Members of NIU, ANL, SLAC, and UTA began collaborating on PFAs, simulations, and software development efforts in January, 2002. Several other groups have since joined the effort, and links have been established with European colleagues who had been active in this area already. The results that emerged through discussions at our regularly scheduled meetings have been presented at the Calor conferences, ECFA and ACFA meetings, the American LC workshops, and at the International LC Physics and Detector Workshops.

Toward the optimization of the HCal design, the NIU and ANL teams have started investigating both analog (cell energy measurements) and digital (hit density measurements) methods as functions of the cell size. Our preliminary findings suggest that with sufficiently small cells, the digital method yields a more precise measurement of the hadron energy, i.e., fluctuations in hit density are smaller than those in the sampled energy of a hadronic shower. Use of local hit density in lieu of the deposited energy to weigh the calorimeter hits results in superior energy resolution and lateral containment of single hadron showers. Two independent approaches to the implementation of a PFA have helped improve our understanding of the optimal cell sizes and geometry for best charged/neutral hadron shower separation in jets within the context of some specific overall detector parameters.

We will now briefly summarize our HCal optimization and algorithm development efforts. The HCal must be optimized to achieve, with due consideration of costs, benefits, and risks, the best balance between the reconstruction and energy resolution of neutral-hadron-initiated clusters in a jet, and the ability to separate them from the charged components. This is intimately related to the first step in the development of a particle-flow algorithm as described below. The elements are highly inter-related, and must be optimized simultaneously. All figures in this section were generated using GEANT4-based full-detector and test-beam simulation programs and reconstruction algorithms developed by our group.

HCal absorber/active media properties:

The detector simulation and analysis of physics events within the Java Analysis Studio (JAS)-based software environment developed at SLAC, is flexible in the choice of absorber and active media type and thickness within the limits of the HCal volume. Our group has put together a GEANT4-based detector simulation package called LCDG4 to work within this environment, and produced many data sets spanning a range of cell shapes and sizes, and event types (single particles as well as benchmark physics processes). Teams from NIU, ANL, SLAC, Kansas, and Iowa, are studying a wide variety of events simulated with this package. We will optimize the HCal by comparing dense materials (e.g. W) to less dense ones (e.g. Stainless Steel) as absorbers, and scintillator- vs. gas-based devices (e.g. RPC, GEM) as active media. Containment of hadronic showers, density of hits, single-particle and jet energy resolutions will be used as performance measures. Substantial progress has been made in this direction already. The left panel of Fig. 2 shows the energy resolution as a function of single energy, estimated using hit density weighting, for two different lateral segmentations of the scintillator option, and the proposed segmentation for a realistic RPC design. The right panel of Fig. 2 shows the density-weighted angular widths of single-hadron showers as functions of their momenta in reasonably realistic scintillator- and gas-based designs. The more realistic gas-based geometry and the scintillator design under consideration give comparable results.


Figure 2: Comparisons of scintillator vs. gas as the HCal active medium. Left: the fractional energy resolution of single using density-weighting clustering in scintillator and gas-based geometry. Scintillator tiles of 1 cm² (stars) is not a practical proposition, but it is studied to understand the dependence of energy resolution on lateral segmentation of the active layer for a given choice of technology. Even the realistic 9 cm² scintillator option (circles) offers a somewhat better resolution than a 1 cm² gas configuration (squares) under this particular weighting scheme. The two are comparable at higher energies. Right: the density-weighted angular width of single showers as function of their momenta, in HCals with 9 cm² square scintillator tiles (circles) and those with 1 cm² square gas-based cells (triangles for ``Geom1'' and squares for ``Geom2''). The ``Geom2'' configuration is fairly close to the RPC design currently under consideration. Other density-weighting schemes remain to be investigated.

HCal transverse granularity/Longitudinal segmentation:

We plan to optimize the 3-d granularity of cells for the most promising PFAs vis-a-vis the active medium technology (see the left panel of Fig. 2) The methods developed here are generalizable to different total detector geometries, i.e., SiD (which uses silicon wafers for tracking), LD (which uses TPCs for tracking), etc. The basic performance measure here is the ability to separate showers initiated by charged and neutral hadrons - the key to any PFA. Indeed, if all the cell energies in a jet could be fully separated and correctly assigned to the parent particle, then a jet energy resolution of (E in GeV) could be achieved. It turns out that the limiting factor in the overall jet energy resolution is the confusion term arising from imperfect association due to finite granularity and misassignment. From the reconstruction algorithm's point of view, it is this term that poses the biggest challenge.

Analog vs. digital readout for the HCal:

The question of optimal 3-d granularity is intimately related to that of the readout method, which needs to be evaluated by comparing jet resolutions with both analog and digital readout. At the extreme, ``digital'' readout means a single-bit ``yes/no'' decision on whether or not a minimum ionizing particle (MIP) has passed through a given cell. Since such digital measurements are less susceptible to Landau and path-length fluctuations than full (12-15 bit) analog measurements, hit counting has smaller spread than energies samples in the active medium. We have shown that for small cell sizes (< 10 cm²), the number of cells hit is a superior estimator of energy of single hadrons below 20 GeV (where more than 95% of the particles in typical jets in multijet events of interest are concentrated) to traditional analog sampling. Since the spatial spread of a shower increases in a less-than-linear proportion to its energy, the advantage gradually disappears at higher energies. We find that a semi-digital readout allowing multiple thresholds to classify the hit status of a cell can be effectively used counter this non-linearity. This supports the contention that the dynamic range sacrificed in order to achieve finer segmentation is not likely to hurt us at all.

Figure 3: The fractional resolution of single energy using full analog (circles), 1-bit digital (squares), and 2-bit digital (triangles) read-outs. We find that 3 thresholds (i.e. 2-bits) is optimal.

