Clustering of very low energy parti lesJulio 5, 2005C. IglesiasTileCal Group-IFIC(Valen ia)Dpto. FAMN-Universidad de Valen ia

Abstra t: This note ompares di�erent ways of re onstru ting the lusters insidethe ATHENA framework of ATLAS: TopoCluster, Sliding Window luster, EGamma luster and one algorithms. We show how these lustering algorithms an be tunedto obtain the best energy resolution when re onstru ting very low energy parti les.The present results are based on single parti le samples of �0�s, ���s and neutrons,simulated with Geant3 during DC1 with energy between 1 and 30 GeV and simulatedwith and without ele troni noise in the alorimeters. Results in this note are obtainedusing 7.8.0 and 8.2.0 releases of the ATLAS software.

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1 Why Clustering is useful for Energy Flow?The main on ept of the Energy Flow algorithm[1℄[2℄[3℄[4℄ for jet-�nding is to use thetra king dete tor for the measurement of harged parti le momentum and use the alorimeter energy resolution for neutral parti les. The �rst step is to identify theenergy deposited in the EM and HAD alorimeters by harged hadrons and substituteit with the momentum measured by the tra king dete tor for the orresponding tra k.We therefore have to re onstru t and subtra t neutral lusters before identifying theenergy deposit of the harged parti les in the alorimeter.We also need pattern re ognition algorithms to asso iate energy deposit in alorime-ter ells with parti les. There are three di�erent ontribution:- The ele tromagneti showers (from ele trons and photons) are energeti ,mu h lo alized and highly orrelated, so the lustering algorithm works well inthem.- Respe t tomuons, they produ e only minimum ionization but they do it through-out all its traje tory, so we an de�ne them using tra king information in alorime-ter and the MIP deposit will be minimal in any ase.- Finally, the hadron showers are broad and un onne ted, so they will be mostdiÆ ult to handle.The use of tra k momentum instead of the alorimeter energy improves the energyresolution only for isolated lusters. If the energy deposited in a luster is released bythe neutral and harged parti les, the improvement in resolution is diluted by the lossin resolution from the remaining luster. In omplex events and within jets, more thanone parti le will deposit their energy in the same alorimeter ell, and showers willoverlap. So, the eÆ ien y of the algorithm is limited by the overlap between neutraland harged parti les in the ells of the alorimeter. We need to know more about thise�e t and its in uen e in the analysis.On the other hand, the method is simple but its realization is a hallenge: it requiresbuilding the parti le ID asso iated with the tra k. This starts running into diÆ ultiesin high tra k multipli ity environment and oarse alorimeter granularity: it requiresuse of advan ed lustering algorithm apable of eÆ ient isolation of the individualshowers, together with an energy deposit model.So, a good lustering algorithm is essential to resolve showers as well as a splittingor merging strategy. This algorithm will be also eÆ ient as many ells are hit by theparti les.2

2 Clustering AlgorithmsIn the present ATLAS s heme[5℄, two di�erent types of luster algorithms are foreseen:a) One type of luster algorithm basi ally sele ts the ore of an ele tromagneti energy deposit in order to provide an optimal measurement of ele trons andphotons. This algorithm de�nes a one around the entre-of-gravity of a middle ell and it in ludes 3x5 ells (for un onverted photons) or 3x7 ells (for ele tronsand onverted photons) as given by the geometry of the middle layer of the EM alorimeter.b) On the other hand, for the re onstru tion of hadroni shower the energy depositsin near ells have to be merged to lusters. This lustering algorithm is therefore alled topologi al lustering algorithm. Depending on the nature of the energydeposit: hadroni , ele tromagneti or muoni , di�erent energy orre tions shouldbe applied.2.1 Sliding Window ClusteringThe Sliding Window (SW) algorithm is simple sear h for lo al maxima of ET depositon a grid using a �xed-size \window" made up of a group of ontiguous trigger towersin �-� spa e. Lo al maxima are found by moving the window by �xed steps in � and �.The window an be adjusted to di�erent sizes, so that it an be optimised for di�erentparti les/energies. They an then be orre ted for di�erent modulation e�e ts, andlongitudinal weights are omputed to further optimise resolution and linearity.This algorithms produ es a very preliminary lusters of ells as no orre tions havebeen applied yet. The default window size is 5 x 5 ells inside ea h luster, entered inthe ell with the biggest value of ET . This value usually de�nes the luster formed byele trons and photons with energy larger than 100 GeV.Di�erent window sizes are used for less energeti parti les (ET<100GeV) are 3x5 ells (for un onverted photons) and 3x7 ells (for ele trons and onverted photons).2.2 EGamma ClustersEGamma re onstru tion ombines Inner dete tor tra ks information with CalorimeterClusters (Sliding Windows) with the default value of SW lusters of 5x5 ells insideea h lusterTypi ally these are the algorithms useful for the identi� ation of the ele tromagneti obje ts, ele trons and photons:a) Ele tron re onstru tion is performed in two ways:- High pT ele trons are sear hed for by asso iating tra ks to sliding window lusters, and omputing shower shape variables, tra k to luster asso ia-tion variables, and TR hits variables. Dedi ated tra k �tting pro edure forele trons are being developed. 3

- Soft ele tron re onstru tion pro eeds by extrapolating harged tra k to the alorimeter, and building a luster around the harged tra k impa t point.This pro edure has a better eÆ ien y for less than 10 GeV transverse mo-mentum ele tron, and for ele tron inside jet, pertinent for b-tagging.b) High pT photons are identi�ed in a similar way, with the main di�eren e that atra k veto is performed, expe t for re onstru ted onversions.2.3 3D Clustering Algorithm: CaloTopoClusterThe 3D Clustering algorithm[6℄ in Athena reated by Sven Menke is based on the ell Nearest Neighbor. This algorithm was developped for LAr (in the LArClusterRe pa kage) and later extended to Tile Calorimeter and implemented inside ATHENAenvironment (in the Re onstru tion/CaloRe pa kage). This algorithm is also used inthe BaBar experiment[7℄.The main hara teristi of this lustering algorithm is that it is independent of thesub-dete tor, i.e., it an be used for LAr and Tile Calorimeters.2.3.1 Basi Prin iple of the AlgorithmThe 3D Clustering algorithm onsists in a simple topologi al lustering algorithm work-ing with three di�erent signal over noise threshold:� Cell ut: jE=�noisej > T ell (default T ell = 0); only ells above this threshold areused� Neighbor ut: jE=�noisej > Tneighbor (default Tneighbor = 3); only ells above thisthreshold are sear hed from their neighbors� Seed ut: E=�noise > Tseed (default Tseed = 30); only ells above this thresholdare used to initiate a luster1.Additional uts on the transverse energy deposited in the alorimeter ells an also beapplied. on all 3 levels: seed, neighbor and ell.A luster is built around a Seed ell whose energy is above a ertain threshold (theSeed ut). The neighbors of the seed ell are added to the luster if their energy isabove another threshold (the Neighbor ut). Finally this is repeated re ursively untilthis pro edure onverges (see �g.1).The uts on the seed and the neighbor ells depend on the noise level in ea h ell.This way lusters are formed around ells with E=�noise above a ertain value and aminimum transverse energy deposited.1Note that in this last ase, threshold is only over the positive value, no over the absolute value ofE=�noise4

Figure 1: In the 3D Clustering algorithm, the lusters are formed around a seed ell above a ertainthreshold (Seed ut = E=�noise ) and they are added to the luster if their energy is above the thresholdNeighbor ut = jE=�noisej .3 Des ription of CaloTopoClusterMaker in 7.8.0In the 7.8.0 release of ATHENA[8℄, the implementation of topologi al lusteringuses an AlgTool alled CaloTopoClusterMaker to reates CaloCluster[9℄ obje ts from a olle tion of CaloCell obje ts by grouping them a ording to their neighbor relations:� all2D: produ es separate lusters in ea h Layer (only lusters in the same layerand alorimeter). When used with the \AllCalo" option the di�erent layers or-respond to:- 4EMB +4EMEC +4HEC +3 FCAL +3 Tile = 22 regionsThe neighbors of a ell are the 2 neighbors in +/- � dire tion, the 2 neighborsin +/- � dire tion and the 4 orner ells in +/- � and +/- �. Cells at the edgesof the alorimeters (or in test beam modules) might have fewer neighbors, butusually ells have 8 all2D neighbors.� all3D: produ es separate lusters in ea h alorimeter EM, HEC, FCal, Tile (only lusters in the same alorimeter):- EM, HEC, FCal, Tile = 4 regionsThis is all the all2D neighbors of the ell plus ells in the sampling before andthe sampling beyond this ell overlapping at least partially in the �-� plane withthe urrent ell. Samplings outside the urrent alorimeter are not onsidered inthis option.The �noise an be de�ned in two ways:- �xed: a �xed value for all ells (ad-ho ut of ET value). This option is onlyuseful for testing.- ele Noise: use the ele troni noise from CaloNoiseTool (default option)The ele troni s noise levels (in MeV on a log s ale) for all ells is shown in �g. 22. Theplot shows that the lustering has to ope with 3 orders of magnitude for the hangesin noise levels ranging from about 10 MeV in the �rst EM Barrel layer up to 1 GeV inthe rear FCal module.2Figure taken from TWiki Web page for Topologi alClustering, made by S. Menke.5

Figure 2: Ele troni s noise levels (in MeV on a log s ale) for all ells as a fun tion of alorimeterlayers ( olor ode) and � (x-axis).4 Basi Idea of the analysisThe main idea of this analysis[10℄ is to ompare the di�erent lustering algorithmsinside the ATHENA framework of ATLAS[11℄: TopoCluster, Sliding Window luster,EGamma luster and one algorithms. We show how these lustering algorithms anbe tuned to obtain the best energy resolution when re onstru ting very low energyparti lesFirst the transverse energy deposited in all ells of the alorimeter is evaluatedand onsidered as the \referen e Energy Flow", i.e., the best resolution that ould berea hed for the most sophisti ated algorithm taking into a ount the whole transverseenergy in all the alorimeter.Then, for neutral pions the \referen e Energy Flow" is ompared with the oneobtained by the di�erent algorithms whi h main features are the following:� Sliding Window luster: the default value of the luster is 5x5 ell, but alsowill be he ked 3x5 and 3x7 ells.� EGAMMA luster: useful for the re onstru tion of lusters in the EM regionof the alorimeter.� TopoCluster[6℄ in EM: as we have seen, in this ase the luster has not a�xed size and it is built around a Seed Cell whi h has an energy above a ertainthreshold.� �R one around seed: the luster is re onstru ted from the ells inside a onewith a ertain value of its radius �R , where �R is de�ned as �R =q��2 +��2.On the other hand, for the ase of neutrons and harged pions, as they depositedtheir energy in Tile Calorimeter as well as in the EM alorimeter, the EGAMMA lusters an not be used, be ause they don't re onstru t properly this type of parti les.6

