ARTICLE IN PRESS. Nuclear Instruments and Methods in Physics Research A

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1 Nuclear Instruments and Methods in Physics Research A 611 (29) 25 4 Contents lists available at ScienceDirect Nuclear Instruments and Methods in Physics Research A journal homeage: Particle flow calorimetry and the PandoraPFA algorithm M.A. Thomson Cavendish Laboratory, JJ Thomson Avenue, Cambridge CB3 HE, UK article info Article history: Received 17 July 29 Received in revised form 2 Setember 29 Acceted 2 Setember 29 Available online 1 Setember 29 Keywords: Particle flow calorimetry Calorimetry ILC abstract The Particle Flow (PFlow) aroach to calorimetry romises to deliver unrecedented jet energy resolution for exeriments at future high energy colliders such as the roosed International Linear Collider (ILC). This aer describes the PandoraPFA article flow algorithm which is then used to erform the first systematic study of the otential of high granularity PFlow calorimetry. For simulated events in the ILD detector concet, a jet energy resolution of s E =Et3:8% is achieved for 4 4 GeV jets. This result, which demonstrates that high granularity PFlow calorimetry can meet the challenging ILC jet energy resolution goals, does not deend strongly on the details of the Monte Carlo modelling of hadronic showers. The PandoraPFA algorithm is also used to investigate the general features of a collider detector otimised for high granularity PFlow calorimetry. Finally, a first study of the otential of high granularity PFlow calorimetry at a multi-tev leton collider, such as CLIC, is resented. & 29 Elsevier B.V. All rights reserved. 1. Introduction In recent years the concet of high granularity Particle Flow calorimetry [1,2] has been develoed in the context of the roosed International Linear Collider (ILC). Many of the interesting hysics rocesses at the ILC [3] will be characterised by multi-jet final states, often accomanied by charged letons and/ or missing transverse momentum associated with neutrinos or the lightest suer-symmetric articles. The reconstruction of the invariant masses of two or more jets will rovide a owerful tool for event reconstruction and event identification. At LEP, kinematic fitting [4] enabled recise invariant mass reconstruction. At the ILC, di-jet mass reconstruction for final states with unobserved articles will rely on the jet energy resolution of the detector. The goal for jet energy resolution at the ILC is that it is sufficient to cleanly searate W and Z hadronic decays. An invariant mass resolution comarable to the gauge boson widths, i.e. s m =m ¼ 2:7% G W =m W G Z =m Z, leads to an effective 3:6s searation of the W-q q and Z-qq mass eaks, i.e. the otimal invariant mass cut corresonds to þ1:8s ð 1:8sÞ in the reconstructed W ðzþ mass distributions. In the traditional calorimetric aroach, the jet energy is obtained from the sum of the energies deosited in the electromagnetic and hadronic calorimeters (ECAL and HCAL). This tyically results in a jet energy resolution of the form s E E ¼ a ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi b: ð1þ E ðgevþ The stochastic term, a, is usually 4 6%. The constant term, b, Tel.: address: thomson@he.hy.cam.ac.uk which encomasses a number of effects, is tyically a few ercent. For high energy jets there also will be a contribution from the non-containment of the hadronic showers. The stochastic term in the jet energy resolution results in a contribution to the di-jet mass resolution of s m =m a= ffiffiffiffiffi E jj, where Ejj is the energy of the di-jet system in GeV. At the ILC, oerating at centre-of-mass ffiffi energies s ¼ :521: TeV, the tyical di-jet energies for interesting hysics rocesses will be in the range GeV. Hence to achieve the ILC goal of s m =m ¼ 2:7%, the stochastic term must be t3%= ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi E ðgevþ. This is unlikely to be achievable with a traditional aroach to calorimetry The article flow aroach to calorimetry Measurements of jet fragmentation at LEP have rovided detailed information on the article comosition of jets (e.g. Refs. [5,6]). On average, after the decay of short-lived articles, roughly 62% of the jet energy is carried by charged articles (mainly hadrons), around 27% by hotons, about 1% by long-lived neutral hadrons (e.g. n, n and K L ), and around 1.5% by neutrinos. Hence, aroximately 72% of the jet energy is measured with the recision of the combined ECAL and HCAL for hadrons and the jet energy resolution is limited by the relatively oor hadronic energy resolution, tyically \55%= ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi E ðgevþ. A number of collider exeriments (e.g. OPAL, H1 and D) obtained imroved jet energy resolution using the Energy Flow aroach, whereby energy deosits in the calorimeters are removed according to the momentum of associated charged article tracks. ALEPH used article flow techniques [7] to attemt to reconstruct the four momenta of the articles in an event. However, due to the relatively low granularity of the calorimeters, energy deositions from neutral hadrons still had to be identified as a /$ - see front matter & 29 Elsevier B.V. All rights reserved. doi:1.116/j.nima

