Motivations Cone-algorithm Criteria of the algorithm optimization

1. Optimization of parameters for jet finding algorithm for p+p collisions at Ecm=200 GeVT. G. Dedovich & M.V. Tokarev JINR, Dubna • Motivations • Cone-algorithm • Criteria of the algorithm optimization • Jet properties vs. algorithm parameters • Jet reconstruction efficiency • PTPart reconstruction accuracy • Parton direction reconstruction • Summary

2. 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.

3. 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 (h,j) space below R are included into jet. where (hJet,fJet) is the direction of the Jet axis, (hi,fi) 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 ETJet 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.

4. 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 5.6 Hard 2g2 proces+Initinal & Final state radiation +Multiple parton interaction.

5. 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 (h,j) 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<PThard/2.

6. Efficiency of the jet reconstruction vs. pThard Efficiency to find 2 or 3 jets • 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<pThard<3*Ecut . • At higher pThard 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 PThard =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 pThard range. 3M generated events

7. Jet reconstruction efficiency vs. Eseed Efficiency to find 2 or 3 jets • 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

8. Parton transverse momentum reconstruction pTPartvs. ETJet • The set of histograms - distribution of dijet events vs. ETjet for narrow pTPart bins is analyzed. • Every histogram was fitted by Gauss function to find <ET Jet> and ETjet distribution width (σ) for each pTPartbin.

9. <ET Jet> & ETjet 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 <ETjet> vs. pT is observed for PT<15 GeV. Jet reconstruction efficiency drops very fast in this range (value of low limit pTpartdepends on Ecut). • Best result for reconstructed ETjet distribution width σ is achieved for 0.7<R<1.1; σ(ETjet)  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.

10. <ET Jet> & ETjet distribution width σ vs. Ecut Efficiency to find 2 or 3 jets • Low Ecut provides better pTPart reconstruction accuracy, but the di-jet reconstruction efficiency is smaller. For example for PTPart=35 GeV decrease Ecut (14g7 GeV) decreases s(4.3g3. GeV), but decreases eff(0.9 g 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.

11. Jet direction Parton direction Parton direction reconstruction accuracy • Minimal mean deviation <ΔRpjet> is observed for 0.7<R<1.1 at fixed Ecut. • The increase of mean deviation <ΔRpjet> is observed as R decreases. • The mean deviation <ΔRpjet> decreases with pTpart. • The mean deviation increases with Ecut at fixed R.

12. 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.

13. THANK YOU

14. <ET Jet> & ETjet distribution width σ vs. R