So, for neutrons the \referen e Energy Flow" will be ompared with the evaluatedby: � TopoCluster in EM and Tile: For 7.8.0 release in CaloTopoCluster, only hasone luster in ea h subdete tor, so, the energy from Tile and EM alorimetermust be added to obtain the total energy.� �R one around seed: where the size of the radius must be bigger than theone orresponding to neutral pions, be ause the shower of �+'s and neutrons iswider than for �0's.Finally, for harged pions,as they have asso iated tra ks, the \referen e EnergyFlow" will be ompared with the evaluated by:� TopoCluster in EM and Tile� �R one around seed� momentum of TRACKS, only al ulated by xKalman (be ause in 7.8.0 releaseiPatRe didn't work).In order to �nd the best energy resolution and the larger amount of energy depositedinside the lusters, the tunning of the TopoClusters will be performed to be moreapropiate for very low energy parti les.In se tion 6, di�erent thresholds for the EM Noise will be he ked for the re on-stru tion of TopoClusters:� EM Noise = 10 MeV: Value of EM Noise lower than the realisti ase. Thisvalue is only useful for he king, be ause the study will be done with very lowenergy (VLE) parti les.� EM Noise = 70 MeV: Fix value by default for EM alorimeter.� CaloNoiseTool=true: Pa kage with a model for the ele troni noise.using the default values for the thresholds of Seed ell (E=�noise = 30) and Neighbor ells (jE=�noisej = 3).In se tion 7, the thresholds of Seed ell and Neighbor ells will be hanged for lowerthresholds:a) Seed ut = E=�noise = 6 and Neighbor ut = jE=�noisej = 3b) Seed ut = E=�noise = 5 and Neighbor ut = jE=�noisej = 2.5 ) Seed ut = E=�noise = 4 and Neighbor ut = jE=�noisej = 2In se tion 8, the luster ET will be re onstru ted from the ell ET inside a one.Di�erent strategies are followed for the di�erent type of parti les:7

a) Neutral pions:{ The enter is � � � of EGamma luster: EGamma- one{ The enter is � � � of TopoCluster in EM al: Topo- one{ The enter is � � � of TRUTH generated �0's: TRUTH- oneb) Charged pions:{ The enter is � � � of TRUTH generated �+'s: TRUTH- one{ The enter is � � � of TRACK at 2nd layer: TRACK- one ) Neutrons:{ The enter is � � � of TRUTH generated neutrons: TRUTH- oneAt the begining, a one with �R <1.0 is used, be ause in this �rst onta t only it isrequired to sele t the one algorithm with the best resolution.But in se tion 8.3 a smaller radius, di�erent for ea h type of parti le depending onthe nature of the shower, will be taken.For the re onstru tion of the lusters from neutral pions, we will used:- �R < 0:1- ��= 0.0875 ��=0.0375 : 7x3 ells- ��= 0.0625 ��=0.0375 : 5x3 ells- �R < 0:0375: 3x3 ells (to study very on entrate ET deposit)For the ase of harged pions and neutrons:- �R < 0:1- �R < 0:2- �R < 0:4The omparison of the best one algorithm with the TopoCluster with di�erentthresholds and with the EGamma lusters will be arried out in the se tion 9.Finally, from the se tion 10 the ele troni noise is in luded to study its in uen ein the size of the TopoClusters and the ET resolution. These samples were generatedused the 8.2.0 release, whi h have several new apli ations for the TopoClusters:- the luster is made a ross all alorimeters (EM+HEC+FCal+TCal)- ET and �-� of the ells whi h form the TopoClusters are availableThey allows us to study of the size of the luster and the energy distribution in thedi�erent alorimeters. These hara terist s will hange when TopoCluster thresholdsrelated to the ele troni noise are swithed on in se tion 10.48

5 Samples of single parti leThe present results are based on single parti le samples of �0�s, ���s and neutrons,simulated by D. Froidevaux3 with Geant3 during DC14. Pions and neutron (the main omponents of jets) have been generated at very low transverse energy5 (between 1and 30 GeV), in order to understand the shape of the shower, the amount of energydeposited in ell and the overlap between harged and neutral parti les.First, samples with only one type of parti les have been used to generate withGeant3 ROOT-tuples of 1000 events of:� �0's with pT = 1, 3, 5, 10 and 30 GeV. To understand the behavior of photonsinside the EM alorimeter.� �+'s and neutrons with pT = 1, 3, 5, 10 and 30 GeV. To know more about thehadroni shower.at �xed pseudorapidity � = 0.3 ( alorimeter barrel) and � = 1.6. Next, the re onstru -tion of these 1000 parti les from the lusters will be arried out using di�erent releasesof ATHENA: 7.8.0 and 8.2.0, omparing the results with and without ele troni noiseapplied6.5.1 Composition of the showersThe omposition of the shower of these samples of parti les is analyzed, i.e., thetype of se ondary parti les that are generated when these parti les intera t with thedete tor material.For �0's, we an see in the �gure 3 that the shower has only ele tromagneti om-ponents (photons, ele trons and positrons), be ause neutral pions usually de ay tophotons: �0 ! and then, photons produ e e+e� pairs. They deposit all theirenergy in EM Calorimeter.On the other hand, the de ays of harged pions and neutrons are mu h more om-pli ated, and a more extensive variety of \se ondary parti les" is obtained, as the �gure4 shows. Next, the main ontributions are explained:� There is an important amount of baryons (protons and neutrons), the biggest ontribution to the \se ondary parti les".{ Neutron beta de ay: n! pe+�3The samples are lo ated at CASTOR area in: = astor= ern: h=user=f=froid=di e03=4Events generated with Geant3 and high statisti s: 107 events, to test the simulation-re onstru tion hain.5This is the best range of energy to apply Energy Flow Algorithm, be ause at very low pT themomentum resolution of tra king is better than the energy resolution of the alorimeters.6Multiparti les samples with ele troni noise have been also used to study the e�e t of the overlapof parti les using Splitter tool with TopoClusters (see Appendix 2).9

Figure 3: Composition of the shower for the neutral pions at 5 GeV.� There are also leptons (ele trons and quarks) and photons as result of the de ayof pions:{ �0 ! ,�0 ! e+e�.{ � ! e + � + , � ! 3e+ �.{ Pion beta de ay: �+ ! �0 + e + �, �+ ! e+ �.� The de ay ��! �� + � has been also analyzed but there are only fewof them, e.g. in the sample of 5 GeV neutrons we have only 12 �'s and13 �'s7.{ KL ! �o , KL ! e+e�e+e�.{ KS ! �oe+e�, KS ! �+��e+e�.And these \se ondary parti les" deposit their energy in E.M. alorimeter as well asin the HAD alorimeter, due to their very low pT 8.

Figure 4: Composition of the shower for the harged pions at 5 GeV.7The �0 de ays to e+, e� and gamma ray by the e.m. intera tion on a time s ale � 1016 s. The�+'s have longer lifetimes � 2.6 x 10�8 s: may be Geant onsider them as stable parti les.8It is known that for high pT parti les, the energy of harged pions and neutrons is usually depositedonly in the hadroni alorimeter 10

5.1.1 Total energy depositedFor the neutral pions, as there are only ele tromagneti parti les we expe t having allthe energy deposited in the E.M alorimeter. From the study of the energy resolution(PETopoEM=Egener), a Gaussian distribution entred in the value of energy for thegenerated parti les is obtained, but with a ertain width due to the u tuation ofenergy, as well as the resolution of the EM alorimeter (� 100%=pE).Nevertheless, for harged pions and neutrons the situation is di�erent. Al-though, as it's known for high pT parti les, the energy of harged pions and neutronsis usually deposited only in the hadroni alorimeter, for the ase of very low energy,they also deposited their energy in the EM alorimeter (around 40-50%), as the table1 shown. This deposited energy in rease with the ET of the parti les. In this ase, thewidth of the Gaussian of the PETopoEM=Egener distribution will be bigger be ause theresolution of the Hadroni alorimeter in ATLAS is worse (� 50%=pE).ET Charged pions Neutronsparti les ET in EM(%) ET in Tile (%) ET in EM (%) ET in Tile (%)1 GeV 84 16 66 343 GeV 70 30 57 435 GeV 62 38 56 4410 GeV 55 45 53 4730 GeV 47 53 49 51Table 1: Proportion of transverse energy deposited by harged pions and neutrons in EM andTile Calorimeter inside TopoEM and TopoTile lusters using CaloNoiseTool and Seed ut=30 andNeighbor ut=3.So, in the ase of TopoClusters, for the study of the �0's only the energy fromTopoCluster in EM will be sum, while for the study of the harged pions and neutrons,we must add the energy from TopoCluster in EM and in Tile if we want to obtain thetotal energy.

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6 Thresholds for EM NoiseThe analysis is done using the 7.8.0 release of ATHENA and taking the usual thresholdsfor the Seed Cell and the Neighbor Cells inside the CaloTopoCluster pa kage, it meansthat the values used by default for parti les with normal energy are:� for Seed Cell: Seed ut = E=�noise = 30� for Neighbor ells: Neighbor ut = jE=�noisej =3In order to �nd the best energy resolution and the larger amount of energy depositedinside the lusters, di�erent thresholds for the EM Noise will be he ked for the re on-stru tion of TopoClusters:� EM Noise = 10 MeV: Value of EM Noise lower than the realisti ase. Thisvalue is only useful for he king, be ause the study will be done with very lowenergy (VLE) parti les.� EM Noise = 70 MeV: Fix value by default for EM alorimeter.� CaloNoiseTool=true: Pa kage with a model for the ele troni noise.6.1 Multipli ity of TopoClustersIn an important amount of events the multipli ity is zero for all parti les due tothe high number of TopoClusters badly de�ned, so it seems to be ne essaty to hangethe Thresholds.Anyway, the table 2 shows the proportion (in %) of the existen e of 0, 1, 2 andmore than 2 TopoClusters in ea h event. The multipli ity of TopoCluster for hargedpions and neutrons is between 1 and 2. The multipli ity equal to 2 indi ates when theparti le has deposited its energy in both LArEM and Tile Calorimeter giving rise toTopoEM and TopoTile lusters. The multipli ity tends to be over 2 as ET of parti lesin rease be ause in this ase the \se ondary parti les" of the hadroni shower extendfurther as more energeti they are.ET (TopoClusters �+'s) TopoClusters (neu)parti les 0 1 2 >2 0 1 2 >21 GeV 92 8 0 0 93 7 0 03 GeV 63 34 3 0 63 34 3 05 GeV 41 50 8 1 44 47 8 110 GeV 16 65 16 3 15 64 16 530 GeV 0.5 42 41 16.5 0.5 35 46 18.5Table 2: Multipli ity of TopoClusters for �+'s and neutrons from 1 to 30 GeV, using EMNoise= 70MeV and the default value for Seed ut (E=�noise = 30) and Neighbor ut (jE=�noisej = 3). Proportion(in %) of the existen e of 0, 1, 2 and more than 2 TopoClusters in ea h event.12

For neutral pions, the table 3 shows the multipli ity of TopoCluster and EGamma lusters from 1 to 30 GeV. It is possible to see how at 1 and 3 GeV the TopoClustersalgorithm does not work properly be ause it an not re onstru t any lusters. On theother hand, EGamma algorithm is managed to re onstru t the 60-70% of the lustersat 1-3 GeV. For longer energies, the multipli ity of TopoClusters and EGamma lustersseems to be around 1. This behavior will be orre t if the photons would be very loseone to ea h other, and the lustering algorithm onsiders them as only one luster9.ET TopoClusters (�0's) EGamma lustersparti les 0 1 2 >2 0 1 2 >21 GeV 100 0 0 0 2 62 35 13 GeV 100 0 0 0 0 74 20 65 GeV 96 4 0 0 0 78 14 810 GeV 0 82 14 4 0 82 14 530 GeV 0 92 6 2 0 90 8 2Table 3: Multipli ity of TopoCluster for �0's and EGamma lusters from 1 to 30 GeV, using EM-Noise= 70 MeV and the default value for Seed ut (E=�noise = 30) and Neighbor ut (jE=�noisej = 3).Proportion (in %) of the existen e of 0, 1, 2 and more than 2 TopoClusters in ea h event.

