Hybrid Electromagnetic Calorimeter Module: Enhanced Performance through Integration of Silicon Pixel Layer into Scintillator Design

Jia-Le Fei¹,†, Ao Yuan¹,†, Chang-Heng Huang¹,†, Liu-Pan An²,∗, and Ji-Ke Wang¹,‡

¹The Institute for Advanced Studies, Wuhan University, Wuhan 430072, China
²School of Physics, State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing 100871, China

†These authors contributed equally to this work
∗Corresponding author, E-mail: anlp@pku.edu.cn
‡Corresponding author, E-mail: jike.wang@cern.ch

Abstract: This study constructs a hybrid module with a multi-material collaborative detection architecture by integrating silicon pixel layers into a longitudinally segmented scintillating fiber sampling calorimeter module and optimizes the placement of the silicon layers. The module utilizes the preshower characteristics of the front-end scintillator units to ensure sufficient energy deposition in the silicon pixel layers, thereby maintaining high-precision detection capability. A dedicated simulation framework combining Geant4 modeling for the scintillator section and a parameterized approach for the silicon pixel layer is employed for module verification and performance studies. The hybrid module demonstrates overall performance enhancement, achieving maximum improvements of 56% for position resolution and 26% for time resolution. These advancements lead to a significant increase in physics sensitivity, especially for channels with low-energy photons—for instance, a 16% boost in signal significance for D⁰ from the B⁻ → D⁰(→ D⁰γ)π⁻ decay.

Keywords: Electromagnetic calorimeters, Detector modeling and simulation, Silicon Pixel Layer

Introduction

Current research in particle physics, supported by a growing number of accelerators worldwide, is advancing along two main directions: the energy frontier and the luminosity frontier. Among these, high-luminosity collider experiments are gradually emerging as the central focus of research, owing to their potential to provide unprecedented precision in exploring fundamental physics. However, such experiments present significant technical challenges to detector systems due to extreme particle flux densities [1]. For instance, the upcoming High-Luminosity Large Hadron Collider (HL-LHC) will increase the instantaneous luminosity by a factor of five compared to present LHC operation, creating an experimental environment with extremely high occupancy and background rates [2]. Similar challenges are expected at Belle II at KEK, which targets an integrated luminosity of 50 ab⁻¹ [3], and in proposals such as the Future Circular Collider (FCC-ee) [4]. These projects impose stringent requirements on calorimeter modules in terms of granularity, time resolution, and radiation hardness.

As a critical component of particle detection systems, electromagnetic calorimeters (ECAL) specialize in measuring photons and electrons while enabling indirect reconstruction of neutral mesons like π⁰ through secondary decay chains. There are two principal ECAL architectures: total absorption and sampling calorimeters. In high-luminosity collider experiments, sampling calorimeters dominate due to their small Molière radius, which ensures good energy resolution and effective π⁰-γ separation, typically employing high-Z metals (e.g., lead and tungsten) as absorbers [5, 6]. Sampling calorimeters typically adopt a sandwich architecture with alternating stacks of absorber and active layers. This design allows the absorber to induce particle showers while the active medium samples the deposited energy, achieving a balance between performance and cost. When scintillating crystals are employed as the active layer, this configuration is specifically termed the Shashlik structure, as it utilizes longitudinally embedded optical fibers to channel scintillation photons to the readout electronics.

Collider experiments in high-luminosity environments are imposing stringent new performance criteria on calorimeter modules, specifically requiring enhanced radiation resistance, more compact design with smaller Molière radius, and greater flexibility in readout cell dimensions. Conventional Shashlik sampling structures struggle to meet these new experimental requirements in the core region adjacent to the beam pipe. Consequently, novel sampling structures are being adopted. As illustrated in [FIGURE:1], the proposed design integrates scintillating fibers into perforated absorber plates, allowing the fibers to serve dual functions as both active sensing elements and optical transmission channels. This configuration achieves concurrent optimization of three critical parameters: (1) increased absorber mass fraction for Molière radius (R_M) and radiation length (X₀) reduction; (2) diminished light scattering and attenuation; and (3) enhanced radiation resistance through the geometric advantages of fiber-shaped scintillators. Owing to the application of scintillating fiber technology, this geometric configuration is formally designated as "SpaCal" (Spaghetti Calorimeter) [7–14]. SpaCal technology has already been adopted in several test-beam campaigns and detector upgrades, including prototypes for the LHCb ECAL Upgrade II [15] and the forward calorimeter of the STAR experiment [19]. These practical examples demonstrate its feasibility, yet they also reveal intrinsic limitations in terms of spatial granularity and uniformity. In particular, the achievable detector cell size is constrained by photon number fluctuations during light transport and by the physical dimensions of photoconversion devices such as photomultiplier tubes or SiPM arrays.