2 26 M.A. Thomson / Nuclear Instruments and Methods in Physics Research A 611 (29) 25 4 Table 1 Contributions from the different article comonents to the jet-energy resolution (all energies in GeV). Comonent Detector Energy fract. Energy res. Jet energy res. Charged articles ðx 7 Þ Tracker :6Ej 1 4 E 2 X o3: E 2 j Photons ðgþ ECAL :3E j :15 ffiffiffiffiffi E g :8 ffiffiffiffi E j Neutral Hadrons ðh Þ HCAL :1E j :55 ffiffiffiffiffiffiffi E h :17 ffiffiffiffi E j The table lists the aroximate fractions of charged articles, hotons and neutral hadrons in a jet of energy, E j, and the assumed single article energy resolution. significant excesses of calorimetric energy comared to the associated charged article tracks. Nevertheless, ALEPH achieved ffiffi a ffiffiffiffiffiffiffiffiffiffiffiffiffiffi jet energy resolution (for s ¼ MZ ) equivalent to s E ¼ð59% E=GeVþ:6Þ GeV [7]. This was the best jet energy resolution of the four LEP exeriments, but is roughly a factor two worse than required for the ILC. Particle flow techniques are also being used by CMS. It is widely believed that the most romising strategy 1 for achieving the ILC jet energy goal is the Particle Flow (PFlow) aroach to calorimetry using a highly granular detector. In contrast to a urely calorimetric measurement, PFlow calorimetry requires the reconstruction of the four-vectors of all visible articles in an event. The reconstructed jet energy is the sum of the energies of the individual articles. The momenta of charged articles are measured in the tracking detectors, while the energy measurements for hotons and neutral hadrons are obtained from the calorimeters. In this manner, the HCAL is used to measure only 1% of the energy in the jet. If one were to assume calorimeter resolutions of s E =E ¼ :15= ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi E ðgevþ for hotons and s E =E ¼ :55 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi E ðgevþ for hadrons, a jet energy resolution of :19= ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi E ðgevþ would be obtained with the contributions from tracks, hotons and neutral hadrons as resented in Table 1. In ractice, this level of erformance cannot be achieved as it is not ossible to erfectly associate all energy deosits with the correct articles. For examle, if the calorimeter hits from a hoton are not resolved from a charged hadron shower, the hoton energy is not accounted for. Similarly, if art of charged hadron shower is identified as a searate cluster, the energy is effectively doublecounted as it is already accounted for by the track momentum. This confusion rather than calorimetric erformance is the limiting factor in PFlow calorimetry. Thus, the crucial asect of PFlow calorimetry is the ability to correctly assign calorimeter energy deosits to the correct reconstructed articles. This laces stringent requirements on the granularity of the ECAL and HCAL. From the oint of view of event reconstruction, the sum of calorimeter energies is relaced by a comlex attern recognition roblem, namely the Particle Flow reconstruction Algorithm (PFA). The jet energy resolution obtained is a combination of the intrinsic detector erformance and the erformance of the PFA software. The PandoraPFA algorithm was develoed to study PFlow calorimetry at the ILC. PandoraPFA is a Cþþ imlementation of a PFA running in the MARLIN [9] reconstruction framework. It was develoed and otimised using simulated hysics events generated with the MOKKA [1] rogram, which rovides a detailed Geant4 [11] simulation of otential detector concets for the ILC. In articular, PandoraPFA was develoed using the MOKKA simulation of the LDC [12] detector concet and, more recently, the ILD [13] detector concet. The algorithm is designed to be sufficiently flexible to allow studies of PFlow for different detector 1 The only alternative roosed to date is that of Dual Readout calorimetry as studied by the DREAM collaboration [8]. designs. Whilst a number of PFAs [2,14,15] have been develoed for the ILC, PandoraPFA is the most sohisticated and best erforming algorithm. In this aer PandoraPFA is described in detail. It is then used to study the otential at a future high energy leton collider of PFlow calorimetry with a highly granular detector, in this case the ILD detector concet. 2. Overview of the ILD detector model The ILD detector concet [13], shown in Fig. 1, consists of a vertex detector, tracking detectors, ECAL, HCAL and muon chambers. It reresents a ossible configuration of a detector suitable for PFlow calorimetry. Secifically, for the ECAL and HCAL the emhasis is on granularity, both longitudinal and transverse, rather than solely energy resolution. Suitable candidate technologies are being studied by the CALICE (calorimetry for the ILC) collaboration [16]. Amongst these are the Silicon Tungsten ECAL and Steel-Scintillator HCAL designs assumed for the ILD reference detector simulation. Both the ECAL and HCAL are located inside a solenoid which is taken to roduce the 3.5 T magnetic field. The main tracking detector is simulated as a time rojection chamber (TPC) with an active gas volume of half-length 2.25 m and inner and outer radii of.39 and 1.74 m, resectively. The vertex detector consists of six layers of Silicon with an inner radius of 15 mm from the interaction oint (IP). The tracking is comlemented by two barrel Silicon stri detectors between the vertex detector and the TPC and seven Silicon forward tracking disks. The ECAL is simulated as a Silicon Tungsten samling calorimeter consisting of 29 layers. The first 2 layers have 2.1 mm thick Tungsten and the last nine layers have 4.2 mm thick Tungsten. The high resistivity Silicon is segmented into 5 5mm 2 ixels. At normal incidence, the ECAL corresonds to 23 radiation lengths ðx Þ and.8 nuclear interaction lengths ðl I Þ. The HCAL is simulated as a Steel-Scintillator samling calorimeter comrising 48 layers of 2 mm thick Steel and 5 mm thick 3 3cm 2 lastic scintillator tiles. At normal incidence the HCAL is 6l I thick. The ECAL and HCAL in the ILD concet are well matched to the requirements of PFlow calorimetry. Tungsten is the ideal absorber Yoke Coil + Cryostat HCAL ECAL TPC Fig. 1. A quadrant of the ILD detector concet (in the rz lane) showing the main dimensions and layout of the sub-detector comonents.

