How To Measure Jet Energy With A Digital Calorimeter

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1 Proc. 25th Winter Workshop on Nuclear Dynamics (2009) th Winter Workshop on Nuclear Dynamics Big Sky, Montana, USA February 1 8, 2009 Digital Calorimeter Edwin Norbeck 1, Burak Bilki 1, Yasar Onel 1, José Repond 2, and Lei Xia 2 1 University of Iowa, Iowa City, IA USA 2 Argonne National Laboratory, Argonne, IL 60439, USA Abstract. A digital calorimeter, as described here, is a tracking device for highly relativistic hadrons. It is a sampling calorimeter, consisting of heavy metal plates separated by thin detectors of high granularity. Each pixel of a detector produces a single bit or a zero. This digital map is made useful by an elaborate computer program, a Particle Flow Algorithm, PFA. Keywords: digital calorimeter, particle flow algorithms PACS: Vj, Gx 1. Introduction Conventional calorimeters used for energy measurement in recent high energy particle and heavy ion collisions fall into two main categories: homogeneous and sampling calorimeters. Examples of homogeneous calorimeters consist of scintillating crystals, Čerenkov radiators and ionizing noble liquids, whereas sampling calorimeters employ alternating layers of metal absorbers and a variety of active media of which scintillators and gas-filled detectors can be considered as examples. Metal absorbers allow a large reduction in cost and size. The use of higher Z materials also results in a larger difference between electromagnetic and hadronic showers. To effectively deal with hadrons, the depth should be at least 10 nuclear reaction lengths. For silicon this is 4.55 m, but for iron it is 1.68 m, and for tungsten it is only 0.96 m. The goal of a calorimeter is to measure the energy and mass of the final state particles as precisely as possible. A significant part of new physics also requires a careful measurement of the missing energy. The energy resolution of a calorimeter can be expressed as σ(e)/e = α/ E where E is the particle energy in GeV and α is a constant which varies between 0.6 and 0.8 for most existing calorimeters. A future lepton collider (International Linear Collider) will probe Standard Model (SM) physics and beyond the SM near the electroweak energy scale [1]. The methodology of such physics analysis requires a clear identification of W ± and Z o bosons. In terms of calorimetry, this implies a precise measurement of jet energies

2 2 E. Norbeck et al. requiring α 0.3, about a factor of two better than currently accomplished values. The most promising approach to achieve jet energy resolutions at this level makes use of a Particle Flow Algorithm (PFA). In this approach, particles in a hadronic jet are individually measured by the detector component that provides the best momentum/energy resolution. These measurements are then combined to obtain the jet energy. The application of PFAs sets constraints on the design of active media and the readout of the tracker and the calorimeters. After a brief discussion of PFAs, the basic idea of digital calorimetry is introduced with a brief description of a digital hadron calorimeter with Resistive Plate Chambers that has been extensively studied. 2. Particle Flow Algorithms Jets consist of four components: charged particles, photons, neutral hadrons and neutrinos. Since the PFA requires utilizing the part of the detector that provides the best momentum/energy resolution for each distinct jet component, charged particles are measured with a tracking system, photons are measured with an electromagnetic calorimeter, neutral hadrons are measured by a combination of electromagnetic and hadronic calorimeters, and neutrinos escape without being detected. The PFA identifies the energy deposited in the calorimeters by each of the jet components [2 5]. We are concerned here primarily with the hadronic calorimeter. A typical PFA starts by grouping calorimeter hits into clusters according to a density driven clustering algorithm. To construct a cluster, the program starts with a seed, which is defined as a hit that is not in an existing cluster. Neighboring hits are attached to the seed to grow the cluster. After finding all clusters, a photon identification algorithm identifies clusters originating from EM showers by comparing their longitudinal shower profile to the expected shower profile of a photon (photons are important even in hadronic calorimeters because hadronic showers contain neutral pions). The momenta of the charged particles are measured by a tracker in front of the calorimeter (this requires a tracker with a large volume and a large magnetic field, of the order of 5 T). The paths of these particles are extrapolated into the calorimeter and matched with calorimeter clusters. Neutral hadron clusters are identified as being unmatched with any of the charged particle clusters. The main task is to distinguish between the two types of clusters. A cluster with both charged and neutral particle content could be identified as a neutral particle later in the PFA leading to a double counting of energy, or it could be identified as a charged particle resulting in a loss of reconstructed energy. To a good approximation, the energy represented by a cluster is proportional to the number of hits. The calibration factor can be provided by isolated charged particle clusters, for which the energy is known.