9This supposition will be analyzed in Appendix 1 in a deeper study of the angle between the twophotons of the �0 de ay ( �0 ! ). 13

6.2 Number of TopoClusters with di�erent EM NoiseThe �gures 5 and 6 show the number of TopoClusters using the di�erent values ofEM Noise, for �+'s, neutrons and �0's respe tively.In general, there is a low eÆ ien y of TopoClusters mainly at 1, 3 and 5 GeV. ThiseÆ ien y is even smaller in the ase of neutral pions, where, by ontrast, EGamma lusters are de�ned always for all the range of the parti le energy.

Figure 5: Number of TopoCluster for �+'s and neutrons, using EM Noise=10 MeV (red),EM Noise=70 MeV (green) and CaloNoiseTool (blue).For harged pions and neutrons, the best result is for EM Noise=10 MeV, butthis isn't a realisti ase. The multipli ity of TopoClusters is similar for EM Noise=70MeV and CaloNoiseTool, being slightly larger in the last ase.

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Figure 6: Number of TopoCluster for �0's, using EM Noise=10 MeV (red), EM Noise=70 MeV(green) and CaloNoiseTool (blue).For neutral pions, the multipli ity is mu h better applying CaloNoiseTool:� with CaloNoiseTool, although at 1 GeV there isn't TopoCluster de�ned, around50% are well-de�ned at 5 GeV� while using EM Noise=70 MeV, there are non-de�ned TOPO at 1 and 3 GeV,and only around 40% at 5 GeVSo, the rest of the analysis with TopoClusters will be done using the CaloNoiseToolpa kage for the treatment of the Noise in the alorimeter for the three types of parti les.And the next point to study will be to �nd other values for the thresholds of Seed elland the Neighbor ells whi h should allow a better re onstru tion of very low energy lusters.

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6.3 ET resolution with di�erent EM NoiseThe �gures 7 and 8 show the ET resolution for TopoCluster where di�erent EM Noisethresholds are applied (10 MeV, 70 MeV and CaloNoiseTool) for harged pions, neu-trons and �0's. They are ompared with the resolution of the ET deposited in all the alorimeter ells, the pT resolution of tra ks and the EGamma lusters resolution.For harged pions, the best energy resolution omes from the pT of the tra ks,but it gets worse as the energy of the parti le in reases, as we expe t. Respe t tothe alorimeter energy, the best resolution omes from the energy deposited in all the ells of the alorimeters, it is the maximum resolution that an algorithms ould get.Around 30 GeV, the alorimeter energy resolution gets better than the pT resolutionof the tra ks, that indi ates the limit for the appli ation of the Energy Flow.

Figure 7: ET resolution for 1-30 GeV �+'s and neutrons for TopoCluster with di�erent EM Noisethresholds applied (10 MeV, 70 MeV and CaloNoiseTool), the pT resolution of tra ks and the resolutionof the ET deposited in all the alorimeter ells.16

In general, the neutral pions (see �g. 8) have better resolution than �+'s andneutrons, be ause they deposit all the energy in the EM alorimeter with a resolution� 50% while the �+'s and neutrons share the energy deposits between the EM andTile alorimeter, with worse resolution the last one (� 100%).The worst result is from neutrons at 1 GeV, be ause this transverse energy isvery similar to the value of the mass of neutron (mn � 940 MeV). This is an intrinsi problem and we must deal with it during all the analysis.The analysis for Sliding Window algorithm has been done also, but the same resultsas for EGamma lusters have been always obtained, maybe be ause for 7.8.0 releasethe more ompli ated alibration whi h must be applied to EGamma luster have notbeen still implemented.Respe t to TopoClusters, for �+'s and neutrons at 1, 3, 5 and 10 GeV, results havenon-sense, the resolution in rease instead of de reasing with the ET of the parti les,and for �0's, even there are not TopoClusters de�ned at 1 and 3 GeV. Anyway, thebest resolution10 omes from CaloNoiseTool.

Figure 8: ET resolution for 1-30 GeV �0's for TopoCluster with di�erent EM Noise thresholdsapplied (10 MeV, 70 MeV and CaloNoiseTool), EGamma lusters resolution and the resolution of theET deposited in all the alorimeter ells.Finally, for the ase of neutral pions, the energy resolution from TopoClusters isworse than EGamma lusters at 1, 3 and 5 GeV.So, it will be needed to do hanges in the re onstru tion of the TopoCluster, i.e.,apply more appropriated thresholds for parti les with very low energy (VLE) insteadof normal energy.10Ex epting the non-realisti ase of EM Noise=10 MeV17

6.4 Mean value of ET lusterETgenerated with di�erent EM NoiseThe relation ET lusterETgenerated gives us the amount of transverse energy deposited inside the lusters from the total generated energy, and it shows the loss in energy due to thedete tor hara teristi s as well as the eÆ ien y of the lustering algorithm.

Figure 9: Mean value of the ET lusterETgenerated ratio for 1-30 GeV �0's for TopoCluster with di�erentEM Noise thresholds applied (10 MeV, 70 MeV and CaloNoiseTool), EGamma lusters resolution andthe resolution of the ET deposited in all the alorimeter ells.This ratio for all the alorimeter ells indi ates the maximum transverse energydeposited in all ells of the alorimeter for ea h type of parti les respe t to the totalenergy deposited in the dete tor. This value is below 1, so the transverse energy inside ells is smaller than the generated energy, as it is expe ted:a) For �0's be ause the EM alorimeter is a sampling alorimeter, so only a partof the energy is deposited in the a tive layers, whi h gives rise to the so- alled\intrinsi sampling u tuation" (negligible ontributions at high energies,where the onstant term dominates the ET resolution).b) For harged pions and neutrons the mean value is even more far from 1 than inthe ase of �0's, be ause ATLAS has a non- ompensated hadroni alorimeterand they deposit their energy between EM and HAD Calorimeter.

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Figure 10: Mean value of the ET lusterETgenerated ratio for 1-30 GeV �+'s and neutrons for TopoCluster withdi�erent EM Noise thresholds applied (10 MeV, 70 MeV and CaloNoiseTool), the pT resolution oftra ks and the resolution of the ET deposited in all the alorimeter ells.Respe t to TopoClusters, the best results for the mean value of ET lusterETgenerated (againex epting the ase of 10 MeV) omes from CaloNoiseTool. Nevertheless there is a lossin the deposited energy due to the low multipli ity of these lusters, mainly at very lowenergies (1 ,3 and sometime 5 GeV) and the behavior at these low energies is di�erentto the expe ted (the mean value de reases with the energy instead of in reasing).

19

7 Lower thresholds for Seed and Neighbor ellsFor the time being, the default values for the thresholds of Seed ell (E=�noise = 30)and Neighbor ells (jE=�noisej = 3) have been used in the analysis of the TopoCluster.In view of the last results, it will be needed to hange these uts to lower threshold:a) Seed ut = E=�noise = 6 and Neighbor ut = jE=�noisej = 3b) Seed ut = E=�noise = 5 and Neighbor ut = jE=�noisej = 2.5a) Seed ut = E=�noise = 4 and Neighbor ut = jE=�noisej = 27.1 Multipli ity of TopoClustersWith the appli ation of these new thresholds in Seed ut and Neighbor ut, the problemwith the non-de�nition of the TopoClusters at very low energies has disappeared.As it shown in table 4 for harged pions and neutrons, the proportion of lusterswith multipli ity zero is almost negligible11. In both ases, the multipli ity of theTopoClusters is between 1 and 2. The multipli ity 2 indi ates when the parti le hasdeposited its energy in both LArEM and Tile alorimeters giving rise to TopoEM andTopoTile lusters. It tends to be over 2 as the energy of the parti les in reases.ET TopoClusters(�+'s) TopoClusters(neu)parti les 0 1 2 >2 0 1 2 >21 GeV 22 50 24 4 62 34 4 03 GeV 1 20 45 34 8 50 32 105 GeV 5 10 40 34 1 30 38 3110 GeV 0 5 40 55 0 19 28 5330 GeV 0 1 35 64 0 12 22 65Table 4: Multipli ity of TopoCluster for �+'s and neutrons from 1 to 30 GeV, using CaloNoise-Tool and Seed ut=4 and Neighbor ut=2. Per entage of the existen e of 0, 1, 2 and more than 2TopoClusters in ea h event.For the ase of neutral pions, when the default value for the SeedCut and Neigh-borCut were used, TopoClusters didn't work at 1 and 3 GeV. But now, using theselower thresholds, the per entage of multipli ity zero is very low and the numbers arevery similar to the EGamma ones, as the table 5 shows.11Only there are some problems at 1 GeV for the ase of neutrons, be ause of the similarity betweenthis range of energy and the mass of the neutrons.20

ET TopoClusters (�0's) EGamma lustersparti les 0 1 2 >2 0 1 2 >21 GeV 7 66 26 1 2 62 35 13 GeV 0 30 63 7 0 74 20 65 GeV 0 62 30 8 0 78 14 810 GeV 0 82 14 4 0 82 14 530 GeV 0 92 6 2 0 90 8 2Table 5: Multipli ity of TopoCluster for neutral pions and EGamma lusters from 1 to 30 GeV,using CaloNoiseTool and Seed ut=4 and Neighbor ut=2. Per entage of the existen e of 0, 1, 2 andmore than 2 TopoClusters in ea h event.7.2 Number of TopoClusters with lower thresholdsAs it is possible to see in 11, with Seed ut = 4 and Neigh ut = 2 the TopoClustersfor harged and neutral pions are almost ompletely de�ned, even at 1 GeV:� 779 TopoClusters for �+'s� 934 TopoClusters for �0'sSo, using these thresholds the low eÆ ien y of TopoClusters for these single parti lesat 1, 3 and 5 GeV has been pra ti ally eliminated.

Figure 11: Number of TopoCluster for �+'s and �0's using EM Noise=10 MeV (red), EM Noise=70MeV (green), CaloNoiseTool with SeedCut=30 (blue), with SeedCut=6 (bla k), with SeedCut=5(pink) and with SeedCut=4 (light blue).21

Figure 12: Number of TopoCluster for neutrons using EM Noise=10 MeV (red), EM Noise=70 MeV(green), CaloNoiseTool with SeedCut=30 (blue), with SeedCut=6 (bla k), with Seed ut=5 (pink) andwith Seed ut=4 (light blue).The worst result is for neutrons at 1 GeV, but it improves with the hanged uts,as the �g. 12 shows:� SeedCut = 6: 299 TopoClusters for 1 GeV neutrons� SeedCut = 5: 376 TopoClusters for 1 GeV neutrons� SeedCut = 4: 468 TopoClusters for 1 GeV neutronsOnly the 50% of the TopoClusters are de�ned for neutrons at 1 GeV in the best ase,but anyway the problem with the mass of neutron at 1 GeV will be always present.

