiencies from fit
$\epsilon^{L1}_{ele}$ 0.9918
$\epsilon^{HLT}_{L1}$ 0.9996
$\epsilon^{HLT}_{ele}$ 0.9914

We should expect that $\epsilon^{HLT}_{ele}=\epsilon^{L1}_{ele}\cdot\epsilon^{HLT}_{L1}$. From Table 2, we obtain $\epsilon^{L1}_{ele}\cdot\epsilon^{HLT}_{L1}=0.9914$.

Many of the efficiency data points in the graph of $\epsilon^{HLT}_{L1}$ were above 1, and are not plotted in the figure. Stricter electron cuts should eliminate this problem.

  • $\eta$ Trigger efficiency plots.

Again in bin 6 and 35 out of 40 bins in the $\epsilon_{L1}^{HLT}$ histogram, the efficiency exceeds 1, and are not displayed.

  • trackIso Trigger efficiency plots.

HLT_Ele15_LW_L1R, Tight Cut

TABLE 3 Barrel Endcap
All electrons
L1 Seed to Electrons Efficiency
HLT to Electrons Efficiency
HLT to L1 Seed Efficiency

The last plot ends prematurely as all the higher transverse momentum efficiencies exceed 1, and are not shown in the plot. This suggests that there are some electrons in the sample which are considered to match an HLT object, but not an L1 seed.

The eta distribution of such electrons (obtained over all events) are shown below:

The problem electrons are confined to an absolute value of eta of about 2.1, which explains why the barrel efficiencies are alright, while the endcap efficiencies are problematic. After removing all electrons between an eta of 2.0 and 2.25, we get the following more reasonable plots:

TABLE 4 Barrel Endcap
All electrons
L1 Seed to Electrons Efficiency
HLT to Electrons Efficiency
HLT to L1 Seed Efficiency

-- HongwanLiu - 10-Jun-2010

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Topic revision: r9 - 2010-06-16 - HongwanLiu
 
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