3 M.A. Thomson / Nuclear Instruments and Methods in Physics Research A 611 (29) Table 2 Comarison of interaction length, l I, radiation length, X, and Moliere radius, r M, for Iron, Coer, Tungsten and Lead. Material l I (cm) X (cm) r M (cm) l I =X Fe Cu W Pb Also given is the ratio of l I =X. γ HCAL ECAL TPC π + K L material for the ECAL; it has a short radiation length and small Moliere radius (see Table 2) which leads to comact electromagnetic (EM) showers. It also has a large ratio of interaction length to radiation length which means that hadronic showers will tend to be longitudinally well searated from EM showers. The 5 5mm 2 transverse segmentation takes full advantage of the small Moliere radius. Steel is chosen as the HCAL absorber, rimarily for its structural roerties. The 3 3cm 2 HCAL transverse segmentation is well matched to the requirements of PFlow calorimetry (see Section 9.5). The detector simulation includes a number of instrumental effects such as: dead regions around the Silicon ixels in the ECAL; gas between modules in the ECAL and HCAL; and Birks law for the scintillator resonse in the HCAL. The effects of noise and channel-by-channel calibration are not included in the simulation at this stage. 3. Reconstruction framework The erformance of PFlow calorimetry deends strongly on the reconstruction software. For the results obtained to be meaningful, it is essential that both the detector simulation and the reconstruction chain are as realistic as ossible. For this reason no Monte Carlo (MC) information is used at any stage in the reconstruction as this is likely to lead to an overly otimistic evaluation of the otential erformance of PFlow calorimetry. PandoraPFA runs in the MARLIN [9] Cþþ framework develoed for the LDC and ILD detector concets. The inut to PandoraPFA (in LCIO [17] format) is a list of digitised hits in the calorimeters and a list of reconstructed tracks. Tracks in the TPC are reconstructed using a MARLIN rocessor, LEPTrackingProcessor, adated from the TPC attern recognition software [18] based on that used by ALEPH and track fitting software used by DELPHI [19]. Reconstruction of tracks in the inner Silicon detectors is erformed by a custom rocessor, SiliconTracking [2]. TPC and Silicon track segments are combined in a final tracking rocessor, FullLDCTracking [2]. PandoraPFA combines the tracking information with hits in the high granularity calorimeters to reconstruct the individual articles in the event. As an examle of the information used in the reconstruction, Fig. 2 shows a hoton, a charged hadron ð þ Þ and a neutral hadron (K L ) as simulated in the ILD detector concet. 4. The PandoraPFA article flow algorithm The PandoraPFA algorithm erforms calorimeter clustering and PFlow reconstruction in eight main stages: (1) Track selection/ toology: Track toologies such as kinks and decays of neutral articles in the detector volume (e.g. K S - þ ) are identified. (2) Calorimeter hit selection and ordering: Isolated hits, defined on the basis of roximity to other hits, are removed from the initial clustering stage. The remaining hits are ordered into seudo-layers and information related to the geometry and the surrounding hits Fig. 2. Examle simulated single article interactions in the ILD detector concet: (a) a 1 GeV hoton; (b) a 1 GeV þ ; and (c) a 1 GeV K L. Hits in the TPC, ECAL and HCAL are shown. For the ECAL (HCAL) all hits with energy deositions 4:5 ð:3þ minimum ionising article equivalent are dislayed. Simulated TPC hits are digitised assuming 227 radial rows of readout ads. are stored for use in the reconstruction. (3) Clustering: The main clustering algorithm is a cone-based forward rojective method [21] working from innermost to outermost seudo-layer. The algorithm starts by seeding clusters using the rojections of reconstructed tracks onto the front face of the ECAL. (3A) Photon clustering: PandoraPFA can be run in a mode where the above clustering algorithm is erformed in two stages. In the first stage, only ECAL hits are considered with the aim of identifying energy deosits from hotons. In the second stage the clustering algorithm is alied to the remaining hits. (4) Toological cluster merging: By design the initial clustering stage errs on the side of slitting u true clusters rather than merging energy deosits from more than one article into a single cluster. Clusters are then combined on the basis of clear toological signatures in the high granularity calorimeters. The toological cluster merging algorithms are only alied to clusters which have not been identified as hotons. (5) Statistical re-clustering: The revious four stages of the algorithm are found to erform well for jets with energies of o5 GeV. For higher energy jets the erformance degrades due to the increasing overla between hadronic showers from different articles. Clusters which are likely to have been created from the merging of hits in showers from more than one article are identified on the basis of the comatibility of the cluster energy, E C, and the associated track momentum,. In the case of an inconsistent energy momentum match, attemts are made to recluster the hits by re-alying the clustering algorithm with different arameters, until the cluster slits to give a cluster energy consistent with the momentum of the associated track. (6) Photon recovery and identification: A more sohisticated, showerrofile based, hoton-identification algorithm is then alied to the clusters, imroving the tagging of hotons. It is also used to recover cases where a rimary hoton is merged with a hadronic shower from a charged article. (7) Fragment removal: Neutral clusters which are fragments of charged article hadronic showers are identified. (8) Formation of article flow objects: The final stage of the algorithm is to create the list of reconstructed articles, Particle Flow Objects (PFOs), and associated fourmomenta. The essential features of each of the above stages are described in more detail below. The descrition includes the main configuration arameters which determine the behaviour of the algorithms. These can be defined at runtime. The default values, which are otimised for the ILD concet, are given Track selection/toology Tracks are rojected onto the front face of the ECAL using a helical fit to the last 5 hits on the reconstructed track (no account is taken for energy loss along the trajectory in the TPC gas). Tracks

4 28 M.A. Thomson / Nuclear Instruments and Methods in Physics Research A 611 (29) 25 4 are then classified according to their likely origin. For examle, neutral article decays resulting in two charged article tracks ðv sþ are identified by searching for airs of tracks which are consistent with coming from a single oint dislaced from the IP. Charged article decays to a single charged article and any number of neutral articles (kinks) are identified on the basis of the distance of closest aroach of the arent and daughter tracks. Similarly, interactions in the tracking volume (rongs) are identified. This information, along with the original track arameters and the rojection of the track onto the front face of the ECAL, is stored in ExtendedTrack objects for use in the subsequent event reconstruction Calorimeter hit selection and ordering In addition to the reconstructed tracks, the inut to PandoraPFA is a list of digitised calorimeter hits. For each hit, the osition ðx; y; zþ, the energy deosition, and the hysical layer in the ECAL/ HCAL are secified. Based on this information, ExtendedCaloHit objects are formed. These hits are self-describing and incororate information relating to both the geometry of the detector (accessed from the GEAR [22] geometry descrition) and information related