Simulation study of Dual-Readout Calorimeter for a forward calorimeter at the Electron-Ion Collider

. The Electron-Ion Collider (EIC) is a future particle accelerator to be built at the Brookhaven


Introduction
The primary purpose of the Electron-Ion Collider (EIC) is to study the partonic structure of protons and nuclei more accurately [1].It is required to be equipped high-quality detectors to achieve precise measurements.At forward rapidity where hadrons are going, electromagnetic (EM) and hadronic calorimeters will be located to measure hadrons and jets, and the required hadronic energy resolution is 50%/ √ E ± 10%.Dual-Readout Calorimeter (DRC), proposed as the main calorimeter in the IDEA detector at the Future Circular Collider [2], can also be utilized for experiments at the EIC.The DRC is a sampling calorimeter consisting of absorber material and two types of optical fiber; Cherenkov and Scintillation fibers.The left panel of Fig. 1 shows a cross-sectional view of the DRC tower, and fibers of yellow and blue color are two different types of fibers.The different responses of EM particles and hadrons in two fiber types can provide information to determine the EM fraction of each hadron shower.The right panel of Fig. 1 shows a correlation of calibrated energy in Cherenkov and Scintillation fibers, data points from hadrons are located around the straight line.The corrected energy is calculated by applying a rotation matrix with the angle θ, and a better energy resolution can be achieved.See the recent review for more details on the DRC [3].For fiber-sampling calorimeters like the dual-readout calorimeter, the conventional 60 approach to get longitudinal information about the shower is taking the time of a peak or 61 arrival.Setting the impact point and the moment of collision as x = 0, t = 0, the observed 62 time can be expressed as a sum of a high-energy particle's time of flight (ToF) plus the 63 propagation time of an optical photon within the fiber with the group velocity v. Also, 64 SiPM's position l can be described as a vector sum of the flight path of the high-energy 65 particle and the distance that the optical photon propagated.

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Performance study with GEANT4 simulation
A simulation framework for the DRC with GEANT4 has been developed for experiments with future e + e − colliders.We utilize the framework and use towers located at the endcap region for the simulation study.We change the tower length from 2.5 m to 1.25 m for the EIC design.Copper is used as an absorber material for the reference design, and performance with other materials like iron and tungsten is also studied.Electrons, charged pions, and jets with various energies are used to evaluate the detector performance.

Single EM particle
Energy calibration is performed separately for Cherenkov and Scintillation fibers using simulations with 20 GeV electrons.The results of the calibration are shown on the left panel of Fig. 2. The middle panel of Fig. 2 shows the energy resolution for electrons as a function of energy, and the resolution of the two channels is similar.We use a linear combination of two channels for the final energy measurement, and the energy resolution is 11%/ √ E + 0.6%.In terms of energy linearity shown on the right panel of Fig. 2, the ratio between measured energy and beam energy is within 1% in a wide range of beam energy.

Single hadron
For the performance of hadrons, we simulate positively charged pion (π + ) with various energies.Figure 3 shows the distribution of measured energy in Cherenkov and Scintillation channel and dual-readout corrected energy, and the left (right) panel shows the simulation results using 1.25 m (2.5 m) DRC towers of copper absorber.There are tails on the left-hand side in distributions with shorter towers, which indicates a longitudinal shower leakage when using 1.25 m towers for the EIC design.Note that a small fraction of events passing through the entire detector without initiating a hadron shower is removed.To account for the non-Gaussian shape due to shower leakage, we use a standard deviation of the histogram for the energy resolution instead of the Gaussian width obtained from fit to the distribution.Figure 4 shows the energy resolution and linearity obtained from π + simulations with the EIC design.In the left plot, the energy resolution is compared with the default length results.The energy resolution with 1.25 m towers worsens as the beam energy increases because of shower leakage.The magenta line represents the requirement of the EIC detector, and the energy resolution with 1.25 m towers still satisfies the requirement below 70 GeV.Note that a single hadron of 70 GeV is expected to be rarely produced at the EIC.Regarding the energy linearity shown on the right side, we can obtain more accurate hadron energy with the dual-readout correction method than with two single channel.