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7.3 Deposited EnergyFor �+'s and neutrons (see table 6), hanging the Seed ut value from 30 to 4, alarge in rease in the deposited energy is obtained, mainly at 1-5 GeV (e.g. the ETdeposited using Seed ut=4 is almost the double that using Seed ut=30.)12.Charged pions (% of ET )ET TopoClusters All Calo(GeV) Seed ut=30 Seed ut=6 Seed ut=5 Seed ut=4 Cells1 5.1 26.1 32.5 41.1 65.73 21.7 49.3 53.5 57.4 72.95 35.6 59.5 62.2 65.1 76.110 59.5 72.7 74.4 76.1 83.430 77.1 79.7 80.5 81.3 84.6Neutrons (% of ET )ET TopoClusters All Calo(GeV) Seed ut=30 Seed ut=6 Seed ut=5 Seed ut=4 Cells1 4.2 11.8 14.0 16.7 28.43 17.2 33.5 36.3 39.3 51.35 25.5 44.1 46.7 49.8 60.410 46.8 60.6 62.5 64.2 72.230 72.2 75.2 76.0 77.0 81.1Table 6: Fra tion of energy deposited in alorimeter for Charged pions and Neutrons from 1 to 30GeV, for TopoClusters with di�erent thresholds (E=�noise) for Seed Cell and Neighbor ells and forall the alorimeter ells. Neutral pions (% of ET )ET TopoClusters Egamma All Calo(GeV) Seed ut=30 Seed ut=6 Seed ut=5 Seed ut=4 lusters Cells1 0.0 52.8 59.8 67.8 76.8 87.13 36.4 83.7 85.2 86.6 81.1 95.25 76.2 90.4 91.0 91.8 91.0 96.810 93.4 94.6 95.0 95.4 95.3 98.430 97.5 97.7 97.8 97.9 97.8 99.5Table 7: Fra tion of energy deposited in alorimeter for Neutral pions from 1 to 30 GeV, forTopoClusters with di�erent thresholds (E=�noise) for Seed Cell and Neighbor ells, for Egamma lusters and for all the alorimeter ells.For �0's, using SeedCut=30 there are no TopoClusters at 1 GeV, but with thesenew values for the threshold of SeedCell up to 67% of the energy is deposited inside the12For neutrons this improvement is not so large at 1 GeV, be ause there are very few luster de�nedat this energy due to the fa t that ET is similar to the mn23

lusters at 1 GeV, as is shown in the table 6. For the rest of the ranges, the values forthe deposited energy are very similar to the EGamma lusters and ompetitive respe tto the total energy in all the alorimeter ells.In any ase, the use of these new values for the threshold in Seed and Neighbor ellre onstru ts better the lusters ome from VLE parti les and be ause gives a largervalue of the energy deposited inside the lusters.7.4 ET resolution results with lower thresholdsThe �gures 13 and 14 show the ET resolution for 1-30 GeV �+'s and neutrons respe -tively, where di�erent thresholds (E=�noise) for Seed Cell and Neighbor ells of theTopoClusters are applied (Seed ut = 30, 6, 5 and 4 orrespond to Neighbor ut = 3,3, 2.5 and 2). Therefore we have al ulated the momentum resolution of the tra kswith xKalman for �+'s and the resolution of the energy deposited in all the ells inthe alorimeter (CELL). The best results for all parti les omes from Seed ut=4 andNeigh ut=2.

Figure 13: ET resolution for 1-30 GeV �+'s, whit di�erent thresholds for TopoClusters, the pTresolution of the tra ks and the resolution of the ET in all the ells.Using these new uts for Seed and Neighbor ells the behavior of TopoClusters ETresolution is more similar to the resolution of the ET deposited by all the ells in the alorimeter (CELL), it means loser to ideal ase.24

Figure 14: ET resolution for 1-30 GeV neutrons, whit di�erent thresholds for TopoClusters and theresolution of the ET deposited in all the ells.On the other hand, the �gure 15 shows the ET resolution for �0's from 1 to 30GeV, where di�erent thresholds (jE=�noisej) for Seed Cell and Neighbor ells of theTopoClusters are applied. Therefore we have al ulated the EGamma lusters reso-lution and the resolution of the energy deposited by all the ells in the alorimeter.Using any of these new uts for TopoClusters, the energy resolution is even better thanthe resolution from EGamma lusters, so there is a huge gain in resolution.

Figure 15: ET resolution for 1-30 GeV �0's, with di�erent thresholds for TopoClusters, the EGamma lusters resolution and the resolution of the ET deposited in all the ells.25

7.5 Mean value of ET lusterETgenerated with lower thresholdsThe �gures 18, 16 and 17 show Mean value of the ET lusterETgenerated ratio for 1-30 GeV�0's, �+'s and neutrons respe tively. With the appli ations of these new uts, thereis a high in rease in the transverse energy deposited inside TopoClusters respe t toSeedCut = 30. Now the value of ET lusterETgenerated is approa hing to 1 as the energy of theparti le in reases. The best result for all types of parti les omes form SeedCut = 4and NeighCut = 2.

Figure 16: Mean value of the ET lusterETgenerated ratio for 1-30 GeV �+'s, whit di�erent thresholds forTopoClusters, pT resolution of the tra ks and ET resolution in all the ells.

Figure 17: Mean value of the ET lusterETgenerated ratio for 1-30 GeV neutrons, whit di�erent thresholds forTopoClusters and ET resolution in all the ells.26

For �0's, ex ept at 1 GeV, the energy deposited inside TopoClusters for all ases islarger than the deposited in EGamma lusters.

Figure 18: Mean value of the ET lusterETgenerated ratio for 1-30 GeV �0's, with di�erent thresholds forTopoClusters, the EGamma lusters resolution and the resolution of the ET deposited in all the ells.These new uts are eÆ ient with the present samples without Ele troni Noise.When later (with 8.2.0 release) the noise will be applied, the uts must be hanged inorder to avoid olle t noise in the re onstru tion of the luster energy.

27

7.6 Possible double ountingThe �gure 19 shows the lineal and logarithmi distributions of ET lusterET ell for theTopoClusters, sliding window and EGamma luster. This ratio relates the ET depositedinside ea h type of luster (Topo, SW or EGamma) with the total ET deposited in thewhole of the alorimeter ells, it means, the maximum value for the ET deposited.When this ratio is larger than 1, it means that the ells are used more than on e inthe re onstru tion of the luster energy. In TopoClusters this fa t does not happend,while this seems to be pla e in the Sliding Window and EGamma luster ases13

Figure 19: Lineal and logarithmi distributions of ET lusterET ell for TopoClusters, EGamma or SlidingWindow lusters.13This re e ts a failure in the development of the ell loop inside these algorithms: the ells mustbe removed from the list after they pass to form a luster.28

8 Cone algorithms for VLE parti lesThe ET of the lusters will be re onstru ted from the ET of the all ells inside a onewith a ertain value of its radius �R , where �R is de�ned as �R =q��2 +��2.Di�erent strategies to hoose the enter of the one are followed for the di�erent typeof parti les:a) Neutral pions:{ The enter is � � � of EGamma luster: EGamma- one{ The enter is � � � of TopoCluster in EM al: Topo- one{ The enter is � � � of TRUTH generated �0's: TRUTH- oneb) Charged pions:{ The enter is � � � of TRUTH generated �+'s: TRUTH- one{ The enter is � � � of TRACK at 2nd layer: TRACK- one ) Neutrons:{ The enter is � � � of TRUTH generated neutrons: TRUTH- oneIn prin iple, it is used a one with �R <1.0, be ause in this �rst onta t only it isrequired to sele t the one algorithm with the best resolution.8.1 Rare behavior of Cone Algorithms for VLE parti lesFor �0's, there are tails in the left side of the E lusterEgenerated distribution at 1 and 3 GeV forEGamma- one and Topo- one. The �gure 20 shows the E lusterEgenerated distribution at 1 GeVfor EGamma- one and Topo- one.

Figure 20: E lusterEgenerated ratio at 1 GeV for EGamma- one (left) and Topo- one (right).29

Seeing the multipli ity of lusters for these ases, we an extra t that the tails omefrom a missing photon, be ause the ones in these ases are entred at one photon andthe other is outside the one (due to the fa t that at VLE, photons from the de ay of�0's are emitted with a larger angle).On the other hand, for �+'s, as it an be seen in �gure 21, there is a deviation of�� at 1 and 3 GeV for the ase of the one entered in � � � of TRUTH generated�+'s (TRUTH- one):� at 1 GeV, �� distribution is entred at 0.5.� at 3 GeV, �� distribution is entred at 0.2.while that for the TRACK- one the �� distribution is always entred at zero. Never-theless, over 5 GeV, the �� distribution is entred at zero in both ases. So, it seemsthat THUTH variables are not well de�ned for very low energies.

Figure 21: �� distributions in TRUTH- one and TRACK- one at 1 and 3 GeV.

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8.2 Preliminary on lusions about Cone AlgorithmThe �gures 23 and 22 show the ET resolution for 1-30 GeV �+'s and �0's, wheredi�erent one algorithm are applied (always with a radius �R = 0:1). For �0's, the one is entered in the � � � of the tra ks (TRACK- one) and of the truth parti le(TRUTH- one). For �0's the one is entered in the � � � of the EGAMMA luster,the TopoEM luster and the truth parti les.

Figure 22: ET resolution for 1-30 GeV �0's, where di�erent one algorithm are applied (always with�R = 0:1).The best ET resolution for �+'s orresponds to the TRUTH- one, but there areproblems with the deviation of �� for VLE. Respe t to the �0's,the TRUTH- onegives the best re onstru tion to the luster energy, as well as there are not tails inE lusterEgenerated distribution.

Figure 23: ET resolution for 1-30 GeV �+'s, where di�erent one algorithm are applied (alwayswith �R = 0:1).31

Taking into a ount these results and the problems derivated to the before \rarebehaviors", in the next analysis, it will be used as one algorithm for the re onstru tionof luster from VLE parti les:� For �+'s: the TRACK- one� For �0's and neutrons: the TRUTH- one8.3 �R de�nitions for one algorithms for VLE parti lesUsing a one with a radius �R around 1, it is taken into a ount more than one showerin the same luster. So it will be needed to de�ne a smaller radius, di�erent for ea htype of parti le depending on the nature of the shower.The radius for neutral pions are extra ted from the \Calorimeter Performan e"analysis where the luster, for parti les with low energies (E< 100 GeV), are takenwith sizes of the order of:� for un onverted photons: 5x3 ells (� �R < 0:073)� for onverted photons and ele trons: 7x3 ells (� �R < 0:095)Following these studies, in this analysis for the re onstru tion of the lusters fromneutral pions, we will use:- �R < 0:1- ��= 0.0875 ��=0.0375 : 7x3 ells- ��= 0.0625 ��=0.0375 : 5x3 ells- �R < 0:0375: 3x3 ells (to study very on entrate ET deposit)For the ase of harged pions, the information has been found in LAr TestBeamanalysis, using there: 7x7 ells, 9x7 ells and 11x11 ells for the re onstru tion of lusters. In this se tion, we apply the next value to the radius of the one:- �R < 0:1- �R < 0:2- �R < 0:4Finally, for neutrons, as their shower is as wide as the harged pions, the samevalues for �R will be he ked.32

8.4 ET resolution from one algorithms for VLE parti lesThe �gure 24 let us to ompare the energy resolution for the di�erent value of �R for harged hadrons. The best results ome from TRACK- one with �R < 0:4, butwith �R < 0:2 also a good resolution is obtained and it allows a better de�nition ofthe shower of only one pion.

Figure 24: ET resolution for 1-30 GeV �+'s, whith di�erent one algorithms: TRACK- one andTRUTH- one are al ulated with �R = 1.0, 0.4, 0.2 and 0.1.On the other hand, for neutrons (see �g.25), the best energy resolution usingTRUTH- one is with �R < 0:4, but applying the value �R < 0:2, the resolution issuÆ iently good. In both ases, the radius �R < 0:1 is too estri t to de�ne hadroni parti les.

Figure 25: ET resolution for neutrons from 1 to 30 GeV, where the one algorithm (TRUTH- one)is al ulated with �R = 1.0, 0.4, 0.2 and 0.1.33

In the �gure 26 the ET resolution and the Mean value of the ET lusterETgenerated ratio forneutral pions are plotted. The energy resolution using TRUTH- one with the radius�R < 0:1 is the best. The lusters re onstru ted with 7x3 and 5x3 ells gives us agood resolution but not enough14. Finally, the results of the energy resolution from3x3 ells are very bad15.