to the density of calorimeter hits in the neighbouring region. The five main stes in the calorimeter hit rocessing (calibration, geometry, isolation, MIP identification, ordering) are described below Calibration The energy of each calorimeter hit is converted to a minimum ionising article (MIP) equivalent (at normal incidence) using a calibration factor CALMIPcalibration. Different calibration factors are used for ECAL and HCAL hits. Hits are only retained if they are above a MIP-equivalent threshold of CalMIPThreshold (with default values of ½:5Š and ½:3Š for ECAL and HCAL, resectively). Provided single MIP hits are retained with high efficiency, the jet energy resolution obtained from PandoraPFA deends only weakly on the thresholds used. The MIP equivalent energy deosit is then converted into calorimetric measurement using MIP to GeV calibration factors, CalMIPToGeV, for the ECAL and HCAL. In general, the calorimeters will not be comensating, and searate energy measurements are calculated for the hyotheses that the hit is either art of an EM or hadronic shower. The final choice of which energy to use deends on the whether the shower to which a hit is associated is ultimately identified as being EM in nature. To allow for calorimeters with different absorber thicknesses as a function of deth, the calibration factor alied is roortional to the absorber thickness of the layer in front of the hit. Initial values for the calibration factors are determined from MC samles of single muons, hotons and K L s. The muon samle is used to determine the MIP calibration, the hoton samle is used to determine the ECAL calibrations and the K L s are used to determine the initial HCAL calibration. Since the neutral hadrons in jets are a mixture of K L s, neutrons and anti-neutrons, the initial HCAL calibration is modified (tyically by 5%) on the basis of minimising the jet energy resolutions for MC samles of jets. A single set of calibration factors is used for the subsequent studies Geometry information The PandoraPFA reconstruction is designed to minimise the deendence on the detector geometry to enable comarisons of different detector designs. For this reason, information is added to the digitised calorimeter hits such that they become self describing. For examle, the ExtendedCaloHit objects store the size of the corresonding detector ixel. To reduce the y deendency of the clustering algorithms on the detector geometry, hits are ordered in increasing deth in the calorimeter. This is achieved by defining seudo-layers which follow the general layer structure of the calorimeters. This is necessary for calorimeter layouts such as in the ECAL stave-like structure being studied by the CALICE collaboration, shown schematically in Fig. 3. Here there are regions where the first layer in a calorimeter stave can be dee in the overall calorimeter structure Isolation requirements Low energy neutrons roduced in hadronic showers can travel a significant distance from the oint of roduction and thus roduce isolated energy deosits. For PFlow calorimetry, these energy deosits are of little use as it is imossible to unambiguously associate them with a articular hadronic shower. For this reason, and to imrove the erformance of the clustering algorithms, isolated hits are identified and excluded from the initial cluster finding. Isolated hits are defined using one of two ossible criteria: (i) less than a minimum number of calorimeter hits within a re-defined distance from the hit in question; or (ii) a cut on the local weighted hit number density, r i, defined by r i ¼ X j where x Fig. 3. Schematic showing the definition of the seudo-layer assignment for calorimeter hits. The solid lines indicate the ositions of the hysical ECAL layers and the dashed lines show the definition of the virtual seudo-layers. (a) The xyview showing the CALICE stave structure for the ECAL. Here hits in the first layer of the stave can be dee in the overall calorimeter. (b) The xz- view showing a ossible layout for the ECAL barrel/endca overla region. Here the seudo-layers are defined using the rojection back to the IP such that the seudo-layer is closely related to the deth in the calorimeter. w ij ¼ X j r ij? ¼ r i ðr i r j Þ : jr i j 1 ðr? ij Þn Here r i is the osition of the hit in question, the sum over j is for all hits within a certain number of seudo-layers of hit i, and the default value for n is 2. By default, method (ii) is used with a default cut value IsolationDensityWeightCut of :1mm MIP identification Hits which are consistent with having originated from a minimum ionising article (MIP) are flagged based on energy deosition and the surrounding hits in the same calorimeter layer. For a hit to be tagged as MIP-like: (a) the energy deosition must be no more than MiLikeMiCut [5.] times the mean exected MIP signal and (b) of the adjacent (usually 8) ixels in the same layer, no more than MiMaxCellsHit [1] should have hits above threshold. This information is used in the identification of minimum ionising tracks within the calorimeter. y z IP

5 M.A. Thomson / Nuclear Instruments and Methods in Physics Research A 611 (29) Hit ordering Prior to alying the clustering algorithm, hits within each seudo-layer are ordered either by energy (the default) or by local hit density, r i, defined above. The latter otion is intended rimarily to be used for the case of digital calorimetry, where a simle hit count relaces the analogue energy information Clustering The main clustering algorithm of PandoraPFA is a cone-based forward rojective method working from innermost to outermost seudo-layer. In this manner hits are either added to existing clusters or they are used to seed new clusters. Throughout the algorithm clusters are assigned a direction (or otentially directions) in which they are roagating. This allows the clustering algorithm to follow tracks in the calorimeters. The inut to the clustering algorithm is a vector of hits (Extended- CaloHits) ordered by seudo-layer and energy (or local hit density) and a vector of tracks (ExtendedTracks). The algorithm starts by seeding clusters using the rojections of reconstructed tracks onto the front face of the ECAL. The initial direction of a track-seeded cluster is obtained from the track direction at the ECAL front face. The hits in each subsequent seudo-layer are then looed over. Each hit, i, is comared to each clustered hit, j, in the revious layer. The vector dislacement, r ij, is used to calculate the arallel and erendicular dislacement of the hit with resect to the unit vector(s) ^u describing the cluster roagation direction(s), d J ¼ r ij : ^u and d? ¼jr ij ^uj. Associations are made using a cone-cut, d? od J tanaþbd ad, where A is the cone half-angle, D ad is the size of a sensor ixel in the layer being considered, and b is the number of ixels added to the cone radius. Different values of A and b are used for the ECAL and HCAL with the default values set to ftana E ¼ :3; b E ¼ 1:5g and ftan A H ¼ :5; b H ¼ 2:5g, resectively. The values can be modified using the steering arameters ClusterFormationAngle and ClusterFormationPads. For hits in layer k, associations are first searched for in layer k 1. If no association is made, ossible associations with clustered hits in layers k 2 and k 3 are considered in turn. If still no association is made, associations can be made with nearby hits in existing clusters in the same seudolayer as the hit in question, roviding the distance between the hit centres is less than SameLayerPadCut = [2.8] ([1.8]) for ixels in the ECAL (HCAL). If a hit remains unassociated, it is used to seed a new cluster. Clusters seeded with calorimeter hits are assigned an initial direction corresonding