3 Digital Calorimeter 3 3. Calorimetry The usual function of a sampling calorimeter is to measure the energy deposited by a group of particles incident on the device. The signal is the sum of all the signals generated by individual particles in the active layers. Unless a reasonably large fraction of the energy is deposited in the active layers, the fluctuations seriously degrade the measurement. Thick detectors are expensive, and each type has some sort of problem [6]. Thin, high granularity detectors have been developed to optimize the utilization of PFAs in jet energy measurements. These include the Resistive Plate Chamber (RPC)[7], the Gas Electron Multiplier (GEM)[8] and the MicroMEsh GAseous Structure (MICROMEGAS) [9]. The energy resolution for MIPs in these detectors is abysmal; the pulse height spectrum has a shape something like that shown in Fig. 1. However, if the particle is known to be a MIP, the energy loss in the adjacent absorber layer and the detector is reasonably well known. In a digital calorimeter, the signal from the pixel is registered as a one if it is above threshold and a zero otherwise. A single-bit readout is sufficient to provide the necessary single particle energy resolution. Fig. 1. Signal from MIP in a thin detector There are situations for which it would be desirable to reconstruct the actual tracks. The energy, and sometimes even the type of particle, would be derived from the tracks. Figure 2 shows some of the tasks required of the computer program. The isolated noise pixels and the gaps in the tracks, caused by below threshold signals, should be easy. There is also the situation where a MIP will be near the edge of a pixel so that it leaves a one in two adjacent pixels. If there are branches, the tracks can be extrapolated back to the vertex to determine the pixels that represent more than one MIP. The angle of the tracks can be taken into account in calculating the energy deposited in each layer. The pixel spacing must be smaller than the average spacing between incoming particles, even when the particles are part of a jet. For hadronic calorimeters, 1 cm 2 cells are adequate [4].

4 4 E. Norbeck et al. Fig. 2. A digital event. Note isolated noise points and breaks in tracks. With an analog calorimeter the gain of each detector must be precisely known. This can be difficult because there are many factors that cause the gain to change. An accurate calibration of an analog calorimeter with many pixels can be a huge task. With a digital calorimeter, a gain shift causes a small shift in the threshold that will cause more noise signals or an excess of blank pixels in a track. It is advantageous to have small pixels in a tracking calorimeter, but then the data files are large. If the pixels are digital the structure of the data is simpler, and the files can be smaller. 4. A Digital Calorimeter Prototype with RPCs Individual events from a small prototype device [10, 11] are shown in Fig. 3 for muons and in Fig. 4 for pions. There are 16 x 16 = 256 pixels, each 1.0 cm x 1.0 cm, in each RPC (Resistive Plate Chamber). The detectors are separated by absorber plates, 16 mm of steel and 4 mm of copper. In these figures, the last few chambers are not operational. To show clearly the configuration of hits, the isometric view is supplemented with projections from the end, top and side. Figure 5 shows the hit pattern for multiple 120 GeV protons. This device is a prototype for a cubic meter calorimeter that will have 40 planes, each with 10, cm 2 pixels for a total of 400,000 single bit channels [12]. Figure 6 shows the hit patterns for two 8 GeV e + events. The transverse and longitudinal position resolution does not allow identification of individual shower particles in an electromagnetic shower. However, the shape of the shower does allow an estimation of the energy. Good agreement was found between the data and Geant4 simulations for the e + events [11].

5 Digital Calorimeter 5 Fig. 3. The display of a typical muon event (top) and an event with multiple muons (bottom).

6 6 E. Norbeck et al. Fig. 4. A typical 8 GeV pion event. Fig. 5. An event with multiple 120 GeV protons.

7 Digital Calorimeter 7 Fig. 6. Typical 8 GeV e + events (Chamber 7 was not in operation).

8 8 E. Norbeck et al. 5. Conclusions A promising method for improving the measurement of the energy of jets makes use of a Particle Flow Algorithm (PFA). It allows the measurement of each constituent of the jet to be made with a detector that provides the best momentum/energy resolution. This could be a tracker in a strong magnetic field followed by highly segmented calorimeters, both electromagnetic and hadronic. The PFA tracks the particles through the calorimeters and then combines all the information to yield the energy of the jet. Because of the separation of the tracks, the hadronic calorimeter itself need only measure the energy of the neutral hadrons, which carry only 10% to 20% of the jet energy. Tracks from the charged particles can be used for energy calibration. With sufficiently fine segmentation, so that usually no more than one particle passes through each pixel, a readout of a single bit is sufficient. This digital approach avoids the cost and complexity of an analog to digital conversion of the output from each pixel and allows the use of thin gas detectors in the calorimeters. Digital calorimetry is a rapidly developing field that depends heavily on the capabilities of the PFA and therefore on the capabilities of computers. It can be expected that digital calorimeters will be an important component in detector arrays used with future accelerators of energetic particles. References Session on PFAs in XII International Conference on Calorimetry in High Energy Physics, Chicago, AIP Conf. Proc. 867 (2006) N. Graf et al., 523; L. Xia, 531; P. Krstonosic, 538; D. Chakraborty et al., J. Repond, Nucl. Inst. and Meth. A 572 (2007) J. Repond, Nucl. Inst. and Meth. A 518 (2004) J. Repond, Nucl. Inst. and Meth. A 533 (2004) R. Wigmans, XII International Conference on Calorimetry in High Energy Physics, Chicago, AIP Conf.Proc. 867 (2006) G. Drake, J. Repond, D. Underwood and L. Xia, Nucl. Inst. and Meth. A 578 (2007) G. Anelli et al., (TOTEM Collaboration), JINST 3 (2008) S Y. Giomataris, Ph. Rebourgeard, J.P. Robert and G. Charpak, Nucl. Inst. and Meth. A 376 (1996) B. Bilki et al., JINST 3 (2008) P B. Bilki et al., JINST 4 (2009) P &sessionid=22&confid=2628.