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

• Reference used to calculate bin width with respect to Jet Energy Resoultion (Calculated using dijet sample): Jet_Energy_Resolution.eps (Jet_Energy_Resolution.eps was taken from the Jet energy Resolution Group URL https://atlas.web.cern.ch/Atlas/GROUPS/PHYSICS/CONFNOTES/ATLAS-CONF-2010-054/ )

Legend Info:

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

Kt Jet Finder

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

1) For each particle i, j in the event the K_t distance is calculated d_ij = min(P^2_ti,P^2_tj) ΔR ^2_ij / R

Where ΔR _ij= (Δeta_i - Δeta_j)^2 + (Δphi_i - Δphi_j)^2

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

d_ij = P^2_iB

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

• INCLUSIVE K_t Jet Algorithm:

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

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

• Exclusive K_t Jet Algorithm:

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

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

3)

• INCLUSIVE K_t Jet Algorithm:

This process is repeated until no more particles are left.

• Exclusive K_t Jet Algorithm:

This process ends when all d_ij and d_iB 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 = P_tmin^(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 = E_t^(2)

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

Signal and Background Comparisons Not Normalized

Fig1.1

• AllDminSigBckKtUnNorm.eps:

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

Fig2.1

• AllDminSigBckKtNorm.eps:

Signal and Background Comparisons Normalized (dsigma/dDmin [pb/GeV^2] )

Fig3.1

• AllDminSigBckKtNormLuminosityBinWidth.eps:

Signal and Sum of Background Comparisons Normalized (dsigma/dDmin [pb/GeV^2] )

Fig4.1

• AllDminSigBckKtSumNormLuminosityBinWidth.eps:

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

Signal and Background Comparisons Not Normalized

Fig5.1

• AllDminSigBckktUnNormLog10.eps

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

Fig6.1

• AllDminSigBckktNormLog10.eps

Signal and Background Comparisons Normalized (dsigma/dDmin [pb/GeV^2] )

Fig7.1

• AllDminSigBckktNormLuminosityBinWidthLog10.eps

Signal and Sum of Background Comparisons Normalized (dsigma/dDmin [pb/GeV^2] )

Fig8.1

• AllDminSigBckKtSumNormLuminosityBinWidthLog10.eps

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

Fig9.1

• AllDminSigBckKtSumNormUnityLog10.eps

AntiKt Jet Finder

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

d_ij = min(1/P^2_ti,1/P^2_tj) ΔR ^2_ij / R

and

d_ij = 1/P^2_iB

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

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

Signal and Background Comparisons Not Normalized

Fig10.1

• AllDminSigBckAntktUnNorm.eps:

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

Fig11.1

• AllDminSigBckAntktNorm.eps:

Signal and Background Comparisons Normalized (dsigma/dDmin [pb/GeV^2] )

Fig12.1

• AllDminSigBckAntktNormLuminosityBinWidth.eps:

Signal and Sum of Background Comparisons Normalized (dsigma/dDmin [pb/GeV^2] )

Fig13.1

• AllDminSigBckAntktSumNormLuminosityBinWidth.eps:

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

Signal and Background Comparisons Not Normalized

Fig14.1

• AllDminSigBckKtAntUnNormLog10.eps

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

Fig15.1

• AllDminSigBckAntKtNormLog10.eps

Signal and Background Comparisons Normalized (dsigma/dDmin [pb/GeV^2] )

Fig16.1

• AllDminSigBckAntktNormLuminosityBinWidthLog10.eps

Signal and Sum of Background Comparisons Normalized (dsigma/dDmin [pb/GeV^2] )

Fig17.1

• AllDminSigBckAntktSumNormLuminosityBinWidthLog10.eps

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

Fig18.1

• AllDminSigBckAntktSumNormUnityLog10.eps

-- MichaelWright - 2010-10-06