Jet
We also study the performance of jet energy measurement with the EIC design of the DRC.The PYTHIA8 is utilized to generate hadrons from a single quark fragmentation, and the anti-k T algorithm with a resolution parameter R = 0.8 is used to reconstruct jets.Not to use jets fragmented out of the endcap region, we select jets at least 80% of the initial quark energy is within the R = 0.8 range.Jets with Cherenkov and Scintillation channels are reconstructed separately, and a dual-readout correction is applied later.Figure 5 shows simulation results of jets with the DRC.The energy resolution with the EIC design is worse than the default design due to hadron shower leakage.The resolution becomes smaller as the jet energy increases, unlike in the single hadron case.This is because the energy of hadrons from jet fragmentation is not large enough to suffer from the shower leakage significantly.The magenta line represents the requirement of the EIC detector, and the energy resolution with 1.25 m towers satisfies the requirement.Regarding the energy linearity shown in the right plot, more accurate jet energy can be obtained with the dual-readout correction method.

Summary and Outlook
We have performed a simulation study of the Dual-Readout Calorimeter for experiments at the EIC.Based on the simulation framework developed for future collider experiments, a modified design with a shorter length (1.25 m) is used for the simulation of single electrons, hadrons, and jets.Although there is a longitudinal leakage of hadron showers with the EIC design, the obtained energy resolution of hadrons and jets satisfies the EIC requirement.For the plan, we will implement detailed features of the DRC simulation to the EIC simulation framework, such as optical photon propagation, light attenuation, and readout electronics.

Figure 1 .
Web of Conferences 276, 05006 (2023) https://doi.org/10.1051/epjconf/202327605006SQM 2022 (a) The dual-readout calorimeter with Čerenkov fibers lit with blue light and scintillation fibers lit with yellow light.b The projective geometry of the dual-readout calorimeter, where only lit fibers on the rear side have a full length that reaches the front of the tower with the copper absorber.In the dual-readout calorimeter, fibers' optical properties determine the timing charac-38 teristics.Therefore detailed descriptions of optical properties are essential.The Čerenkov 39 fiber implemented in the simulation is Mitsubishi Eska SK-40 clear fiber with a Polymethyl-40 methacrylate (PMMA) core and fluorinated polymer cladding.The scintillation fiber is 41 Kuraray SCSF-78, consisting of PMMA cladding and Polystyrene based scintillating core.42 We reflected the refractive index [5][6][7], attenuation length [8][9], emission light yield, 43 spectra, and decay time in the detector descriptions [10].44 The above detector descriptions in DD4hep are interfaced to GEANT4 [11][12][13] 45 Monte-Carlo (MC) simulation.

Figure 2
shows optical physics within the fibers simulated 46 with GEANT4, where we can observe the unique behaviors of Čerenkov and scintillation 47 light emission, as well as the propagation of optical photons via total internal reflection.48 Generated optical photons are detected at the rear end of the tower, and the collected 49 number of photons, time of arrival, and wavelength information are plugged-in into the 50 silicon photomultiplier (SiPM) emulation software library SimSiPM [14].It describes the re-51 sponse of SiPMs driven by parameters obtained from either lab measurements or datasheets 52 from manufacturers.In the simulation, the datasheet of Hamamatsu S14160-1310PS SiPM 53 [15] was used to describe SiPM's behaviors, including dark count rate, afterpulse, cross-talk, 54 and pulse shape as a function of time.Between the rear end of scintillation fibers and 55 SiPMs, Kodak Wratten number 9 yellow filters are inserted to prevent the saturation of 56 SiPMs from high light yields of the scintillation channel.

Figure 1 .
Figure 1.Left: Cross-sectional view of the DRC tower, Right: Correlation of energy in two channels for photons, electrons, and hadrons.

Figure 4 .
Figure 4. Left: Energy resolution for π + with different lengths of towers compared with the EIC requirement.Right: Energy linearity for π + with 1.25 m DRC towers.

Figure 5 .
Figure 5. Left: Energy resolution for jets with different lengths of towers compared with the EIC requirement.Right: Energy linearity for jets with 1.25 m DRC towers.