to radial roagation from the IP. This rocedure is reeated sequentially for the hits in each seudo-layer working outward from ECAL front-face. After associating all hits in a given seudo-layer, the roagation directions of all clusters are udated. The cluster direction is calculated from a linear fit to the centroids of the hits in the last six seudo-layers in the cluster. The cluster direction is only allowed to deviate from the initial direction if the fit w 2 is reasonable. deviation of the hits in the cluster around the linear fit to the centroids in each calorimeter layer must be o4 cm; and the fraction of hits classified as MIP-like must be o3%. In addition, weak cuts on the longitudinal develoment of the shower are imosed. Photon clusters are essentially frozen at this stage in the PandoraPFA algorithm; they are not used in the subsequent toological cluster merging or reclustering algorithms Photon clustering (otional) Rather than attemting to cluster all calorimeter hits in a single ass, PandoraPFA can be run in a mode ðphotonclustering4þ where the clustering algorithm described above is first alied solely to the ECAL hits to identify hotons as the first stage of PFlow reconstruction. The clustering algorithm arameters are chosen to reflect the narrowness of EM showers. Reconstructed clusters which are consistent with the exected EM transverse and longitudinal shower rofiles (see Section 4.6) are stored and the associated calorimeter hits are not considered in the second ass of the clustering algorithm. The identified hoton clusters are added back to the event just rior to the formation of the PFOs. For the results resented in this aer, hoton clustering is run rior to the main clustering algorithm Toological cluster merging By design the initial clustering algorithm errs on the side of slitting u true clusters rather than merging energy deosits from more than one article into a single cluster. Hence, the next stage in the PandoraPFA algorithm is to merge clusters which are not already associated to tracks (termed neutral clusters ) with clusters which have an associated track (termed charged clusters ). The merging algorithms are based on the clear toological signatures shown schematically in Fig. 4. This rocedure takes advantage of the high granularity of the ECAL and HCAL of a detector designed for PFlow reconstruction. For clusters with an associated track, the location of the first hadronic interaction is identified and the roerties of the tracklike segment in the calorimeter before the interaction are reconstructed. For neutral clusters, track-like segments are identified in the first and last six seudo-layers of the cluster based on fraction of hits classified as MIP-like and the rms deviation of the hit ositions about straight line fits. For track-like Fast hoton identification Clusters which are consistent with being from EM showers from hotons are identified. For reasons of seed, simle cut based criteria are used. The fast hoton identification requirements 2 are: no associated track; the cluster must start within 1X of the front face of the ECAL; the cluster direction (obtained from a linear fit to the energy-weighted centroids of the hits in each seudo-layer) must oint to within 2 3 of the IP; the rms 2 The exact cut values deend on the cluster energy and the values below are those given in the text are the default values for a 1 GeV cluster. Fig. 4. The main toological rules for cluster merging: (i) looing track segments; (ii) track segments with gas; (iii) track segments ointing to hadronic showers; (iv) track-like neutral clusters ointing back to a hadronic shower; (v) backscattered tracks from hadronic showers; (vi) neutral clusters which are close to a charged cluster; (vii) a neutral cluster near to a charged cluster; (viii) cone association; and (ix) recovery of hotons which overla with a track segment. In each case the arrow indicates the track, the filled oints reresent the hits in the associated cluster and the oen oints reresent the hits in the neutral cluster.

6 3 M.A. Thomson / Nuclear Instruments and Methods in Physics Research A 611 (29) 25 4 segments, the fitted line, r þk ^d, is used to roject forwards or backwards in the calorimeter. Similarly, the entire cluster may be classified as track-like. The main toological rules for cluster association are: (i) Looing tracks: Because of the forward rojective nature of the rimary clustering algorithm, tracks which turn back in the calorimeter due to the high magnetic field are often reconstructed as two track-like clusters. The track-like segments at the ends of the clusters are rojected forwards and the clusters are combined if the distance of closest aroach of the two forward-going track rojections is less than LooerClosestAroachCutECAL [5 cm]. (ii) Broken tracks: Non-continuous tracks in the calorimeters can arise when articles cross boundaries between hysical sub-detectors or cross dead regions of the calorimeters. Such instances are identified using track-like segments in the last six layers of a charged cluster and the first six layers in a neutral cluster. The clusters may be merged if the distance of closest aroach of the forward-going and backward-going track-like segment rojections is less than TrackMergeCutEcal [2.5 cm]. (iii) Tracks ointing to showers: If, when rojected forward, a track-like charged cluster oints to within TrackMerge- CutEcal [2.5 cm] of the start of a cluster deeer in the calorimeter, the clusters may be merged. (iv) Track-like clusters ointing back to hadronic interactions: If the start of a neutral cluster is a track-like segment and it oints to within TrackBackMergeCut [3. cm] of the identified first hadronic interaction of charged cluster, the clusters may be merged. (v) Back-scattered tracks: Hadronic interactions can roduce tracks in the calorimeter which roagate backwards in the calorimeter. Due to the forward rojective nature of the clustering algorithm, these often will be reconstructed as searate clusters. Back-scattered tracks are identified as track-like clusters which oint to within TrackBackMergeCut [3. cm] of the identified hadronic interaction of a charged cluster. (vi) Hadronic interactions ointing to neutral clusters: If a charged-cluster has track-like segment rior to the identified interaction oint, and it oints to within TrackForwardMergeCut [5. cm] of the start of a cluster deeer in the calorimeter, the clusters may be merged. (vii) Proximity-based merging: The minimum distance between a charged cluster, of energy E C, and a neutral cluster, of energy E N, is defined as the smallest distance between any of the hits in the two clusters. If this distance is less than ProximityCutDistance [5 cm] then the clusters maybe merged if there is additional evidence that the two clusters originate from a single hadronic shower. To suress false matches the w 2 consistency between the original and merged cluster energies and the associated track momentum,, is used. The merged cluster energy, E ¼ E C þe N, must be consistent with the track momentum, w ¼ðE Þ=s E oenergychi2forcrudemerging ½2:5Š, where s E is the uncertainty on the merged cluster energy assuming that it is a hadronic shower. In addition, the w 2 consistency must not be significantly worse than that for the original cluster, Dw 2 ¼ðw Þ 2 w 2 o EnergyDeltaChi2ForCrudeMerging ½1:Š, where w ¼ðE C Þ=s EC. (viii) Cone-base merging: Starting from the identified hadronic interaction oint of each charged cluster, a cone of halfangle CosineConeAngle [.9] is defined in the direction of the track-like segment of the cluster. Neutral clusters deeer in the calorimeter with more than 5% of the energy of lying within this cone may be merged