Figure 26: ET resolution (top) and Mean value of the ET lusterETgenerated ratio (bottom) for �0's from 1 to30 GeV, where the one algorithm (TRUTH- one) is al ulated with �R = 1.0 and 0.1, as well asde�ning lusters sizes of 7x3, 5x3 and 3x3 ells.In the next analysis, the values of �R whi h will be used in the one-algorithm forthe re onstru tion of lusters from VLE parti les will be:- For harged pions, the TRACK- one with �R < 0:2- For neutrons, the TRUTH- one with �R < 0:2- For neutral pions, the TRUTH- one with �R < 0:114They ould be useful when ele troni noise will be applied.15So they won't be used in the next analysis, it only have been studied to he k the possibility of avery on entrate deposit of energy for VLE parti les.34

9 Comparison of Cone-algorithms with TopoClus-ter and EGamma analysisThe �gures 27, 28 and 29 allow to ompare the best result of ET resolution using onealgorithms with the TopoClusters of di�erents thresholds and with the ET resolutionfrom the deposited energy in all the ells (pink line). In the ase of �0's EGamma luster is also in luded (yellow line).For harged hadrons, the best TOPO algorithms is obtained using the thresholdsSeedCut=4 and NeighCut=2 (dark blue line), as it is possible to see in 27. Nevertheles,the TopoCluster algorithm gives worse energy resolution than any of the two onealgorithms: TRACK- one with �R = 0.2 (grey line) and TRUTH- one with �R =0.4 (bla k line), very lose one to ea h other, and with better energy resolution mainlyat 1-5 GeV.

Figure 27: Comparison of ET resolution of the best one algorithms with the rest of lusteringalgorithms, for 1-30 GeV harged pions. The best algorithms are TRACK- one with �R = 0.2 (darkblue line in the �gure) and TRUTH- one with �R = 0.4 (bla k line), very lose one to ea h other.On the other hand, the �gure 28 shows the di�erent result of ET resolution forneutrons. The TRUTH- one with radius �R < 0:2, is the best algorithm in general16,but TOPO with Seed ut=4 and Neighbor ut=2 is very near and it is better at 1 and3 GeV.16At 1 GeV, it has a worse behaviour due to the �� deviation.35

Figure 28: Comparison of ET resolution of the one algorithm with the rest of lustering algorithmsfor 1-30 GeV neutrons. The best algorithm is TRUTH- one (�R <0.2).Finally, for neutral pions (see �g. 29), the TRUTH- one with �R < 0:1 give thebest energy resolution in general, but TOPO with Seed ut=4 and Neighbor ut=2 hasagain very lose results and even at 1 GeV a better energy resolution is obtained usingit. EGamma lusters give worse results, in general, than TOPO and TRUTH- one,but it gives the best resolution of all at 1 GeV.

Figure 29: Comparison of ET resolution of the one algorithm with the rest of lustering algorithms,for 1-30 GeV �0's. The best algorithms is TRUTH- one (�R <0.1).It is possible to extra t from these senten es that the results from TOPO algorithmare very ompetitive for neutrons and �0's, and for �+'s TOPO is a good algorithmbut not enough, for the time being. It will be needed to test the next versions of theCaloTopoCluster pa kage in the newer release of Athena: 8.2.0.36

10 CaloTopoCluster in 8.2.0 ReleaseIn the 8.2.0 release of ATHENA, CaloTopoClusterMaker[12℄ makes CaloClustersnot only in separate way in ea h Layer (all2D) and in ea h alorimeter EM, HEC,FCal, Tile (all3D) but also:� super3D: anywhere a ross all alorimeters ( lusters everything = 1 region). Itmeans EM+HEC+FCal+TCal = 1 super- luster.Respe t to the noise, in this version in addition to the �xed value and the ele -noisefrom CaloNoiseTool, CaloTopoClusterMaker works with:- ele -noise � pile-up-noise from CaloNoiseToolAnd �nally CaloTopoClusterMaker works with optional additional jEjj(Ej) thresh-olds against Pile-Up on ea h level (defaults: 0 MeV, 100 MeV, 1000MeV)Another important hange in this new version in the implementation of the Split-ter. It split lusters based on topologi al neighbouring and de�ne lo al maxima basedon energy density riteria. This will be a very interesting tool to study the overlap be-tween harged and neutral parti les, and perhaps it will let us to separate and subtra tneutral ontribution to the luster mat hed to one tra k.The information about the ells whi h form the TopoClusters (energy, posi-tion...) is now available in the root ntuple variables. So, it will be possible to analysethe transverse energy deposited in the ells inside TopoClusters and study the best utin ET of ell without and with noise17.Finally, a ROOT ma ro pa kage for ATLAS Calorimeter Event Displays[14℄, is alsoavailable from this release18, and it allows to see the distribution of the energy in the ells inside the TopoCluster and the possible overlapping between luster.10.1 Size of the TopoCluster: Number of ellsThe tables 8 and 9 show that for both, harged pions and neutrons, the majorityof the ells in the TopoClusters ome from EM alorimeter . This per entage de reaseswhen the energy of the parti les in reases and more and more energy is deposited inTILE, be ause the parti les be ome enough energeti to rea h this alorimeter.17Unfortunately, in 8.2.0 release the TopoCluster pa kage didn�t work with the option DoNoiseequal False, so it wasn�t possible to generate ntuples without noise. Anyway, we try to see how theenergy resolution gets worse when the ele troni noise is in luded18CaloEventDisplay pa kage is available in S. Menke Personal web page:http://www.mppmu.mpg.de/ menke/ 37

ET Total Cells in EM (�+)parti les Cells Total (%) Pres Front Mid Ba k1 GeV 182 170 93 10 82 57 203 GeV 257 233 91 13 111 74 345 GeV 311 276 89 14 131 86 4510 GeV 380 330 87 16 154 99 6030 GeV 513 432 84 20 196 122 94ET Total Cells in TILE (�+)parti les Cells Total (%) A BC D1 GeV 182 11 7 8 8 33 GeV 257 24 9 13 8 45 GeV 311 35 11 18 14 610 GeV 380 50 13 23 19 930 GeV 513 81 16 35 32 13Table 8: Mean value of ells in TopoCluster for 1-30 GeV harged pions, using CaloNoiseTool,Seed ut=4 and Neighbor ut=2. The 2nd olumn shows the total number of ells in all alorimeter.The 1st table shows the total number of ells in the EM alorimeter, next to the values for thedi�erent layers of this alorimeter (Presampler, Front, Middle and Ba k). The 2nd table shows thetotal number of ells in TILE, next to the values in its samples (A, BC, D).A large per entage of the ells in EM omes from the se ond layer:- the se ond layer (Front): �48-46% of the ell in EM- the third layer: Middle (�34-30% of the ell in EMSo, respe t to the total number of ells, the most of them are lo ated between these2nd and 3th layer of EM: �83-75% of the total ells.In TILE the �rst sample (Sample A) has the large ammount of ells, but with anamount mu h smaller: �4-6% of the total ellsThe behavior in the alorimeters of the very low energy harged pions and neutronsis very di�erent to the high energeti parti les, and they intera t mostly in the EM alorimeter.Respe t to the neutral pions, in prin iple, they only hit in EM, so the ells ofTopoCluster must be all of them in this alorimeter. Nevertheless, in the table 10 thereis a di�eren e of 10 ells between the total number of ell all alorimeter and the totalnumber of ells in EM. They ome from TILE and it ould be really ele troni noisenot signal19 .19The number of ells in TILE is the same from 1 to 30 GeV and the ET deposited inside these ellsis very low (almost negligible). Therefore, this level of noise (similar energy deposited and similarnumber of ells de�ned) is also found in FCal and HEC alorimeters, where we don't expe t to haveany signal for these parti les samples (be ause they have been generated with a pseudorapidity �=0.3 ( alorimeter barrel) and �=1.6). So it is de�nitively ele troni noise.38

ET Total Cells in EM (neu)parti les Cells Total (%) Pres Front Mid Ba k1 GeV 153 141 92 9 67 48 173 GeV 221 198 90 11 53 64 305 GeV 282 248 87 13 116 77 4210 GeV 378 325 86 16 149 96 6330 GeV 549 463 84 21 209 130 103ET Total Cells in TILE (neu)parti les Cells Total (%) A BC D1 GeV 153 12 8 7 7 33 GeV 221 23 10 12 9 45 GeV 282 34 13 16 13 610 GeV 378 53 14 25 21 830 GeV 549 86 16 39 34 13Table 9: Mean value of ells in TopoCluster for 1-30 GeV neutrons, using CaloNoiseTool andSeed ut=4. The 2nd olumn shows the total number of ells in all alorimeter. The 1st table showsthe total number of ells in the EM alorimeter, next to the values for the di�erent layers of this alorimeter (Presampler, Front, Middle and Ba k). The 2nd table shows the total ells in TILE, nextto the values in its samples (A, BC, D).On the other hand, the number of ells in the last layer of the EM alorimeter ifmu h smaller for �0's than for harged pions and neutrons, be ause the �0's shower islo ated in the �rst samples of EM and they do not get the TILE alorimeter.Finally, we an see as the behavior in the EM alorimeter at very low energies (1-10GeV) is very similar for �0's and neutrons20. As both are neutral parti les we only an start to distinguish them from energies above 10 GeV, when the neutrons have aspread of the shower (460 ells) bigger than the �0's one (338 ells).ET Total Cells in EM (�0)parti les Cells Total Pres Front Mid Ba k1 GeV 197 187 12 96 62 173 GeV 267 253 16 133 82 215 GeV 284 275 18 146 87 2410 GeV 305 295 19 158 92 2630 GeV 350 338 20 180 25 33Table 10: Mean value of ells in TopoCluster for 1-30 GeV �0's, using CaloNoiseTool and Seed ut=4.The 2nd olumn shows the total number of ells in all alorimeter. The 3th olumn shows the totalnumber of ells in the EM alorimeter, next to the values for the di�erent layers (Presampler, Front,Middle and Ba k).20The behaviour of �0's from 1-10 GeV in EM is also similar to the harged pions one, but it willbe possible to distinguish them, asking for a mat hing tra k- luster in the ase of harged parti les39

10.1.1 Geometry of the TopoClusterThe �gures 30 and 31 show the energy deposit of the ells whi h form the TopoClus-ters in the �-� map of the whole alorimeter system for 5 GeV harged pions and �0'srespe tively. It is possible to see that the �0's energy is more lo alized, while the harged hadrons have a wither shower development.

Figure 30: Energy deposit of the ells whi h form the TopoClusters in the �-� map of the whole alorimeter system for harged pions at 5 GeV.

