Progress with Particle Flow Calorimetry

Many of the interesting physics processes at the ILC will be characterised by multi-jet final states, often accompanied by charged leptons and/or missing transverse energy associated with neutrinos or the lightest super-symmetric particles. The reconstruction of the invariant masses of two or more jets will provide a powerful tool for event reconstruction and identification. Unlike at LEP, where kinematic fitting[1] enabled precise jet-jet invariant mass reconstruction almost independent of the jet energy resolution, at the ILC this mass reconstruction will rely on the detector having excellent jet energy resolution. The ILC goal is to achieve a mass resolution for W → q ′ q and Z → qq decays which is comparable to their natural widths, i.e. σ m /m = 2.7 % ≈ Γ W /m W ≈ Γ Z /m Z . For a traditional calorimetric approach, a jet energy resolution of σ E /E = α/ E(GeV) leads to a di-jet mass resolution of roughly σ m /m = α/ E jj (GeV), where E jj is the energy of the di-jet system. At the ILC typical di-jet energies will be in the range 150 -350 GeV, suggesting the goal of σ E /E ∼ 0.3/ E(GeV). This is more than a factor two better than the best jet energy resolution achieved at LEP, σ E /E = 0.6(1 + | cos θ|)/ E(GeV) [2]. Meeting the jet energy resolution goal is a major factor in the overall design of a detector for the ILC.

It is widely believed that the most promising strategy for achieving the ILC jet energy goal is the particle flow analysis (PFA) approach to calorimetry. In contrast to a purely calorimetric measurement, PFA requires the reconstruction of the four-vectors of all visible particles in an event. The reconstructed jet energy is the sum of the energies of the individual particles. The momenta of charged particles are measured in the tracking detectors, while the energy measurements for photons and neutral hadrons are obtained from the calorimeters. The crucial step in PFA is to assign the correct calorimeter hits to reconstructed particles, requiring efficient separation of nearby showers.

Measurements of jet fragmentation at LEP have provided detailed information on the particle composition of jets (e.g. [3,4]). On average, after the decay of short-lived particles, roughly 62% of the energy of jets is carried by charged particles (mainly hadrons), around 27% by photons, about 10% by long-lived neutral hadrons (e.g. n/K 0 L ), and around 1.5% by neutrinos. Assuming calorimeter resolutions of σ E /E = 0.15/ E(GeV) for photons and σ E /E = 0.55 E(GeV) for hadrons, a jet energy resolution of 0.19/ E(GeV) is obtained with the contributions from tracks, photons and neutral hadrons shown in Tab. I. In practise it is not possible to reach this level of performance for two main reasons. Firstly, particles travelling at small angles to the beam axis will not be detected. Secondly, and more importantly, it is not possible to perfectly associate all energy deposits with the correct particles. For example, if a photon is not resolved from a charged hadron shower, the photon energy is not counted. Similarly, if part of charged hadron shower is identified as a separate cluster the energy is effectively double-counted. This confusion degrades particle flow performance. Because confusion, rather than calorimetric performance, determines the overall performance, the jet energy resolution achieved will not, in general, be of the form σ E /E = α/ E(GeV).

The crucial aspect of particle flow is the ability to correctly assign calorimeter energy deposits to the correct reconstructed particles. This places stringent requirements on the granularity of electromagnetic and hadron calorimeters. Consequently, particle flow performance is one of the main factors driving the overall ILC detector design. It should be noted that the jet energy resolution obtained for a particular detector concept is the combination of the intrinsic detector performance and the performance of the PFA software.

PandoraPFA is a C++ implementation of a PFA algorithm running in the Marlin[5, 6] framework. It was designed to be sufficiently generic for ILC detector optimisation studies and was developed and optimised using events generated with the Mokka[7] program, which provides a GEANT4 [8] simulation of the Tesla TDR [9] detector concept. The PandoraPFA algorithm performs both calorimeter clustering and particle flow in eight main stages: i) Tracking: for the studies presented in this paper, the track pattern recognition is performed using Monte Carlo information [5]. The track parameters are extracted using a helical fit. The projections of tracks onto the front face of the electromagnetic calorimeter are calculated using helical fits (with no accounting for energy loss along the track). Neutral particle decays resulting in two charged particle tracks (V 0 s) are identified by searching from pairs of non-vertex tracks which are consistent with coming from a single point in the central tracking chamber. Kinked tracks from charged particle

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