roviding the above w 2 consistency requirements are satisfied. If there is no track-like segment at the start of the charged cluster, the track direction is used. (ix) Photon recovery: In dense jets minimum ionising articles may ass through the EM shower from a hoton, resulting in a single reconstructed cluster. Cases where the hadron interacts a significant distance after the end of the EM shower are identified and hotons overlaing with charged clusters are recovered Re-clustering The revious four stages of the PandoraPFA algorithm are found to erform well for jets with energy less than about 5 GeV. At higher energies the jet energy resolution degrades due to the increasing overla between the hadronic showers from different articles. It is ossible to detect such reconstruction failures by comaring the charged cluster energy, E C, with the momentum of the associated track,. A ossible reconstruction failure is identified if jðe C Þ=s EC j4chitoattemtreclustering ½3:Š. In this case the PandoraPFA algorithm attemts to find a more self-consistent clustering of the calorimeter hits. If, for examle, a 1 GeV track is associated with a 2 GeV calorimeter cluster, shown schematically in Fig. 5(a), a otential reconstruction failure is identified. One ossible aroach would be to simly remove hits from the cluster until the cluster energy matched the track momentum. However, this does not use the full information in the event. Instead, the clustering algorithm is modified iteratively c 2 = c Track Track Fig. 5. Schematic examles of the main reclustering strategies used in PandoraPFA. The arrows indicates the track, the filled oints reresent the hits in the associated charged cluster and the oen oints reresent the hits in the neutral cluster. (a) Here the charged cluster energy is initially significantly greater than the associated track momentum. The hits are reclustered using modified arameters for the clustering algorithm in the hoe that a more consistent solution can be found. (b) Here the cluster energy is significantly less than the associated track momentum. The toological association algorithms (vii) and (viii) have not added the neutral cluster as this would have resulted in a charged cluster with too much energy for the track momentum. The hits are reclustered in the hoe that the neutral cluster naturally slits in such a way that the toological association algorithm will now make the correct association. = 2 2 =,,

7 M.A. Thomson / Nuclear Instruments and Methods in Physics Research A 611 (29) with the hoe that a more correct clustering of the hits will be found. This is imlemented by assing the hits in the cluster and the associated track(s) to the main clustering algorithm described in Sections 4.3 and 4.4. The algorithm is alied reeatedly, using successively smaller values of the arameters A and b, with the aim of slitting the original cluster so that the track momentum and associated cluster energy are comatible, as indicated in Fig. 5(a). In rincile, comletely different clustering algorithms could be tried. In cases where no significant imrovement in the w 2 comatibility of the track and associated cluster is found, the original cluster is retained. In stes (vii) and (viii) of the toological clustering, described in Section 4.4, the case where too little energy is associated with the track is addressed. However, in a dense jet environment, the neutral cluster which should be associated with a charged cluster may itself be merged with another neutral cluster, as indicated in Fig. 5(b). In such cases the reclustering rocedure acts on the combination of hits in the charged cluster associated to the track and nearby neutral clusters Photon identification and recovery A relatively sohisticated hoton identification algorithm is alied to the reconstructed clusters. The longitudinal rofile of the energy deosition, DE obs, as a function of number of radiation lengths from the shower start, t, is comared to that exected [23] for an EM shower: ðt=2þ a 1 e t=2 DE EM E t GðaÞ where a ¼ 1:25þ 1 2 ln E E c E is the shower energy and E c is the critical energy, which is chosen to give the aroriate average MC shower rofile in the ECAL. The level of agreement is arameterised by the sum over samlings in radiation length of the fractional deviation of the cluster rofile comared the exectation for an EM shower: d ¼ 1 X jde i obs E DEi EM j: i This aroach was referred to a w 2 - based metric as it is less sensitive to large local deviations which might arise from energy deosits from other nearby articles. The quantity d is minimised as a function of the assumed starting oint of the shower, t. Hence the outut of the shower shae algorithm is a measure of the consistency with the exected EM shower rofile, d, and the starting deth of the shower in the ECAL, t (in radiation lengths). These variables are used as the basis for identifying clusters as hotons. Transverse information is not used as this would make the hoton identification algorithm more sensitive to over-laing EM showers from very close hotons. Cases where removing the candidate hoton would result in the remaining cluster energy being inconsistent with the associated track momentum are vetoed Fragment removal At this late stage in PandoraPFA there are still a significant number of neutral clusters (not identified as hotons) which are fragments of charged article hadronic showers. An attemt is made to identify these clusters and merge them with the aroriate arent charged cluster. All non-hoton neutral clusters, i, are comared to all charged clusters, j. For each air of clusters a quantity, e ij, is defined which encasulates the evidence that cluster i is a fragment from cluster j using the following information: the number of calorimeter layers in which the minimum distance between the hits in the two clusters are searated by less than FragmentRemovalContactCut [2] ixels; the fractions of the energy of cluster i within three narrow cones defined by the first hadronic interaction in cluster j; the minimum distance of the centroid within a layer of cluster i to the fitted helix describing the track associated to cluster j; and the minimum distance between any of the hits in the two clusters. The requirement, R ij, for the clusters to be merged, i.e. the cut on e ij, deends on the location of the deth of the neutral cluster in the calorimeter and the change in the w 2 for the trackcluster energy consistency that would occur if the clusters were merged, Dw 2 ¼ð E j Þ 2 =s 2 E j ð E j E i Þ 2 =s 2 E ij : If e ij 4R ij the clusters are merged. This ad hoc rocedure gives extra weight to cases where the consistency of the track momentum and associated cluster energy imroves as a result of merging the neutral cluster with the charged cluster Formation of article flow objects The final stage of PandoraPFA is to create Particle Flow Objects (PFOs) from the results of the clustering. Tracks are matched to y/mm Photon recovery The comact nature of EM showers is utilised in an attemt to identify hotons which may have been merged into the cluster associated with a hadronic shower. The transverse energy distribution (ECAL only) of the reconstructed clusters is determined assuming that the cluster originates from the IP. A eak finding algorithm attemts to identify localised energy deositions which are dislaced from the associated track. If the longitudinal energy rofile in these regions is consistent with being an EM shower, the relevant hits are removed from the cluster and used to form a new cluster (assumed to be a hoton) x/mm Fig. 6. PandoraPFA reconstruction of a 1 GeV jet in the MOKKA simulation of the ILD detector. The different PFOs are shown by colour/grey-shade according to energy.

