V. Calorimeter simulation results
1. Introduction
Since a primary role of the hadron calorimeter is the identification and energy measurement of neutral hadrons, it is essential for calorimeter design purposes to study the impact of variations of longitudinal and transverse segmentation, calorimeter depth, absorber material, magnetic field and other parameters on performance. Neutral hadrons have been studied through simulation in an effort to aid design decisions. All simulations used GEANT4, with the LCPhys physics model. First, single particles were studied in (semi)infinite sampling calorimeters, varying design parameters and studying responses, resolution and transverse spread of the showers. These results were then used for calibrations, allowing the study of full detector simulations. For four variations of hadron calorimeter designs, the jet energy resolution in mono-energetic jets and the dijet mass resolution in 500 GeV ZZ events were also studied.
2. Single particles in uniform (semi)infinite detectors
To study the response of neutral hadrons in sampling calorimeters, simulations have been performed using semi-infinite (1000 layer) calorimeters. The absorber, active medium, and B-field were varied, with the mean and rms of responses observed. These responses were also studied as a function of depth of the calorimeter, analog/digital readout and incident angle of the particle. The hadron calorimeter simulations had 1cm by 1cm transverse segmentation, and studies of the effect of segmentation were done by combining cells. For each data set, k0L’s, neutrons, and antineutrons were generated at a fixed energy and angle, with the mean and rms of the response recorded.
The mean and rms varied according to particle type, so a “combined” neutral hadron was defined as (.5k0L + .25n + .25nbar). A sample plot showing the resolution of this “combined” neutral hadron for four detector variations is shown in Fig. 1. The parameter space is enormous, but enough variations were examined to see trends. Comparisons were made by fixing all parameters but one and varying that parameter. A summary of observations follows:
B-field: No significant variation in response or resolution was observed between 0 and 5 Tesla. However, the radial and transverse spreads have not yet been studied. Fig 2.
Incident angle: Results indicate that significant response corrections are needed. At 45 degree incidence, corrections are ~5% for plastic and ~12% for gas active media. Fig 3.
Segmentation: 20 – 30% worse resolution for 3cm by 3cm segmentation vs. 1cm by 1cm. (Digital) Fig. 4.
Comparison of analog vs. digital modes: The results seem to depend on absorber type and lambda/layer. Below ~ 10 GeV, digital resolutions are better. For W absorber with .08 lambda/layer, and plastic active medium, ~20% improvement in resolution at higher energies is seen using analog mode. Fig. 5. (Note: analog responses used the straight sum of all energy deposits above threshold. More sophisticated algorithms may yield more improvement.)
Depth: Resolution is energy and active medium dependent. For 50GeV a 20-30% worse resolution is seen from a 5-4 lambda HCal. Fig. 6.
Absorber: W and Pb show similar and worse resolution than SS or Cu. Shower spread smaller in W than SS. The energy resolution for Wcan be improved by using a smaller lambda/layer, at cost of shower transverse spread. Fig. 7.
Active medium: Plastic shows better resolution than gas at lower energies. However, plastic shows a worse transverse spread than gas. Fig 8.
Note: These plots point out the model change in GEANT4 LCPhys physics list between 10 and 15 GeV. While the absolute scale may be suspect, comparisons between detector configurations should be valid.
Fig 1 – Resolution vs energy for 4 HCal configurations
Fig. 2 – Response comparison, B=0,5 tesla
Fig. 3 – Response comparison for 45 and 90 degree incidence
Fig. 4 – Effect of segmentation on neutral hadron resolution
Fig. 5 – Resolution of analog vs digital response
Fig 6 – Resolution for different absorbers
Fig. 7 – Resolution vs depth of HCal
Fig. 8 – Transverse spread of neutral hadron showers
3. Calibrations
Calibrations were performed for each of four detector configurations: (W absorber, .08 lambda/layer + SS absorber, .118 lambda/layer) x (plastic, gas). Mean responses from isolated detector simulations on each HCal configuration plus isolated ECal simulations were used. Because of the non-linear responses, the calibration uses linear extrapolations between data points, and an iterative algorithm to combine energy from different detector components. The algorithm estimates the hadron energy adding the detector contributions, then estimates the contribution from each detector as a fraction of the response to the energy estimate. Three iterations were found to be sufficient. Full detector simulations at the Z-pole were then used to provide a detector response -> neutral hadron energy mapping, with particle type and energy distributions from a physics process. Results are shown in fig. 9.
