Exclusive Jet Study With Kt, AntiKt and Cambridge Aachen Jet Finders

Legend Info:

  • Signal - Purple
  • NP0 - Black
  • NP1 - Red
  • NP2 - Green (Also Sum of the Backgrounds)
  • NP3 - Blue

Kt Jet Finder

The Kt jet finding algorithm can be broken down into three steps.

1) For each particle i, j in the event the Kt distance is calculated dij = min(P^2ti,P^2tj) ΔR ^2ij / R

Where ΔR ij= (Δetai - Δetaj)^2 + (Δphii - Δphij)^2

The Kt distance from particle i to the beam is also calculated

dij = P^2iB

2) The next step is to find the dmin value for all dij and diB. (Note there are differences between the Inclusive and Exclusive Kt Jet algorithms)

  • INCLUSIVE Kt Jet Algorithm:

If dij is the dmin value then the i, j particles are combined ( the particles four momenta are summed together).

if diB is the dmin value then the particle i is a final jet and the particle i is removed from the list.

  • Exclusive Kt Jet Algorithm:

If dij is the dmin value and is less than dcut then the i, j particles are combined ( the particles four momenta are summed together).

if diB is the dmin value and is less than dcut then the particle i combined with the beam jet.

3)

  • INCLUSIVE Kt Jet Algorithm:

This process is repeated until no more particles are left.

  • Exclusive Kt Jet Algorithm:

This process ends when all dij and diB are above the dcut value.

The dcut variable again varies when considering an inclusive or exclusive event.

When looking at an exclusive n-jet event.

dcut = Ptmin^(2)

This maintains the jet algorithm ability to factorize the initial-state of the collinear singularities, which allows you to obtain a finite cross-section.

When looking at an inclusive jet event.

dcut = Et^(2)

Signal and Background Comparisons (Bin Width 100 GeV^2)

Signal and Background Comparisons Not Normalized
Fig1.1 AllDminSigBckKtUnNorm.png
Signal and Background Comparisons Normalized (1/sigma dsigma/dDmin [GeV-2] )
Fig2.1 AllDminSigBckKtNorm.png
Signal and Background Comparisons Normalized (dsigma/dDmin [pb/GeV^2] )
Fig3.1 AllDminSigBckKtNormLuminosityBinWidth.png
Signal and Sum of Background Comparisons Normalized (dsigma/dDmin [pb/GeV^2] )
Fig4.1 AllDminSigBckKtNormLuminosityBinWidth.png

Signal and Background Comparisons (Binned in Log(Dmin))

Signal and Background Comparisons Not Normalized
Fig5.1 AllDminSigBckktUnNormLog10.png

Signal and Background Comparisons Normalized (1/sigma dsigma/dDmin [GeV-2] )
Fig6.1 AllDminSigBckktNormLog10.png

Signal and Background Comparisons Normalized (dsigma/dDmin [pb/GeV^2] )
Fig7.1 AllDminSigBckktNormLuminosityBinWidthLog10.png
Signal and Sum of Background Comparisons Normalized (dsigma/dDmin [pb/GeV^2] )
Fig8.1 AllDminSigBckKtSumNormLuminosityBinWidthLog10.png

Signal and Sum of Background Comparisons Normalized (1/sigma dsigma/dDmin [GeV-2] )
Fig9.1 AllDminSigBckKtSumNormUnityLog10.png

AntiKt Jet Finder

The Anti-Kt Algorithm follows the same procedure as the Kt algorithm explained above. The differences between these two algorithms are the definitions for dij and diB.

dij = min(1/P^2ti,1/P^2tj) ΔR ^2ij / R

and

dij = 1/P^2iB

*************** These plots are for R=1 *******************************************

Signal and Background Comparisons (Bin Width 100 GeV^2)

Signal and Background Comparisons Not Normalized
Fig10.1 AllDminSigBckAntktUnNorm.png
Signal and Background Comparisons Normalized (1/sigma dsigma/dDmin [GeV-2] )
Fig11.1 AllDminSigBckAntktNorm.png
Signal and Background Comparisons Normalized (dsigma/dDmin [pb/GeV^2] )
Fig12.1 AllDminSigBckAntktNormLuminosityBinWidth.png
Signal and Sum of Background Comparisons Normalized (dsigma/dDmin [pb/GeV^2] )
Fig13.1 AllDminSigBckAntktSumNormLuminosityBinWidth.png

Signal and Background Comparisons (Binned in Log(Dmin))

Signal and Background Comparisons Not Normalized
Fig14.1 AllDminSigBckKtAntUnNormLog10.png
Signal and Background Comparisons Normalized (1/sigma dsigma/dDmin [GeV-2] )
Fig15.1 AllDminSigBckAntKtNormLog10.png
Signal and Background Comparisons Normalized (dsigma/dDmin [pb/GeV^2] )
Fig16.1 AllDminSigBckAntktNormLuminosityBinWidthLog10.png
Signal and Sum of Background Comparisons Normalized (dsigma/dDmin [pb/GeV^2] )
Fig17.1 AllDminSigBckAntktSumNormLuminosityBinWidthLog10.png

Signal and Sum of Background Comparisons Normalized (1/sigma dsigma/dDmin [GeV-2] )
Fig18.1 AllDminSigBckAntktSumNormUnityLog10.png

-- MichaelWright - 2010-10-06

Topic attachments
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