To overcome these limitations and achieve even finer spatial granularity, alternative technologies are being explored. Silicon-based semiconductor detectors exhibit fast response time and low carrier fluctuation, offering better response linearity and precise timing measurement. Meanwhile, the direct charge collection mechanism, on-chip readout technology, and mature semiconductor fabrication processes enable silicon-based detectors to achieve smaller unit sizes in both transverse and longitudinal dimensions while maintaining excellent performance. However, if used to cover sufficient radiation length, their fabrication costs remain significantly higher compared to scintillator-based systems.

Notably, silicon pixel and strip detectors have already proven their advantages in large-scale collider experiments. The CMS High Granularity Calorimeter (HGCAL) [16] employs silicon sensors in its endcap region to achieve unprecedented spatial resolution, while the ALICE Inner Tracking System (ITS) [17] demonstrates the scalability of pixel technology in harsh environments. ATLAS has also developed the High-Granularity Timing Detector (HGTD) [18] to cope with pile-up by providing precise time information. These examples illustrate the potential of silicon technology but also highlight its prohibitive cost when considered as a standalone absorber system.

By integrating a multi-material collaborative detection architecture, the respective advantageous detection characteristics of different materials can be effectively combined to enhance overall module performance. This study proposes a hybrid electromagnetic calorimeter module design that combines SpaCal-type scintillator units with silicon pixel detectors in an integrated architecture. The design strategically leverages silicon's inherent advantages in fast timing response and fine spatial granularity while maintaining scintillator-based energy measurement capabilities. A simulation framework integrating Monte Carlo methods with parametrization techniques is established for the hybrid module, and comprehensive validation is conducted across a single-photon bench and multiple physics decay channels, demonstrating baseline performance.

II. Design of Hybrid Module

Early-generation ECAL designs primarily captured transverse shower profiles and energy deposition while lacking sufficient granularity to resolve detailed longitudinal shower development [20–22]. Precise reconstruction of longitudinal shower characteristics plays a critical role in particle identification and time measurement accuracy, necessitating longitudinal multi-layer sampling structures in calorimeters. Consequently, longitudinal layered sampling technology has become the mainstream solution, as adopted in CMS's HGCAL endcap calorimeter, ALICE's FoCal detector, and LHCb's upgraded PicoCal [23–27].

Through longitudinal segmentation and dual-end readout design, the SpaCal module achieves additional granularity along the longitudinal direction. The segmentation interface precisely provides the necessary space for installation of silicon pixel layers. The combination of absorber and active materials in the SpaCal module significantly impacts its performance. This study introduces silicon pixel layers into the SpaCal module, with particular emphasis on analyzing their effects on SpaCal modules with different material systems. Two representative combinations are selected as research subjects: SpaCal modules constructed with W-GAGG and Pb-Polystyrene (absorber-active material) configurations. Compared to the Pb-Polystyrene configuration, the W-GAGG configuration exhibits a smaller Molière radius [8, 9].

As conceptualized in [FIGURE:2], the silicon pixel region (located at position 2) comprises two pixel layers (red) at the SpaCal segmentation boundary, sharing a unified copper cooling layer (yellow). Substrate PCBs manufactured from FR-4 material flank both sides of the pixel layers (green). Optical reflective films (cyan) are also used adjacent to the SpaCal zones (zones 1 and 3) to optimize light collection efficiency. In the following text, we refer to this hybrid module as the SpaCal-Silicon module.

The design philosophy of this hybrid architecture is based on the principle of material complementarity. While scintillating fibers embedded in absorber plates provide a cost-effective solution for large-volume energy measurement with good light yield, silicon pixel layers contribute fine granularity, low electronic noise, and precise timing. By embedding silicon layers exactly at the shower development stages where the density of minimum ionizing particles (MIP) is highest, the calorimeter gains access to detailed spatial and temporal shower information without sacrificing the total radiation length required for energy containment. This "division of labor" between materials allows the module to combine the strengths of both technologies while minimizing their individual drawbacks.

[FIGURE:3] illustrates the development of electromagnetic showers in SpaCal modules. The performance of silicon pixel layers depends on the density of minimum ionizing particles, which is governed by the longitudinal development stage of electromagnetic showers. Meanwhile, the transverse size of the shower is also closely related to the longitudinal development stage. Consequently, their longitudinal placement must be balanced between two considerations and is inherently related to the position where shower maximum (X_max) occurs: (1) electron density increases with proximity to shower maximum (higher particle flux near X_max), and (2) shower splitting capability enhances with distance from X_max.

