11.03.2006

Optimization of parameters for jet finding algorithm

for p+p collisions at Ecm=200 GeV T. G. Dedovich & M.V. Tokarev

JINR, Dubna

Motivations Cone-algorithm Criteria of the algorithm optimization Jet properties vs. algorithm parameters

Jet reconstruction efficiency PT

Part reconstruction accuracy

Parton direction reconstruction

Summary

11.03.2006

Motivations Perturbative QCD predicts the production cross

sections at large PT for parton-parton scattering in p+p collisions. The outgoing partons from the parton-parton scattering hadronise to form jets of particles.

Calculations of high-PT jet production involve the folding of parton scattering cross sections with experimentally determined parton distribution functions (PDFs).

Measurements of the inclusive jet cross section, the di-jet angular distribution, and the di-jet mass spectrum, can be used to test the predictions of pQCD.

11.03.2006

Jet cone algorithm

1) Particles with PT> Eseed are“seeds”.

2) Chooses “seed” with the highest-PT. The “seed”-direction give the first approximation of jet axis.

3) All particles have distance to jet axis in space below R are included into jet.

where (Jet,Jet) is the direction of the Jet axis, (i,i) are the coordinates of the particle.

4) Energy and direction of Jet are calculated

5) Step (3)-(4) are iterated until the Jet direction is stabile.6) Only Jet with ET>Ecut are retained.

7) Jets are merged or split according to the following criteria: Two Jet are merged into one Jet if more than 50% of the ET

Jet of the Jet with the smaller ETJet is contained in the overlap region.

Otherwise the jets are split into two Jets and particles contained in the overlap region are assigned to the nearest Jet.

The Jet directions are recalculated using the alternative definition.

11.03.2006

The criteria of the algorithm optimization

Find parameters range for which algorithm is stable, i.e. small variations doesn’t affect results.

Find parameters range which provide the best algorithm efficiency and accuracy.

Event generation: PYTHIA 5.6Hard 22 proces+Initinal & Final state radiation +Multiple parton interaction.

11.03.2006

Efficiency of di-jet event reconstruction vs. Ecut, R

Efficiency reconstruction= Ndi-jet /Nall. Maximum of the reconstruction efficiency at R~2 means

just division of the () space on 2 hemisphere and may not be used in practice.

The reconstruction efficiency for each PThard is a flat for

0.6<R<1.1 at PThard/4<Ecut<PT

hard/2.

11.03.2006

Efficiency of the jet reconstruction vs. pT

hard

Ecut define low limit of PT spectrum (at Ecut =7 GeV efficiency drops very fast for Pt<13 GeV). It is better to keep Ecut as low as possible.

2-jet reconstruction efficiency is almost the same for all 0.7<R<1.1 while 2*Ecut<pT

hard<3*Ecut . At higher pT

hard efficiency of 2-jet events decreases with decrease R (but not very crucial ~10%). Part of events is reconstructed as 3-jets.

It is possible to use Ecut 5-7 GeV for jet reconstruction in the range PT

hard =10-50 GeV. Although it is not optimal for all moments.

It is impossible to find single set of parameters of the algorithm for jet reconstruction at low and high pT

hard range.

Efficiency to find 2 or 3 jets

3M generated events

11.03.2006

Jet reconstruction efficiency vs. Eseed

Eseed influence on jet reconstruction is very small until Eseed<<PT

0.5<Eseed<1. GeV is usable for parton transverse momentum range 10<PT<50 GeV

Following results is presented for Eseed=1.0 GeV

Efficiency to find 2 or 3 jets

11.03.2006

Parton transverse momentum reconstruction

pTPart vs. ET

Jet

The set of histograms - distribution of dijet events vs. ETjet

for narrow pT

Part bins is analyzed. Every histogram was fitted by Gauss function to find <ET

Jet> and ETjet distribution width (σ) for each pT

Part bin.

11.03.2006

<ET Jet> & ET

jet distribution width σ vs. R

The linear dependence, <ETjet> vs. pT is observed for pT>15 GeV

at all parameter values R=0.4-1.1 Nonlinear dependence <ET

jet> vs. pT is observed for PT<15 GeV. Jet reconstruction efficiency drops very fast in this range (value of low limit pT

part depends on Ecut). Best result for reconstructed ET

jet distribution width σ is achieved for 0.7<R<1.1; σ(ET

jet) 2.5 GeV and it weak growths up with pTPart.

The width σ raises substantially for R=0.4. Small difference between values for σ at R=0.7 and 1.1 is found.

Analysis with higher R is potentially more sensitive to background.

11.03.2006

Low Ecut provides better pTPart reconstruction accuracy,

but the di-jet reconstruction efficiency is smaller. For example for PT

Part=35 GeV decrease Ecut (147 GeV) decreases GeV), but decreases eff(0.9 0.7).

The type of some jet events (2 or 3-jet event) depends on choice of the parameter Ecut . More detail analysis of events to determine additional criteria for choice of event type (2,3,… n-jets) is required.

<ET Jet> & ET

jet distribution width σ vs. Ecut

Efficiency to find 2 or 3 jets

11.03.2006

Parton direction reconstruction accuracy

Minimal mean deviation <ΔRpjet> is

observed for 0.7<R<1.1 at fixed Ecut.

The increase of mean deviation <ΔRp

jet> is observed as R decreases.

The mean deviation <ΔRpjet>

decreases with pTpart.

The mean deviation increases with Ecut at fixed R.

Jet dire

ction

2PartJet

2PartJet

Jetp )()η(ηΔR

Parton direction

11.03.2006

Summary Optimization of parameters (Ecut, Eseed, R) for jet

finding cone algorithm for p-p collisions at Ecm=200 GeV was studied.

Dependence of di-jet reconstruction efficiency, accuracy of parton energy and direction reconstruction on algorithm parameters was determined.

The use of the optimal algorithm parameters found for di-jet reconstruction at high PT range gives low di-jet reconstruction efficiency at low PT range and vise versa.

More detail analysis of jet events to determine additional criteria for choice of event type (2,3,… n-jets) is required.

11.03.2006

THANK YOU

11.03.2006

<ET Jet> & ET

jet distribution width σ vs. R