Optimization of parameters for jet finding algorithm for p+p collisions at E cm =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 P T Part reconstruction accuracy Parton direction reconstruction  Summary

Motivations  Perturbative QCD predicts the production cross sections at large P T 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-P T 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.

Jet cone algorithm 1) Particles with P T > E seed are“seeds”. 2) Chooses “seed” with the highest-P T. 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 E T >E cut 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 E T 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.

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 2  2 proces+Initinal & Final state radiation +Multiple parton interaction.

Efficiency of di-jet event reconstruction vs. E cut, R  Efficiency reconstruction= N di-jet /N all.  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 P T hard is a flat for 0.6<R<1.1 at P T hard /4<Ecut<P T hard /2.

Efficiency of the jet reconstruction vs. p T hard  E cut define low limit of P T spectrum (at E cut =7 GeV efficiency drops very fast for Pt<13 GeV). It is better to keep E cut as low as possible.  2-jet reconstruction efficiency is almost the same for all 0.7<R<1.1 while 2*E cut <p T hard <3*E cut.  At higher p T 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 E cut  5-7 GeV for jet reconstruction in the range P T 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 p T hard range. Efficiency to find 2 or 3 jets 3M generated events

Jet reconstruction efficiency vs. E seed  E seed influence on jet reconstruction is very small until E seed <<P T  0.5<E seed <1. GeV is usable for parton transverse momentum range 10<P T <50 GeV  Following results is presented for E seed =1.0 GeV Efficiency to find 2 or 3 jets

Parton transverse momentum reconstruction p T Part vs. E T Jet  The set of histograms - distribution of dijet events vs. E T jet for narrow p T Part bins is analyzed.  Every histogram was fitted by Gauss function to find and E T jet distribution width (σ) for each p T Part bin.

& E T jet distribution width σ vs. R  The linear dependence, vs. p T is observed for p T >15 GeV at all parameter values R=  Nonlinear dependence vs. p T is observed for P T <15 GeV. Jet reconstruction efficiency drops very fast in this range (value of low limit p T part depends on E cut ).  Best result for reconstructed E T jet distribution width σ is achieved for 0.7<R<1.1; σ(E T jet )  2.5 GeV and it weak growths up with p T Part.  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.

 Low E cut provides better p T Part reconstruction accuracy, but the di-jet reconstruction efficiency is smaller. For example for P T Part =35 GeV decrease E cut (14  7 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 E cut. More detail analysis of events to determine additional criteria for choice of event type (2,3,… n-jets) is required. & E T jet distribution width σ vs. E cut Efficiency to find 2 or 3 jets

Parton direction reconstruction accuracy  Minimal mean deviation is observed for 0.7<R<1.1 at fixed E cut.  The increase of mean deviation is observed as R decreases.  The mean deviation decreases with p T part.  The mean deviation increases with E cut at fixed R. Jet direction Parton direction

Summary  Optimization of parameters (E cut, E seed, R) for jet finding cone algorithm for p-p collisions at E cm =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 P T range gives low di-jet reconstruction efficiency at low P T 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.

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& E T jet distribution width σ vs. R