8 32 M.A. Thomson / Nuclear Instruments and Methods in Physics Research A 611 (29) 25 4 clusters on the basis of the distance of closest aroach of the track rojection into the first 1 layers of the calorimeter. If a hit is found within TrackClusterAssociationDistance [1 mm] of the track extraolation, an association is made. If an identified kink is consistent with being from a K 7 -m 7 n or 7 -m 7 n decay the arent track is used to form the PFO, otherwise the daughter track is used. Relatively rimitive article identification is alied and the reconstructed PFOs, including four-momenta, are written out in LCIO [17] format. Fig. 6a shows an examle of a PandoraPFA reconstruction of a 1 GeV jet from a ffiffi Z-uu decay at s ¼ 2 GeV. The ability to track articles in the high granularity calorimeter in the ILD detector concet can be seen clearly. Events PandoraPFA G(rms) G(rms 9 ) 5. Parameterising article flow erformance: rms Reconstructed Energy/GeV Fig. 7 shows the distribution of PFA reconstructed energy for simulated ðz=gþ -qq events (light quarks only, i.e. q ¼ u; d; s) ffiffi generated at s ¼ 2 GeV with the Z decaying at rest, termed Z-uds events. A cut on the olar angle of the generated qq system, y qq, is chosen to avoid the barrel/endca overla region, jcosy qq jo:7. Only light quark decays are considered as, currently, PandoraPFA does not include secific reconstruction algorithms to attemt to recover missing energy from semi-letonic decays of heavy quarks. The reconstructed energy distribution of Fig. 7 is not Gaussian. This is not surrising; one might exect a Gaussian core for erfectly reconstructed events, and tails corresonding to the oulation of events where confusion is significant. Quoting the rms, in this case 5.8 GeV, as a measure of the jet energy resolution over-emhasises the imortance of these tails. In this aer, erformance is quoted in terms of rms 9, which is defined as the rms in the smallest range of reconstructed energy which contains 9% of the events. For the data shown in Fig. 7, rms 9 ¼ 4:1 GeV (equivalent to a single jet energy resolution of 2.9%). The advantage of using rms 9 is that it is robust and is relatively insensitive to the tails of the distribution; it arameterises the resolution for the bulk of the data. One ossible criticism of this erformance measure is that for a true Gaussian distribution, rms 9 would be 21% smaller than the true rms. However, for the non-gaussian distribution from PFlow reconstruction, this is not a fair comarison. For examle, the central region of the reconstructed energy distribution 3 is 15% narrower than the equivalent Gaussian of s ¼ rms 9 as shown in Fig. 7. To determine the equivalent Gaussian statistical ower, a MC study was erformed assuming a signal with the shae of the PFA reconstructed energy distribution centred on x and a flat background. A fit to determine the value of x was erformed using the shae of the PFA distribution as a resolution function (fitting temlate). The rocess was reeated assuming a signal with same number of events but now with a Gaussian energy distribution. The width of the Gaussian (for both the signal and the fitting function) was chosen to give the same statistical recision on x as obtained with the PFA resolution function. From a fit to signal and background comonents the same fitted uncertainty, s x, is obtained for a Gaussian with standard deviation of 1:1 rms 9. On this basis it is concluded that the statistical ower for PFlow reconstruction with PandoraPFA yielding rms 9 is equivalent to a Gaussian resolution with s ¼ 1:1 rms 9. This conclusion does not deend strongly on the assumed relative normalisation of the signal and background or the total energy of the generated events. 3 Here the best fit Gaussian to the region GeV has an rms of 3.5 GeV. Fig. 7. The total reconstructed energy from reconstructed PFOs in 2 GeV Z-uds events for initial quark directions within the olar angle accetance jcosy qq jo:7. The dotted line shows the best fit Gaussian distribution with an rms of 5.8 GeV. The solid line shows a Gaussian distribution, normalised to the same number of events, with standard deviation equal to rms 9 (i.e. s ¼ 4:1 GeV). E/GeV rms 9 / GeV Jets 1 GeV Jets 18 GeV Jets 25 GeV Jets cosθ Fig. 8. The jet energy resolution, defined as the a in s E =E ¼ a= ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi E ðgevþ, lotted ffiffi versus cosy qq for four different values of s. The lot shows the resolution obtained from ðz=gþ -qq events ðq ¼ u; d; sþ generated at rest. 6. Particle flow erformance The erformance of the PandoraPFA algorithm with the ILD detector concet is studied using MC samles of aroximately 1, Z-uds generated with the Z decaying at rest with E Z ¼ 91:2, 2, 36, and 5 GeV. These jet energies are tyical ffiffi of those exected at the ILC oerating at s ¼ :521: TeV. In addition, to study the erformance at higher energies, events were generated with E Z ¼ 75 GeV and 1 TeV. Jet fragmentation and hadronisation was erformed using the PYTHIA [24] rogram tuned to the fragmentation data from the OPAL exeriment [25]. The events were assed through the MOKKA simulation of the ILD detector concet which is described in detail in Ref. [13]. The LCPHYS [26] Geant4 hysics list was used for the modelling of hadronic showers. For each set of events, the total energy is reconstructed and the jet energy resolution ffiffiffi is obtained by dividing the total energy resolution by 2. Fig. 8 shows the jet energy resolution as a function of the olar angle of the quarks in Z-qq events. The energy resolution does not vary significantly in the region jcos yjo:975. A small degradation in the energy resolution is seen for the barrel-endca overla region,