Figure 31: Energy deposit of the ells whi h form the TopoClusters in the �-� map in the EM alorimeter for neutral pions at 5 GeV.40

10.2 Study of the TopoCluster with more energyIn order to see if the energy from the generated parti les an be studied from theenergy inside the TopoClusters, in the next se tion we will analyze the behavior ofthe TopoCluster with the maximum energy deposit ( alled the \1st TopoClusters",be ause they are ordered by ET in the ode). The next TopoCluster in energy will bethe \2nd TopoCluster".For the TopoClusters from harged hadrons, the table 11 shows that the main ontribution to the ET omes from the �rst TopoCluster . This proportion in reaseswith the energy of the parti les.ET Total TopoClusters 1st TopoCluster (�+) 2nd TopoCluster (�+)parti les ET (MeV) ET (MeV) ET (%) ET (MeV) ET (%)1 GeV 1259 560.9 44.5 274.7 20.03 GeV 2654 1407 53.1 504.3 19.05 GeV 4196 2517 59.9 707.7 16.810 GeV 8641 6082 70.3 1169 13.530 GeV 25530 20370 79.8 2711 10.6Table 11: Mean value of the ET deposited in TopoClusters and the proportion (in %) respe t to thetotal ET deposited for the TopoCluster with the maximum energy (1st TopoClusters) and the nextin energy (2nd TopoCluster) for �+'s using Seed ut=4.Respe t to the behavior in ea h alorimeter, the table 12 allows to see that at1-3 GeV �80% of the ET is deposited in the EM alorimeter, in both 1st and 2ndTopoClusters.ET 1st TopoCluster (�+) ET 2nd TopoCluster (�+) ETparti les Calo (MeV) EM (%) Tile (%) Calo (MeV) EM (%) Tile (%)1 GeV 560.9 84.1 10.2 274.7 87.9 6.73 GeV 1407 70.4 29.6 504.3 82.9 14.05 GeV 2517 61.8 39.1 707.7 77.4 22.710 GeV 6082 53.5 51.3 1169 76.2 24.130 GeV 20370 41.8 59.8 2711 69.7 30.3Table 12: Mean value of the energy deposited in TopoClusters in EM and Tile alorimeter and theproportion (in %) respe t to the total energy deposited in all for the TopoCluster with the maximumenergy (1st TopoClusters) and the next in energy (2nd TopoCluster) for �+'s, using CaloNoiseTooland Seed ut=4.The energies in the EM alorimeter de rease with the energy of the parti les, atthe same time in reases the energy in the Tile alorimeter.41

The results of the TopoClusters from neutrons are very similar, as the tables 13and 14 shown.ET Total TopoClusters 1st TopoCluster (neu) 2nd TopoCluster (neu)parti les ET (MeV) ET (MeV) ET (%) ET (MeV) ET (%)1 GeV 964 443.6 46.0 209.9 21.73 GeV 2059 1069 51.9 398.9 19.35 GeV 3437 1943 56.5 608.4 17.710 GeV 7493 5061 67.5 1074 14.330 GeV 24330 18470 75.9 3050 12.5Table 13: Mean value of the energy deposited in TopoClusters and the per entage with respe t tothe total energy deposited for the 1st and the 2nd TopoCluster for neutrons.ET 1st TopoCluster (neu) ET 2nd TopoCluster (neu) ETparti les Calo (MeV) EM (%) Tile (%) Calo (MeV) EM (%) Tile (%)1 GeV 443.6 75.8 12.6 209.9 84.5 6.13 GeV 1609 61.9 39.6 398.9 82.4 16.65 GeV 1943 56.1 45.2 608.4 76.8 21.710 GeV 5061 50.4 50.8 1074 73.3 27.530 GeV 18470 44.2 56.8 3050 68.3 32.9Table 14: Mean value of the ET deposited in TopoClusters in EM and Tile and the per entage withrespe t to the total ET for the 1st and the 2nd TopoCluster for neutrons.Finally for neutral pions, the energy is deposited only in EM alorimeter. Thetable 15 shows that the most important ontribution to the energy omes from the �rstTopoCluster and this proportion in reases with the energy of the parti les.ET Total TopoClusters 1st TopoCluster (�0) 2nd TopoCluster (�0)parti les ET (MeV) ET (MeV) ET (%) ET (MeV) ET (%)1 GeV 1436 659.8 45.9 282.5 19.63 GeV 3427 2133.1 62.2 688.2 20.15 GeV 5414 3712 68.5 1113.4 20.610 GeV 10380 8035 77.4 1959.6 18.830 GeV 30290 28170 93.0 2813 9.3Table 15: Mean value of the ET deposited in TopoClusters and the per entage with respe t to thetotal ET deposited in EM for the 1st and the 2nd TopoCluster for �0's.Note that the re onstru ted energy from TopoCluster in this ase rea hes the largestvalues with respe t to the energy of the generated parti les21.21Maybe the ele troni noise is in luded in the re onstru tion of the TopoClusters energy as well asthe �0 signal 42

10.3 ET resolutions for TopoClusters in 8.2.0 ReleaseFor harged pions and neutrons the energy resolution of TopoCluster in 8.2.0 releaseseems to improve (see tables 16 and 17). But we must remember that in this ase, theele troni noise is applied22, so the resolution may be worse due to the e�e t of thenoise. ET ET Resolution Mean of ET lusterETgeneratedparti les 7.8.0 8.2.0 7.8.0 8.2.01 GeV 56.30 44.57 0.528 1.053 GeV 45.65 38.87 0.581 0.8715 GeV 33.82 30.65 0.652 0.84110 GeV 22.41 20.84 0.761 0.86430 GeV 13.91 13.36 0.813 0.851Table 16: Energy resolution and Mean value of ET lusterETgenerated in TopoClusters for 1-30 GeV hargedpions, using CaloNoiseTool and Seed ut=4 and Neighbor ut=2.ET ET Resolution Mean of ET lusterETgeneratedparti les 7.8.0 8.2.0 7.8.0 8.2.01 GeV 64.31 |- 0.357 |-3 GeV 57.54 46.19 0.406 0.6815 GeV 40.41 34.04 0.498 0.68710 GeV 23.98 22.43 0.643 0.74930 GeV 12.39 11.94 0.110 0.811Table 17: Energy resolution and Mean value of ET lusterETgenerated in TopoClusters for 1-30 GeV neutrons,using CaloNoiseTool and Seed ut=4 and Neighbor ut=2.Seeing the results for neutral pions shown in the table 18, it is possible to betterunderstand what is happening. In the analysis, the thesholds of the TopoClustersrelated to the ele troni noise of the ells have been swi thed o� (the default a tion).It means that in the jobOption �le of the CaloReC pa kage related to CaloTopoCluster:- CellThresholdOnAbsEt = -1.0*MeV- NeighborThresholdOnAbsEt = -1.0*MeV- SeedThresholdOnEt = -1.0*MeVIt implies that all the energy deposited in the ells of the TopoCluster has been takeinto a ount in the analysis: the energy omes from the generated parti les, but alsothe energy of the ele troni noise ontributions.22For this version CaloTopoCluster pa kage only worked putting doNoise=True.43

For this reason, the values of the ET lusterETgenerated are also larger in 8.2.0 than in 7.8.0.And in the ase of �+'s some non-sense results are obtained: ET lusterETgenerated >1 means thatthe energy deposited in TopoCluster are even bigger that the ET generated.ET ET Resolution Mean of ET lusterETgeneratedparti les 7.8.0 8.2.0 7.8.0 8.2.01 GeV 30.52 35.50 0.678 1.2173 GeV 12.66 20.72 0.866 1.1355 GeV 7.35 14.35 0.918 1.08410 GeV 4.02 7.77 0.954 1.03830 GeV 2.21 3.11 0.919 1.010Table 18: Energy resolution and Mean value of ET lusterETgenerated in TopoClusters for 1-30 GeV neutralpions, using CaloNoiseTool and Seed ut=4.10.4 Topo lusters with the ele troni noise thresholdsSo, now the thesholds of the TopoClusters related to the ele troni noise23 of the ells are swithed on, with some values whi h taken into a ount that we are workingwith very low energy parti les:- CellThresholdOnAbsEt = 10.0*MeV- NeighborThresholdOnAbsEt = 80.0*MeV24- SeedThresholdOnEt = 200.0*MeV2523The value of �noise per ell have been extra t from [17℄ and [19℄24The neighbor ells of the TopoClusters must be longer than the �noise per ell:- EM Presampler: �noise= 60-150 MeV- EM Front: �noise= 32-55 MeV- EM Middle: �noise= 60-130 MeV- EM Ba k: �noise= 70-100 MeV- Tile A: �noise= 25-70 MeV- Tile BC: �noise= 25-70 MeV- Tile D: �noise= 25-65 MeVas in this release of Athena is not possible to sele t a value of NeighborThresholdOnAbsEt for ea hlayer of the EM alorimeter and TileCal, and also putting NeighborOption = "super3D" is not possibleto sele t ea h subdete tor options in a separated way, a \mean value" of the level of noise is hoosen.25The Seed ell of the TopoCluster is the ell with the bigest ET . As you an se later, the mostenergeti ells in the 2nd layer of the EM alorimeter has ET > 200MeV .44

10.4.1 Size of the TopoCluster: Number of ellsThe tables 19 and 20 show the mean value of the number of ells for �+ and �0's inTopoCluster with noise thesholds applied26. The majority of the ells in the TopoClus-ters ome from EM alorimeter, as in the ase of tables 8. But now, this proportionde reases when the energy of the parti les in reases only for harged hadrons, for neu-trons it seems to be in uen ed by the theshold in the ele troni noise.The majority of the ells in EM do not ome from the 2nd layer (Front), as in tables8, but from the 3rd layer (Middle) and 4th layer (Ba k):- Middle: �28-31% of the ells in EM- Ba k: �34-39% of the ells in EMThey onstitute around 52-55% of the total ells. This is due to the fa t that theele troni noise in Front is smaller than the NeighborThresholdOnAbsEt value hoosenand a loss in de�nition of Topo luster happens27.ET Total Cells in EM (�+)parti les Cells Total (%) Pres Front Mid Ba k1 GeV 12.8 11.4 88.6 2.4 2.3 2.6 3.93 GeV 38.7 32.0 82.7 2.9 7.5 9.8 11.75 GeV 62.6 50.5 80.7 3.3 13.1 15.5 18.710 GeV 97.0 77.3 79.6 3.9 20.5 24.0 28.830 GeV 168 130 77.2 5.6 37.3 36.3 51.3ET Total Cells in TILE (�+)parti les Cells Total (%) A BC D1 GeV 12.8 1.46 11.4 1.10 0.28 {3 GeV 38.7 6.67 17.2 4.16 2.07 0.235 GeV 62.6 12.08 19.3 7.01 4.32 0.5510 GeV 97.0 19.62 20.2 10.52 7.55 1.2830 GeV 168 38.10 22.5 18.1 15.8 4.15Table 19: Mean value of the ells in TopoCluster for �+ with noise thesholds using Seed ut=4. The2nd olumn is the ells in all alorimeter. The 1st table shows the total ells in the EM alo, next tothe values in ea h layer (Pres, Front, Middle and Ba k). The 2nd table shows the total ells in TILE,next to the values in its samples (A, BC, D).On the other hand, the sample with more ells in TILE is the �rst one (Sample A)and the proportion respe t to the total ell has in reased from �4-6% to �10-12%.The tables 21 and 22 show that the total size of the TopoCluster - when the noisethesholds are added - is from 3 to 19 times smaller. The di�eren e in size in reases26The results for neutrons are very similar, so they are not shown here.27It woul be better ould put the orre t �noise for ea h layer of the EM alorimeter, but it is notpossible in this release of Athena 45

