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Jet Energy Scale

General description

Select the 2 leading QCD jets that are balanced in $E_T$ and correlate the unbalancing with a measurable variable that depend on the jet composition.

What do we learn ?

  • nothing on the absolute energy scale : we can very well have a correct energy scale (in average) and a dependence wrt the jet content.

  • if there is a correlation between $\Delat E_T$ and the jets composition, it means that :
    • the calibration method calibrates well only a given type of jets (those with a high hadronic part for instance)
    • this contributes to increase the spread on the jet energy measurement (how much with respect to the expected resolution ?)

Some preliminary results

On these plots we can see the correlation between E(rec)/E(truth) before and after calibration as a function of E(charged)/E(truth).
  • there is a correlation (almost identical) before and after calibration : just a scale factor between E(em) and E(cal) ??

  • 20 GeV, |eta|<0.7:
    20-GeV-1.gif

  • 100 GeV, |eta|<0.7:
    100-GeV-1.gif

  • A strange result : linearity for (Cone4H1TowerJets)
    • what is this 4% shift after calibration ?? Linearity.gif

Discution on the method

The first idea was to take balanced jets and to compare their "charged" energy (total energy $E_{charged}$ of all charged tracks at particle level). The main problem is that the $E_T$ balance is true only on average. Since in average we have also a strong correlation between $E_T$ and $E_{charged}$ this produces the following effect that is independent on the jet calibration :
  • $ \langle E_T^{jet1}-E_T^{jet2}\rangle<0$ Right $\langle E_{charged}^{jet1}-E_{charged}^{jet2}\rangle<0$ Correlation.gif

As an other try, one can correlate the relative $E_{T}$ unbalancing between jets with the relative difference of energy fraction brought by charged particles : $E_{charged}/E_{jet}$ (or $E_{T}^{charged}/E_{T}^{jet}$ which is equivalent). The main advantage is that $E_{charged}/E_{jet}$ is on average independent on $E_{T}^{jet}$.

  • $ \frac{ E_T^{jet1}-E_T^{jet2} }{ E_T^{jet1}+E_T^{jet2} }$ vs $\frac{E_{charged}^{jet1}/E^{jet1}- E_{charged}^{jet2}/E^{jet2}}{E_{jet2}/E_{charged}^{jet1}/E^{jet1} + E_{charged}^{jet2}/E_{jet2}}$ Correlation-2.gif

  • NB : the following cuts have been applied :
    • #jets$\ge$2
    • $ |\eta_{jet 1}|<0.7$ and $ |\eta_{jet 2}|<0.7$
    • $ E_{jet 1}<50$GeV and $ E_{jet 2}<50$GeV

Some results

The following cuts have been applied :
  • #jets=2
  • $ |\eta_{jet 1}|<0.7$ and $ |\eta_{jet 2}|<0.7$
  • $ E_{jet 1}<50$GeV and $ E_{jet 2}<50$GeV

  • Unbalancing at truth particle level :
    Unbal-mc.gif

  • Unbalancing before calibration (em scale) :
    Unbal-uncalib.gif

  • Unbalancing after calibration :
    Unbal-calib.gif
slope
Truth particle level ~0
Uncalibrated jets -14 $\pm$ 2 %
Calibrated jets -8.0 $\pm$ 0.9 %

How to quantify the effect of the miscalibration

$ \frac{ E_T^{jet1}-E_T^{jet2} }{ E_T^{jet1}+E_T^{jet2} }$ represents $\frac{ \Delta E_T }{ 2 \langle E_T \rangle }$=$\frac{ \Delta E }{ 2 \langle E \rangle }$. The maximum variation of this quantity is obtained when the unbalancing between the fraction of energy brought by the charged particles varies between -1 and 1. We have then $\frac{ \Delta E }{ 2 \langle E \rangle } = 2 \times $slope. As a consequence, the maximum fluctuation of the reconstructed energy $E$ due to the miscalibration is : $\frac{ \Delta E }{ \langle E \rangle } = 4 \times $slope.
$\frac{ \Delta E }{ \langle E \rangle }$
Uncalibrated jets 56 $\pm$ 8 %
Calibrated jets 32 $\pm$ 4 %
Is this estimate realistic ?

  • Uncalibrated jets :
    Check-uncalib.gif

  • Calibrated jets :
    Check-calib.gif

-- VincentGiangiobbe - 04 Feb 2008
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Topic attachments
I Attachment History Action Size Date Who Comment
GIFgif 100-GeV-1.gif r1 manage 17.0 K 2008-02-04 - 16:36 VincentGiangiobbe 100 GeV, |eta|<0.7
GIFgif 20-GeV-1.gif r1 manage 16.0 K 2008-02-04 - 16:35 VincentGiangiobbe 20 GeV, |eta|<0.7
GIFgif Check-calib.gif r1 manage 9.0 K 2008-02-05 - 12:00 VincentGiangiobbe Check the calibration -calibrated-
GIFgif Check-uncalib.gif r1 manage 9.0 K 2008-02-05 - 11:59 VincentGiangiobbe Check the calibration -em scale-
GIFgif Correlation-2.gif r1 manage 14.0 K 2008-02-04 - 18:47 VincentGiangiobbe Correlation ET jets vs Echarged/Ejet (truth level)
GIFgif Correlation.gif r2 r1 manage 13.9 K 2008-02-04 - 18:45 VincentGiangiobbe Correlation ET jets vs Echarged (truth level)
GIFgif Linearity.gif r1 manage 10.2 K 2008-02-04 - 16:50 VincentGiangiobbe Linearity
GIFgif Unbal-calib.gif r2 r1 manage 12.8 K 2008-02-05 - 11:05 VincentGiangiobbe Unbalancing -calibrated-
GIFgif Unbal-mc.gif r2 r1 manage 12.7 K 2008-02-05 - 11:06 VincentGiangiobbe Unbalancing -mc-
GIFgif Unbal-uncalib.gif r2 r1 manage 13.1 K 2008-02-05 - 11:08 VincentGiangiobbe Unbalancing -em scale-
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Topic revision: r4 - 2008-02-05 - VincentGiangiobbe
 
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