The calibrations could be improved, most notably by correcting for depth of interaction (losses beyond the HCal) and using a neutral hadron energy distribution from a 500 GeV cm physics process for the inversion. The weighted neutral hadron energy distributions in Z-pole events and 500 GeV ZZ events are shown in fig. 10.
Fig. 9 – Effective resolution of neutral hadrons in Zpole events
Fig. 10 – Fraction of neutral hadron energy vs energy in Zpole and 500 GeV ZZ events
4. Perfect pattern recognition
The calibrations were used to analyze full detector simulations with perfect pattern recognition, i.e. all calorimeter hits are correctly associated with the final state particle from which they originate. Energy sums in mono-energetic jets were studied in 2 light quark (uds) events at 91, 200, 500 GeV cm energy. Results are shown in fig. 11. For comparisons, the quantity alpha = (rms90/mean90)*sqrtE is shown, where 90 means the 90% of the events with the smallest rms were used.
The transverse spreads were also studied in these events. A cylinder was defined through the HCal for each neutral hadron. For a given radius of the cylinder, the number of hits from the neutral hadron inside the cylinder divided by the total number of hits in the HCal from the neutral hadron (summed over all neutral hadrons) was used to define an efficiency. Similarly, the number of hits inside the cylinder from charged hadrons over the number of hits inside the cylinder (again summed over all neutral hadrons) defined a purity. The results are shown in fig. 12 and13.
Also studied were full detector simulations of ZZ events at 500 GeV, where one Z->nu nu, and the other to 2 light quarks. Using perfect pattern recognition for both the neutral hadrons and the photons, and requiring 2 jets from the jet finder, both the dijet mass and delta (dijet mass – generated Z mass) are shown in fig. 14 and 15. The direction of both quarks was required to have abs(cos(theta)) < 0.8 to minimize losses down the beampipe. The effective resolution for neutral hadrons in these events is shown in fig. 16. For a significant difference in neutral hadron resolution, little or no difference is seen in the width of the dijet mass distribution.
The same events were analyzed with a different level of cheating. Instead of perfectly associating the hits with the correct particle, first all the hits in the calorimeters were clustered using a weighted density clustering algorithm. (Directed Tree ). The clusters were then associated with the particle contributing the most hits to the cluster. Dijet mass and delta mass are shown in fig. 17and 18.
Fig. 11 – Energy sums in uds events at 91, 200, 500 GeV
Fig. 12 – Efficiency/Purity curves for neutral hadrons using a fixed radius cylinder at 91 GeV
Fig. 13 – Efficiency/Purity curves for neutral hadrons using a fixed radius cylinder at 200,500 GeV
Fig. 14 – Dijet mass distribution using “perfect” pattern recognition
Fig. 15 – Perfect pattern recognition dijet mass – generated Z mass
Fig. 16 – Effective resolution of neutral hadrons in 500 GeV ZZ events
Fig. 17 – Dijet mass cheating on cluster association
Fig. 18 – Cluster association cheating dijet mass – generated Z mass
5. Summary
Simulations of single neutral hadrons in isolated detectors have been studied varying several design parameters, yielding an overall picture of tradeoffs in resolution and shower spread. With a limited set of parameters, the effect of intrinsic HCal resolution on jet energy and dijet mass resolution has been quantified. With both perfect pattern recognition and real clustering, no significant gain in dijet mass resolution is seen with better intrinsic neutral hadron resolution. Attempts to quantify the effect of shower spread on confusion in PFAs have been made, but the algorithms themselves will probably be needed.