ET Cells in EM (�0)parti les Total Pres Front Mid Ba k1 GeV 9.82 2.49 2.81 2.41 2.123 GeV 45.64 5.83 19.0 15.64 5.165 GeV 63.6 7.21 27.62 21..56 7.2010 GeV 81.25 8.81 36.23 26.62 9.5830 GeV 107.3 10.29 46.67 36.37 13.94Table 20: Mean value of the ells in TopoCluster for �0's with noise thesholds using Seed ut=4.The 2nd olumn shows the total ells in the EM alo, next to the values in ea h layer (Presampler,Front, Middle and Ba k).when the ET of the parti les de reases. This di�eren e is more important for the EM alo than for Tile, be ause in the �rst one the level of noise with respe t to the signalis bigger. Cells of �+'sET No Cut Cut Times No Cut Cut Times No Cut Cut Times(GeV) Total Total Size EM EM Size Tile Tile Size1 182 12.8 14.2 170 11.4 14.9 11 1.4 7.53 257 38.7 6.6 233 32.0 7.3 24 6.7 3.65 311 62.6 4.9 276 50.5 5.4 35 12.1 2.910 380 97.0 3.9 330 77.3 4.3 50 19.6 2.530 513 168 3.0 432 130 3.3 81 38.1 2.1Table 21: Comparison of the Mean value of the number of ells in ea h TopoCluster for �+'s without(no ut) and with ( ut) noise thesholds, using Seed ut=4.ET No Cut Cut Times(GeV) EM EM Size1 187 9.8 19.03 253 45.6 5.55 275 63.6 4.310 295 81.2 3.630 338 107.3 3.1Table 22: Comparison of the Mean value of the number of ells in ea h TopoCluster for �0's without(no ut) and with ( ut) noise thesholds, using Seed ut=4.So the type of parti le most a�e ted to the fa t that in lude the thesholds of theele troni noise will be the neutal pions - whi h deposited all their energy in EM alorimeter. As we an see in the new values of the energy resolution and the Meanvalue of ET lusterETgenerated .46

10.4.2 Energy resolutionThe ET resolution gets worse when the ele troni noise is in luded in all parti les,but applying the noise ut we obtain a ET lusterETgenerated ratio similar to the ase without noise,it means a more realisti method to olle t the ET deposited in ells.ET ET Resolution Mean of ET lusterETgeneratedparti les No Noise With Noise No Noise With Noise(GeV) 7.8.0 8.2.0 8.2.0 ( ut) 7.8.0 8.2.0 8.2.0 ( ut)1 56.30 44.57 60.71 0.528 1.05 0.4373 45.65 38.87 55.77 0.581 0.871 0.5585 33.82 30.65 41.39 0.652 0.841 0.64610 22.41 20.84 26.25 0.761 0.864 0.76130 13.91 13.36 13.09 0.813 0.851 0.817Table 23: Energy resolution and Mean value of ET lusterETgenerated in TopoClusters for harged pions , usingCaloNoiseTool and Seed ut=4 and Neighbor ut=2.ET ET Resolution Mean of ET lusterETgeneratedparti les No Noise With Noise No Noise With Noise(GeV) 7.8.0 8.2.0 8.2.0 ( ut) 7.8.0 8.2.0 8.2.0 ( ut)1 64.31 |- 70.20 0.357 |- 0.4033 57.54 46.19 65.12 0.406 0.681 0.4245 40.41 34.04 51.07 0.498 0.687 0.49710 23.98 22.43 28.67 0.643 0.749 0.63630 12.39 11.94 12.60 0.110 0.811 0.771Table 24: Energy resolution and Mean value of ET lusterETgenerated in TopoClusters for neutrons, usingCaloNoiseTool and Seed ut=4 and Neighbor ut=2.ET ET Resolution Mean of ET lusterETgeneratedparti les No Noise With Noise No Noise With Noise(GeV) 7.8.0 8.2.0 8.2.0 ( ut) 7.8.0 8.2.0 8.2.0 ( ut)1 30.52 35.50 | 0.678 1.217 0.5233 12.66 20.72 25.89 0.866 1.135 0.8415 7.35 14.35 15.19 0.918 1.084 0.92510 4.02 7.77 7.30 0.954 1.038 0.96830 2.21 3.11 2.89 0.919 1.010 0.986Table 25: Energy resolution and Mean value of ET lusterETgenerated in TopoClusters for neutral pions, usingCaloNoiseTool and Seed ut=4 and Neighbor ut=2.47

11 Con lusionsTopoClusters is a very useful tool in the study of the lusters and it provides avery good re onstru tion of the lusters, even in the ase of parti les at very lowenergy. From the �rst part of this note, we an on lude that using TopoClusters withCaloNoiseTool pa kage and applying Seed ut = 4 and NeighborCut= 2:- The best values of energy resolution are obtained for �+'s, �0's and neutrons.- The low eÆ ien y of TopoClusters for single parti les at 1, 3, and 5 GeV iseliminated.- The largest amount of ET is deposited inside the TopoClustersTopoCluster results are even better than the obtained from EGamma lusters for the ase of neutral pions.Comparing with another lustering algorithms, TopoCluster algorithm is very om-petitive for neutrons, �+'s and �0's at very low energies with the best algorithm inthese ases:- the TRUTH- one, i.e. the one algorithm entred in the ��� of Truth generatedparti les, for neutrons and �0's- the TRACK- one, for harged pionsWhen the ele troni noise is in luded, the ET resolution from TopoClusters getworse, but applying these noise uts:- CellThresholdOnAbsEt = 10.0*MeV- NeighborThresholdOnAbsEt = 80.0*MeV- SeedThresholdOnEt = 200.0*MeVwe get a ET lusterETgenerated similar to the ase without noise, it means a more realisti methodto olle t the ET deposited in ells.So, TopoClusters algorithm (with the hanges performed before) ould be used as\standard" tool in the study of lusters from parti les at very low energies28.28In fa t, it will be used as basi algorithm in the Signal Chara terization of ele tromagneti andhadroni shower and the next alibration level, see ATLAS Calorimetry Calibration Workshop pre-sentations, De 2004 48

12 Next Step in Clustering of VLE parti lesCluster formation and Cluster alibration of very low energy parti les must be validatedwith real data. During 2004, a Combined TestBeam of the di�erent sub-dete tor ofATLAS have been done. Single parti le beam of pions and ele tron at very low energy(from 1 to 9 GeV) have been sent to the ombined- alorimeter set-up, so they will bea useful tool to understand the lustering formation[16℄[18℄[17℄.On the other hand, samples based on DC2 events are simulated using Geant4[15℄,in luding the geometry of the Combined TestBeam (a la ATLAS) and we an usedthem to get more easily the orre t sele tion uts in the beam parti les to extra t the harged pions or ele trons in ea h ase.

49

13 Appendix 1: Analysis of the de ay �0 ! The more frequent multipli ity of TopoClusters for �0�s is 1. This behavior wouldbe orre t if the photons would be very lose to ea h other, and the lustering algorithm onsiders them as only one luster.In order to see if this hypothesis is orre t and there is not any problem with there onstru tion of the neutral pions at VLE inside the lustering algorithm, next westudy the angle between the photons of the �0 de ay (�0 ! ) and relate it with themultipli ity of TopoClusters.13.1 Proximity �0- First, using a sample of neutral pions at 5 GeV, it has been veri�ed that the wholeof the 1000 generated �0�s de ay into two photons.Then, de�ning �� = ��0�� and �� = ��0�� it possible to he k that the ��� oordinates of the �0�s are very lose to the �� � oordinates of the two photons, see�g. 32.Figure 32: �� = ��0 � � and �� = ��0 � � distribution from �� � oordinates of the �0�s andthe two de ayed photons.Finally, the radius is de�ned as �R = q��2 +��2. The majority of the photonsare inside a one with �R < 0:01 from the �� � oordinates of the �0, as it is shownin the �g. 33. So it an be said that the �0�s are very lose to the de ayed photonsand it's orre t to use their �� � oordinates in the analysis to re onstru t the energydeposited.Figure 33: �R distribution from �� � oordinates of the �0�s and the two de ayed photons.

50

13.2 Proximity - Now the angle between the photons of the �0 de ay ( �0 ! ) is studied, in orderto understand the multipli ity of TopoClusters. The majority of the multipli ity ofTopoClusters for �0�s is 1, this would be orre t if the photons would be very loseea h other.Then, de�ning �� = � 1 �� 2 and �� = � 1 � � 2 it possible to he k as the �� � oordinates of the photons are very lose to ea h other, as the �g. 34 shown.

Figure 34: �� = � 1 � � 2 and �� = � 1 � � 2 distributions from � � � oordinates of the twode ayed photons.Again, using the above given de�nition of the radius, it an be seen that the majorityof the photons are inside a one of �R < 0:01 from the � � � oordinates of eitherphoton. So, their lusters are very lose and they an be onsidered only one luster.

Figure 35: �R distribution from �� � oordinates of the two de ayed photons.13.2.1 RMS of the �� and �� distributionComparing the di�erent results for the RMS of the �� and �� distribution of thetwo de ayed photons, it an be seen that the RMS hanges with the transverse energyof the generated �0�s. As the energy of the �0�s in reases the de ayed photons are loser. 51

Figure 36: RMS of the �� and �� distribution of the two de ayed photons.13.2.2 MEAN value and the RMS of the �RIn the same way, the MEAN value and the RMS of the �R from the ��� oordinatesof both photons gets smaller as the ET of the generated �0�s in reases.Figure 37: The MEAN value and the RMS of the �R from the �� � oordinates of the one photonto the other.13.2.3 Case of �0�s at 1 and 3 GeVThe �� and �� distributions of the photon from the generated �0�s at 1 and 3GeV, see �g. 38 are wider than at higher energies.

Figure 38: �� and �� distribution of the de ayed photons from 1 and 3 GeV �0�s.Therefore, the �R at 1-3 GeV present a strange distribution (see �g. 39). At 1GeV, the de ayed photons are separated at a value for the radius near to �R � 0:3,52

instead of being the majority of them inside a one of �R < 0:1. In a similar way, at3 GeV the photons are separated at �R � 0:1, why appears this strange behavior?The best explanation an be the next: The MINIMUM separation of the two gam-mas from �0 de ay o urs when the de ay angle is perpendi ular to the dire tion ofmotion, and in that ase the tangent of the half-angle is mE .- For E�0=1000 MeV (and m=140), this is 0.140 so the separation � 0:280 rad- For E�0=3000 MeV (and m=140), this is 0.046 so the separation � 0:092 radThe separation in reases monotoni ally as the de ay angle moves away from perpen-di ular, rea hing 180_ for the de ay when one gamma is forward and the other isba kward29.

Figure 39: �R distribution of the two de ayed photons from 1 and 3 GeV �0�s.29Be ause for massive de ay produ ts we expe t the parti les to have max separation at 90_.53

14 Appendix 2: Study of the overlapThe eÆ ien y of the Energy Flow Algorithm will be limited by the overlap betweenneutral and harged parti les in the ells of the alorimeter. So, to try to estimate thepresen e of a neutral hadron inside a luster de�ned from the tra k of the harged pionand its in uen e in the energy resolution, we pass to use multiparti le samples insteadof single parti le samples.These samples are a mixing of neutral and harged pions as well as neutrons, all ofthem at very low energy (5, 7 or 10 GeV). These multiparti les samples are based onDC1 events simulated by D. Froidevaux30 with ele troni noise (but without pileup) inthe barrel region (j�j <1.5).To study the grade of overlapping, we use di�erent multiparti les samples with theparti les generated at di�erent distan es (�R) between them:� Parti les far away in �R spa e- pi0pimneu10hfar: �0 = 10 GeV, �� = 10 GeV, neu = 10 GeV- pi0pimneu5hfar: �0 = 5 GeV, �� = 5 GeV, neu = 5 GeV� Parti les loser in �R spa e (�R = 0.1)- pi0pimneu10d1010: �0 = 10 GeV, �� = 10 GeV, neu = 10 GeV- pi0pimneu555d1010: �0 = 5 GeV, �� = 5 GeV, neu = 5 GeV� Parti les loser in �R spa e bellow 0.1- pi0pim77d05: �0 = 7 GeV, �� = 7 GeV in a distan e �R = 0.05- pi0pimneu555d0505: �0 = 5 GeV, �� = 5 GeV, neu = 5 GeV in a distan e�R = 0.05- pi0pip1010d05: �0 = 10 GeV, �� = 10 GeV in �R = 0.05- pi0pip55d07: �0 = 5 GeV, �� = 5 GeV in a distan e �R = 0.07Event Display of TopoClusters[14℄ shows us the di�eren e between these samples.This tool permits us to see the same �� x �� region of the di�erent alorimeterse tions. The olor boxes denote the energy per ell in MeV on a log-s ale with di�erents ale for ea h plot.30The samples are lo ated at CASTOR area in: = astor= ern: h=user=f=froid=di e03=54

For the example of parti les far away in �R spa e (see �g. 40), it's possible todistinguish the three luster orresponding to ea h parti les from ECAL Middle layer,while for parti les loser in �R (bellow 0.1) the lusters are very lose and they arediÆ ult to be distinguished (see �g. 41).