It may be prudent to consider both the best analog and the best digital version of the HCal for eventual evaluation with test beams provided both prove potentially capable of meeting the energy resolution requirement. Such testing could spur future advances in readout technology.

Particle-flow algorithms:

For the first time in calorimeter development, it is necessary to take into account the reconstruction algorithms in designing the detector(s). How good the jet energy resolution will be depends ultimately on how well the PFA is formulated and tuned. We have implemented, as the first step of a PFA, an algorithm that produces ``pre-clusters'' of calorimeter cells using energy and local density as weights. The user can choose the parameters such as thresholds, neighborhood definitions etc. These preclusters serve as a quasi-geometry-independent set of objects for the subsequent steps. The second step is to extrapolate the tracks and match them to preclusters whenever appropriate, so that the energies of all charged-hadron-induced preclusters can be replaced with the corresponding track momenta. The third step is to identify the photons by shower-shape analysis in the ECal. The final step involves combining the track momenta with photon and neutral hadron energies to produce high-precision jet energy measurements. Our goal is to minimize the dependence of implementations of the high-level algorithms on detector geometry details. This will greatly facilitate portability of the algorithms across regional boundaries and detector design choices. In addition to the preclustering algorithm from NIU, we already have separate preliminary codes for identification of track segments minimum-ionizing-particles (Iowa), propagating the tracks through the calorimeter taking energy loss into account (FNAL, NIU), photon reconstruction (SLAC, Kansas), and reconstruction from these of PFA jets (ANL, NIU). We are now working to combine these pieces into a fully functional jet-finding algorithm.

The PFA developed at NIU, performs full jet reconstruction using Monte Carlo ``truth'' for track matching. The result of this is shown in Fig. 4. We see that this PFA affords a 40% improvement in jet energy resolution compared to a traditional purely calorimetric measurement.

Figure 4: The estimated jet energy normalized to the true energy in e+e- --> ZZ --> 4 jets events at GeV events using purely calorimetric measurement (left) and the PFA developed at NIU (right). The calorimetric estimation uses traditional analog energy measurement, while the PFA uses semi-digital (2-bit) measurement in this case. The PFA can be used in analog mode as well. No kinematic fitting based on event topology is used in either measurement.

The NIU group has also made significant contributions to LC detector simulation software during the past 3 years. We ported and have been maintaining all of the current American software on the Linux platform. Since mid-2002, we have been processing simulation requests from several groups engaged in LC R&D, on Linux farms at NIU and FNAL. We organized a workshop at NIU/NICADD in November, 2002 (http://nicadd.niu.edu/ws/), to bring the groups together, chart a plan, and set out in an organized manner. This was followed by similar workshops at SLAC in 2003 and at ANL in 2004. Following are the simulation software projects where we have made substantial progress and hope to remain commited:

Simulation of full detector concepts:

We have developed, in close collaboration with our colleagues at SLAC, a stand-alone GEANT4-based simulation package. This package, named ``LCDG4'', fully complies with the model put forth by the ALCPG simulation group, and adds several useful functionalities to it.[4] It produces ``raw'' hit output in the globally accepted LCIO format and supports projective geometries in as well as non-projective ones with cells of constant linear dimensions. After extensive testing, this package has been adopted as the standard for ALCPG. Figure 5 shows an example event display from LCDG4.


Figure 5: Side view (left) and end view (right) of an 4 jets event at GeV in the SD detector simulated using the LCDG4 program developed at NIU.

Simulation of test-beam prototype modules:

Further, as members of the CALICE collaboration (CAlorimeter for the LInear Collider with Electrons,[2]), and in active cooperation with our European colleagues, we have produced a GEANT4-based simulator for the detector prototype module that is expected to be exposed to test beams at Fermilab over a period of 3 years starting in mid-2005. This program, called ``TBMokka'' is built on an alternative simulation framework called ``Mokka'', developed independently by our European colleagues. Figure 6 shows an example event display from a stand-alone GEANT4-based program to simulate a test-beam module (this program is used as a cross-check for TBMokka).[5]

Figure 6: Side view of a 2 GeV passing through a near-final test-beam prototype module simulated using the GEANT4-based simulation program developed at NIU.
We are well on our way to combining the best features of LCDG4 and Mokka. The new ``next generation'' simulation program incorporates a more advanced XML-based geometry description system. Like its predecessors, it supports run-time geometry specification, but offers a wider range of options and easier changes to geometries using GDML (Geometry Description Mark-up Language), a Geant4-specific extension of XML (eXtensible Mark-up Language).

Simulation of the signal extraction process following energy deposition:

In another endeavor, we have designed and coded the first version of a package, called ``DigiSim'', to simulate the conversion of energy deposits produced by GEANT4 to electronic read-outs.[6] This package offers the user a simple, flexible, and standard way to simulate the effects of thresholds, noise, cross-talk, inefficiencies, attenuation, and timing, that are involved in signal collection, propagation, and conversion (digitization). In essence, it allows the user to model an arbitrary transfer function from the energy deposited at the cell to the corresponding ``raw data''. DigiSim can be used either in a stand-alone mode to produce a persistent output, or as an on-the-fly preprocessor to the reconstruction program. In stand-alone mode, it produces output in the same format as that envisaged from the real detector (except, of course, the simulation output also contains the ``Monte Carlo truth'', which the real data does not). No high claim to the performance of an algorithm can be substantiated without a realistic accounting of the above-mentioned detector effects. Thus, DigiSim plays a vital role, and has been warmly welcomed by the user community worldwide. We expect it to be used for the simulation of both the various test-beam prototypes and full-detector designs.

A summary of recent results from the above activities can be found in the 3 presentations made by the project leader, on behalf of the NIU/NICADD group, at the ILCD05 meeting at Paris.[7]