9 M.A. Thomson / Nuclear Instruments and Methods in Physics Research A 611 (29) :7ojcos yjo:8. In addition, there is a small degradation in erformance at cos y due to the TPC central membrane and gas between sections of the HCAL as simulated in the ILD detector model. Table 3 summarises the current erformance of the PandoraPFA algorithm alied to ILD detector simulation. For the tyical ILC jet energy range, GeV, the energy resolution is significantly better than the best resolution achieved at LEP, s E =E :65= ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi EðGeVÞ. Table 3 also lists the single jet energy resolution. For jet energies in the range GeV this is better than 3.8%, which is necessary to resolve hadronic decays of W and Z bosons. These results clearly demonstrate the otential of PFlow calorimetry at the ILC; the jet energy resolution obtained is aroximately a factor two better than might be achievable with a traditional calorimetric aroach. Furthermore, it is exected that the erformance of PandoraPFA will imrove with future refinements to the algorithm. It is worth noting, that for erfect PFlow reconstruction, the energy resolution would be described by s E =E a= ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi E ðgevþ, where a is a constant. The fact that this does not aly is not surrising; as the article density increases it becomes harder to correctly associate the calorimetric energy deosits to the articles and the confusion term increases. Also it should be noted that in a hysics analysis involving multi-jet final states, the resolution may be degraded by imerfect jet finding. 7. Understanding article flow erformance PandoraPFA is a fairly comlex algorithm, consisting of over 1, lines of Cþþ. It has a number of distinct stages which interact with each other in the sense that reconstruction failures in one art of the software can be corrected at a later stage. The relative imortance of the different stages in the reconstruction is investigated by turning off arts of the PandoraPFA algorithm. Table 4 comares the full PandoraPFA reconstruction with the algorithm run: (a) without the toological cluster merging hase; (b) without the reclustering hase; (c) without running the hoton clustering stage rior to the running the full clustering; (d) without fragment removal; and (e) the case where tracks from V s and kinks are not used in the event reconstruction. There are a number of notable features. The toological clustering and fragment removal algorithms are imortant at all energies. For low energy jets, the reclustering stage is not articularly imortant. This is because the rimary clustering and toological clustering algorithms are sufficient in the relatively low article density environment. With increasing jet energy, the reclustering stage becomes more imortant. For high energy jets ðe41 GeVÞ it is the single most imortant ste in the reconstruction after the initial clustering. Running the dedicated hoton clustering stage before the main clustering algorithm is advantageous for higher energy jets. The V =kink finding does not significantly imrove the resolution, although it is an imortant art in the identification of the final reconstructed articles. The contributions to the jet energy resolution have been estimated by relacing different stes in PandoraPFA with algorithms which use MC information to erform: (a) erfect reconstruction of hotons as the first hase of the algorithm; (b) erfect reconstruction of neutral hadrons; and (c) erfect identification of fragments from charged hadrons. The jet energy resolutions obtained using these erfect algorithms enable the contributions from confusion to be estimated. In addition, studies using a dee HCAL enable the contribution from leakage to be estimated. Finally, MC information can be used to erform ideal track attern recognition enabling the imact of imerfect track finding code to be assessed. Table 5 lists the estimated breakdown of the total jet energy into its comonents, including the contributions from calorimetric energy resolution (i.e. the energy resolution for hotons and neutral hadrons). For the current PandoraPFA algorithm, the contribution from the calorimetric energy resolution, 21%= ffiffiffi E, dominates the jet energy resolution for 45 GeV jets. For higher energy jets, the confusion term dominates. This behaviour is summarised in Fig. 9. The contributions from resolution and confusion are roughly equal for 12 GeV jets. From Table 5 it can be seen that the most imortant contribution for high energy jets is confusion due to Table 3 Jet energy resolution for Z-uds events with jcosy qq jo:7, exressed as: (i) the rms of the reconstructed di-jet energy distribution, E jj ; (ii) rms 9 for E jj ; (iii) the effective ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi constant a in rms 9 ðe jj Þ=E jj ¼ aðe jj Þ= E jj ðgevþ; and (iv) the fractional jet energy resolution for a single jet where rms 9 ðe j Þ¼rms 9 ðe jj Þ= ffiffiffi 2. Jet energy (GeV) rms (GeV) rms 9 ðe jj Þ (GeV) rms 9 ðe jj Þ= ffiffiffiffiffi E jj (%) rms9 ðe j Þ=E j (%) ð3:747:5þ ð2:927:4þ ð3:7:4þ ð3:117:5þ ð3:647:5þ ð4:97:7þ Table 4 Jet energy resolutions ðrms 9 =EÞ for the full PandoraPFA reconstruction comared to that obtained: (a) without the toological cluster merging hase; (b) without the reclustering hase; (c) without running the hoton clustering stage rior to the running the full clustering; (d) without fragment removal; and (e) the case where tracks from V s and kinks are not used in the event reconstruction. Algorithm Jet energy resolution rms 9 ðe j Þ=E j E j ¼ 45 GeV E j ¼ 1 GeV E j ¼ 18 GeV E j ¼ 25 GeV Full PandoraPFA (%) ð3:747:5þ ð2:927:4þ ð3:7:4þ ð3:117:5þ (a) No toological clustering (%) ð4:27:5þ ð3:257:4þ ð3:527:5þ ð3:677:6þ (b) No reclustering (%) ð3:837:5þ ð3:37:4þ ð3:917:5þ ð4:197:7þ (c) No hoton clustering stage (%) ð3:667:5þ ð2:997:4þ ð3:137:4þ ð3:317:5þ (d) No fragment removal (%) ð4:57:5þ ð3:217:4þ ð3:257:4þ ð3:47:6þ (e) No V =kink tracks ð%þ ð3:787:5þ ð2:967:4þ ð3:27:4þ ð3:137:5þ