Figure 40: Event display for a multiparti le sample with �0 = 10 GeV, �� = 10 GeV and neu =10 GeV generated far away between them. It's possible to distinguish 3 lusters from ECAL Middlelayer up to Tile2.

Figure 41: Event display for a multiparti le sample with �0=10 GeV and ��=10 GeV generated tobe very lose (�R=0.05). It's diÆ ult to distinguish the lusters in Tile.55

14.1 First luster splitter in CaloRe The �rst version of a topologi al luster splitting tool is now available. The toolsname is CaloTopoClusterSplitter[13℄ and falls in the maker-type ategory of the new lustering tools in CaloRe . It is meant to re- luster existing lusters around lo al max-ima in energy density in a topologi al manner similar to the CaloTopoClusterMaker:- based on Signal over Noise thresholds- and topologi al neighborsSplit lusters based on topologi al neighbouring and lo al maxima of the lustersbased on energy density values. The ells in a luster are sear hed for lo al maxima bymeans of energy density. The so found lo al maxima are used as seeds for a topologi al lustering as in the CaloTopoClusterMaker. The spe ial ase of zero thresholds forneighbors and ells is used su h that all ells in the parent luster will be re- lustered.A further di�eren e to the normal topologi al lustering is that proto- lusters on-taining a lo al maximum an never be merged. Therefore the number of lustersresulting from the splitting of the parent is determined by the number of lo al maximafound in the luster. If no lo al maximum was found, the parent luster will be leftun-altered in the luster ontainer. If parts of the original luster are not onne tedwith lo al maximum ontaining parts (di�erent luster algorithm or di�erent neighboroption) all ells of a luster in this ategory are in luded in a rest- luster and addedto the new luster list. Thus the total energy of all lusters and the number of ells ofall lusters should be the same before and after splitting.So, the lassi� ation done by CaloTopoClusterSplitter requires identi� ation of\Hot-Spots", needed to split lusters around lo al maxima in real physi al observables.The transverse ell energy density � = ET =V seems best 31.The tool a epts three parameters:� NeighborOption (default = "super3D")� NumberOfCellsCut (default = 4)� EtDensityCut (default = 500*MeV/600000*mm3)The NeighborOption sele ts the type of neighbors looked for as in the Calo-TopoClusterMaker. By default both take "super3D" - i.e. neighbors a ross all alorime-ter systems, but it might be useful to restri t the lo al maxima in the splitting toseparate systems ("all3D") or even separate layers ("all2D").The NumberOfCellsCut spe i�es how many neighbor ells a given ell has tohave in the parent luster in order to be quali�ed as lo al maximum andidate.31Energy density is hosen instead of only transverse energy as seed for the ClusterSplitter be ausethe granularity of the alorimeter hanges so often. Look e.g. at the Strips and the Layer 2 ells inthe EM - they di�er by an order of magnitude in volume and thus transverse energy by itself is rathermeaningless if you onsider just one ell. 56

All lo al maximum andidates must also pass the EtDensityCut spe ifying theminimumEt divided by the volume of the ell in order to be a epted as lo al maximum.The default value orresponds to a transverse energy of 500 MeV in a typi al LArEMbarrel ell in the se ond layer.CaloTopoClusterSplitter re- lusters ea h existing luster into one or more lusters:- around the lo al maxima above a seed threshold- with same (or di�erent) topologi al neighbors- without ell or neighbor thresholds- keeping lo al maxima in separate lusters- with � ordered seeds in every iterationSo, the re- lustering works as in the normal topo luster maker, but all ells area epted without thresholds and at ea h iteration the urrent set of seed ells is orderedin energy density su h that ells with higher energy density are more likely to attra ta neighbouring ell.No sharing of ells between lusters is introdu ed at this point, but this might hangein the future. The tool is enabled in the default python �le CaloTopoClusterjobOptions.14.2 Energy Resolution with and without SplitterNext table shows the energy resolution values for the di�erent multiparti les sampleswith and without the Splitter[13℄ applied.ET Resolution Mean of ET lusterETgeneratedNo Splitter Splitter No Splitter Splitterpi0pimneu10d10hfar 10.26 10.21 0.8171 0.8185pi0pimneu5hfar 14.97 14.70 0.7535 0.7543pi0pimneu10d1010 9.34 9.32 0.8282 0.8287pi0pimneu555d1010 13.96 14.17 0.7715 0.7717pi0pim77d05 11.87 11.89 0.8969 0.8975pi0pimneu555d0505 14.51 14.55 0.7786 0.7801pi0pip1010d05 9.04 9.00 0.9093 0.91pi0pim55d07 14.77 14.74 0.8926 0.8944The Energy resolution results with and without Splitter are very similar, even inthe ase of parti les generated to be very lose (�R = 0.05 and �R = 0.07)!!32.32The total energy of all lusters must be the same at the end of the re onstru tion with and withoutSplitter by de�nition, so it's expe ted that the results for ET lusterETgenerated will be similar but not for theenergy resolution. 57

As we have seen, all maximum andidates must pass EtDensityCut to be a eptedas lo al maxima, but the very low energeti parti les don't produ e big lo al maxima,so it needed to hange the value of the EtDensityCut investigating the deposited energyin a LarEM ell in the 2nd layer by VLE parti les.14.3 Energy deposited in LArEM ell of 2nd layerThe energy deposited in LArEM ell of 2nd layer by harged and neutral pions of verylow energy (3, 5 and 10 GeV) is shown in �g. 42 in order to �nd the orre t value forthe EtDensityCut and apply orre tly the ClusterSplitter to TopoCluster oming fromVLE parti les.

Figure 42: The energy deposited in LArEM ell of 2nd layer by harged and neutral pions of verylow energy (3, 5 and 10 GeV). The mean value of the energy deposited is around 280 GeV, so the orre t value for the EtDensityCut and apply orre tly the ClusterSplitter to TopoCluster omingfrom VLE parti les ould be 250 MeV/600000 mm3.The mean value of the energy deposited in LArEM ell of the 2nd layer is �280GeV, so the EtDensityCut will be hanged to 250*MeV/600000*mm3.14.4 Final on lusion about Splitter in VLE parti lesNevertheless, the value of energy resolution using the default EtDensityCut and usingthe new value of 250 MeV/600000 mm3 are identi al in the 3 ases of multiparti lessamples. Even the Root plots from the event display are the same. So it's only possibleto on lude that the CaloTopoSplitterCluster in 8.2.0 release33 an not be used to studythe overlap of parti les at very low energy (only useful for energeti parti les34.)33No sharing of ells between lusters is introdu ed in CaloTopo pa kage in these release of Athena,maybe with this tool, the shape of the luster ould be studied more a urately.34As Sven Menke show in O tober 2004 during the ATLAS Overview Week for jet at 70 GeV in thepresentation \Hadroni Energy Calibration: from TestBeam to ATLAS" on behalf of the Hadroni Calibration Group. 58

Referen es[1℄ e owRe pa kage: Energy Flow Re onstru tion in Athena (Dan Tovey)http://atlas.web. ern. h/Atlas/GROUPS/PHYSICS/JETS//EFLOWREC/e owre .htm[2℄ C. Iglesias, Re onstru ion de Jets mediante el algoritmo Energy Flow en ATLAS,talk in VII Jornadas de Fisi a de Altas Energia, XXIX Reunion Bienal, Madrid,(2003).[3℄ C. Iglesias, M. Bosman, Study of jet omposition at parti le level and its impli a-tions for Energy Flow algorithms. ATL-SOFT-INT-2005-003, De 2004.[4℄ D. Green Energy Flow in CMS Calorimetry Fermilab-FN-0709S. Kunori (CMS Collaboration), Jet Energy Re onstru tion with the CMS Dete -tor, In Pro eedings of the X Int. Conf in Calorimetry in Part.Phys., CALOR2002Conferen e, Pasadena, (2002).D.Green et al., Energy ow obje ts and usage of tra ks for energy measurement inCMS, CMS NOTE 2002/036, Sept (2002).[5℄ ATLAS Collaboration, ATLAS Calorimeter Performan e, CERN/LHCC/96-40,ATLAS TDR 1, (1996).[6℄ S.Menke talks: Status of Topologi al Clustering, presented at Software Perfor-man e Meeting, LAr Week (CERN), 28. Jan 2004[7℄ S.Menke,Calibration of the BaBar ele tromagneti alorimeter with pi0s, BABAR-Note-528, Nov 2000.S.Menke O�ine Corre tion of Non-linearities in the BaBar ele tromagneti alorimeter ele troni s, BABAR-Note-527, Nov 2000.[8℄ Athena User and Developer Guide v.2.0 & Releaseshttp://atlas.web. ern. h/Atlas/GROUPS/SOFTWARE/OO/ar hite -ture/General/[9℄ C.Iglesias talks: TiCal-IFIC Weekly Meetings (Valen ia, SPAIN), at my personalweb page: http://i� .uv.es/�iglesias[10℄ C.Iglesias, Clustering of very low ET parti les, Software Workshop, Re onstru tionWorking Group: Calorimetry, Sep,2004, CERN[11℄ ATLAS Collaboration, ATLAS Dete tor and Physi s Performan e Te hni al De-sign Report CERN/LHCC/99-14, ATLAS TDR 14 (1999).[12℄ S.Menke Status of Topologi al Clustering re ent Re o-Software Changes, Hadroni Calibration meeting, 13. May 2004, CERN59

[13℄ S.Menke Topologi al Cluster Maker Splitter - HOWTO for Athena 8.2.0, JetRe Phone Meeting, 02. June 2004, CERN[14℄ ROOT ma ropa kage for ATLAS Calorimeter Event Displays, (CaloEventDisplay.tar.gz), 06.June 2004. S. Menke Personal web page: http://www.mppmu.mpg.de/ menke/[15℄ Geant4 Users do uments:http://wwwasd.web. ern. h/wwwasd/geant4/G4UsersDo uments//Overview/html/index.html[16℄ C.Iglesias, Clustering of very low ET parti les in Combined TB, ATLAS Calorime-try Calibration Workshop, Hadroni Calibration Session, De 2004, Trata,SlokaviaC.Iglesias, More about very low energy parti le, TileCal Commissioning Meeting2 Feb., 2005C.Iglesias, Clustering for VLE parti les in CBT, TileCal Analysis and CombinedTest Beam, 14 Feb, 2005, TileCal Week, CERN[17℄ C.Iglesias, V. Giangiobbe. Analysis with VLE runs in Combined TB, Final Com-bined Test Beam Workshop, 16 Feb, 2005, CERN[18℄ C.Iglesias, Clustering of very low ET parti les with 2004 Combined TestBeam dataof ATLAS, ATLAS ommuni ation in preparation.[19℄ C.Iglesias, Pedestal analysis, personal web page:http://i� .uv.es/�iglesias/

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