Jet reconstruction with Deterministic Annealing Davide Perrino Dipartimento di Fisica – INFN di Bari Terzo Convegno Nazionale sulla Fisica di Alice – 13/11/2007

Deterministic Annealing It’s a general purpose algorithm customized for jet finding in hadronic collisions Clustering consists of gathering n initial data x i in a set of k codevectors y j that represent the sample depending on its elements closeness Clustering is achieved through the minimization of a cost function D under a constrain (T )

Deterministic Annealing The distance determines how will the algorithm work. A squared cone distance was chosen: Clustering takes place by means of the minimization of a cost function so defined:

Deterministic Annealing To avoid a trivial solution it is necessary the introduction of an entropy term: The minimization of D corresponds to look for the minimum of the function under the constrain of a multiplier T:

Deterministic Annealing The procedure is “deterministic” since for every T are optimized the values of:

Deterministic Annealing  =0  =  =  =  =  =0.0347

Advantages of DA The algorithm is “naturally” infrared and collinear safe. CPU time depends on N  with 1<  <1.5, depending on the method used. Independent of detector segmentation (no grid needed). It needs no further “patches” procedures (merging, splitting etc.) Few parameters needed only to smooth the clusterization process => they don’t affect the physical result. Only two procedures needed: 1) to decide when to stop the clusterization and 2) to select which clusters are jets.

Background subtraction and jets selection Evaluate clusters energy density Is Et > Et bg +rms Start with clusters list Calculate mean ρ(Et bg ) and rms Add cluster to jet list Is clusters list exausted? Start with jets list Recalculate background Subtract background ny y n Store jets

Events settings HIJING 1.36 (Pb-Pb Underlying event) √s NN 5.5 TeV jet quenching On Nuclear effects on PDF On Initial/final state radiation On Resonance decays Off Jet trigger Off Impact Parameter 0 – 5 fm Pythia 6.2 (p-p Jets) Centre mass energy 5.5 TeV Process types MSEL Structure Function CTEQ5L Initial/final state radiation On Multiple interactions Off Jet quenching Off parton pt hard range GeV/c The analysis was performed on the same sets of events generated for cone and k T studies. (taken from Rafael)

Events study Find jets in Pythia events with:  2 no cut on Pt no cut on charge Use jets found in the most populated bin as a trigger for jets found in Pythia+Hijing events with:  9 Pt>2. GeV/c Cuts on particles: no cut on charge cut on charge (w/o FastSimTPC)

Events study Example of input jets selection for 50 GeV sample. Parton distributionDA analysis  2 Selection bin

Jet reconstruction efficiency Efficiency improves with jet energy in all the cases. Were selected jets that satisfied:  

Energy ratio Energy ratio between Et reconstructed and energy input. It remains almost constant w.r.t. input Et.

Energy resolution Energy resolution with charged particles and with fast simulation are similar to those obtained through the cone analysis.

Direction resolution As one can expext, it improves considerably with jet energy in all the cases.

Conclusions DA has been adapted to jet finding in pp and Pb-Pb events. DA owns many interesting features for jet finding. An analysis on five sets of Pythia+Hijing events corresponding to different ranges of jet energies has been performed, adding a fast TPC simulation. An event-by-event background subtraction method has been implemented for DA.