Development of Particle-Flow Algorithms
and Simulation Software for the ILC

The Northern Illinois University(NIU)/Northern Illinois Center for Accelerator and Detector Development (NICADD) group is interested in calorimeter R&D for the proposed ILC.[1] We propose to develop, in simulation and in prototype, designs for a hadron calorimeter (HCal) optimized for jet reconstruction using particle-flow algorithms (a.k.a. ``energy-flow algorithms''). Simulation/algorithm development and hardware prototyping are envisaged as the two main components of our efforts. This proposal addresses the first component while the second is the subject of a separate proposal.

An e+e- linear collider is a precision instrument that can elucidate Standard Model (SM) physics near the electroweak energy scale as well as discover new physics processes in that regime, should they exist. In order to fully realize the potential anticipated from a machine of this type, the collection of standard high energy physics detector components comprising an experiment must be optimized, sometimes in ways not yet realized at current experiments. One such example is the hadron calorimeter which will play a key role in measuring jets from decays of vector bosons and other heavy particles such as the top quark, the Higgs boson(s), etc. In particular, it will be important to be able to distinguish, in the final state of an e+e- interaction, the presence of a Z or a W boson by its hadronic decay into 2 jets. This means that the dijet mass must be measured within ~ 3GeV, or, in terms of jet energy resolution, $\sigma (E) \approx 0.3\sqrt{E}$ (E in GeV). Such high precision in jet energy measurement cannot be achieved by any existing calorimeter in the absence of a kinematically overconstrained event topology. Similar precision in measurements of jet and missing momentum will be crucial for discovery and characterization of several other new physics processes as well as for precision tests of the Standard Model. Such ambitious objectives place strong demands on the performance of the calorimeters working in conjunction with the tracking system at the ILC, and requires development of new algorithms and technology.

The most promising means to achieving such unprecedented jet energy resolutions is through particle-flow algorithms (PFA). A PFA attempts to separately identify in a jet its charged, electromagnetic, and neutral hadron components, in order to use the best means to measure each. On average, neutral hadrons carry only ~11% of a jet's total energy, which can only be measured with the relatively poor resolution of the HCal. The tracker is used to measure with much better precision the charged components (~64% of jet energy), and the electromagnetic calorimeter (ECal) to measure the photons with $\sigma (E) \approx 0.15\sqrt{E}$ (~24% of jet energy). The left panel of Fig. 1 shows the momentum distribution of particles in a representative multijet physics process of interest. On average, only a small fraction of a jet's energy is carried by particles with momenta greater than 20 GeV. The right panel of Fig. 1 shows the precisions of energy measurement by a calorimeter, and momentum measurement by a tracker, of single charged hadrons, as functions of their momenta in one nominal detector design. Measurements from the tracker are at least two orders (one order) of magnitude more precise than those from the calorimeter for particles below 20 GeV (100 GeV). A net jet energy resolution of $\sigma (E) \approx 0.3\sqrt{E}$ is thus deemed achievable by using the HCal only to measure the neutral hadrons with $\sigma (E) \approx 0.6\sqrt{E}$. However, this will certainly require extensive and simultaneous optimization of detector design and tuning of algorithm parameters.

Figure 1a


Figure 1: Left: the momentum distribution of particles in e+e- --> ZZ --> 4 jets events at sqrts500 GeV. Right: the fractional energy (momentum) resolution of an excellent calorimeter and that of a good tracker as functions of particle momentum.

A calorimeter designed for PFAs must be finely segmented both transversely and longitudinally for 3-d shower reconstruction, separation of neutral and charged clusters, and association of the charged clusters to corresponding tracks. This requires realistic simulation of parton shower evolution and of the detector's response to the particles passing through it. Accurate simulation relies heavily on analysis of data from beam test of prototype modules. The detector optimization requires the simulation, visualization, and analysis packages to be highly flexible, which calls for careful design and implementation of the software itself.

Very large numbers of events will have to be simulated to evaluate competing detector designs vis-a-vis ILC physics goals. Characterization of signatures arising from processes predicted by some extensions of the SM will require simultaneous coverage of broad ranges of undetermined parameters. Parametrized fast simulation programs will thus have to be developed once the algorithms have stablized. Parametrization of PFAs will require much work, and is one of our key objectives.