To optimize the silicon layer configuration, this study dynamically adjusts its longitudinal positioning by changing the thickness of the front-end SpaCal units. As demonstrated in [FIGURE:4], the diagram systematically reveals the quantitative correlation between longitudinal position and the time/position resolution of the silicon layer. The results show that time and position resolution achieve optimal performance within approximately 5–8 X₀ radiation lengths. Therefore, positioning the silicon pixel layers within the 5–8 X₀ range is identified as the optimal configuration (marked by red dashed lines in [FIGURE:3]).

Based on the two SpaCal module configurations (W-GAGG and Pb-Polystyrene), we construct two types of SpaCal-Silicon hybrid modules. The 5 mm pixel pitch selection achieves smaller cell size than the Molière radius of the module while maintaining manageable readout channel counts. The key module parameters are summarized in [TABLE:1].

III. Simulation

During calorimeter module development, simulation plays a crucial role in validating design feasibility, optimizing performance, and reducing both cost and technical risk. The simulation of the SpaCal-Silicon module consists of two parts: the SpaCal module and the silicon pixel layer. For the SpaCal module, a simulation framework [28] developed by the LHCb ECAL Upgrade group based on Geant4 [29] is employed to model particle interactions, scintillation light generation, and light transport within the fiber-embedded absorber plates. Additional software development is required for the silicon pixel layer, which involves simulating complex charge collection and signal formation processes.

Accurate hardware-level simulation relies heavily on real experimental data to ensure models reflect actual detector behavior. Research on silicon detectors [30] and development of experimental apparatuses such as HGCAL [25] and FoCal [26] provide valuable references for benchmarking simulation frameworks. Silicon pixel detectors operate through the drift of ionized electron-hole pairs under an applied bias voltage. However, directly simulating charge carrier drift and signal formation is highly complex, as it involves material properties like carrier mobility and conductivity, doping types and methods, bias voltage, and structural design of the semiconductor unit. This paper designs a simplified simulation model based on MIP counts. The simulation workflow is shown in [FIGURE:5], and this section details the modeling approach for the silicon pixel layer.

Energy deposition is simulated using Geant4, requiring the recording of two key parameters from the active layer of each 5 × 5 mm² readout cell: deposited energy within the active volume and the ideal timestamp of the readout unit. The implementation follows this formalism:

$$E_{dep} = \sum_{(x_i,y_i,z_i)\in\Omega} e_i$$

$$t_{tru} = \frac{\sum_{(x_i,y_i,z_i)\in\Omega} e_i \cdot t_i}{\sum_{(x_i,y_i,z_i)\in\Omega} e_i}$$

Here, $r_i$ denotes the coordinates of a Geant4 step [29] (where $r$ can be $x$, $y$, or $z$), $\Omega$ represents the spatial extent of the silicon pixel unit's active layer, $e_i$ is the energy of the step, $E_{dep}$ the total deposited energy, and $t$ the ideal timestamp. The number of MIPs traversing the readout unit is then calculated based on $E_{dep}$. The energy deposited by each MIP in silicon follows a Landau distribution. Therefore, we use the most probable value of the Landau distribution as the deposited energy per MIP to estimate the MIP count from total deposited energy. This first requires determining the energy deposited by a single MIP traversing the silicon pixel unit. While high-energy electrons can be considered MIPs, they generate showers producing numerous secondary particles in material, complicating measurement of individual MIP energy deposition. [FIGURE:6] shows the energy deposition of MIPs in silicon pixel units.

A. Signal and timestamp generation

As shown in [FIGURE:5], after obtaining the number of MIPs passing through each readout unit, we must calculate the corresponding output voltage values and simulate the operational process of the analog-to-digital converter (ADC) to complete analog-to-digital conversion. Finally, noise in the timing information is quantified based on the ADC output values. Therefore, it is necessary to determine the conversion relationship between MIP count and output voltage, and between ADC values and time noise. Additionally, simulation parameters of the ADC—particularly sampling depth, reference voltage, and voltage noise—need to be determined. This paper makes the following configurations and assumptions regarding readout signal and timestamp generation:

• The output voltage ($V_{out}$) has a linear relationship with the number of MIPs and the thickness of the silicon layer's active region. According to Equation 2, the output voltage can be calculated based on MIP count: $V_{out} = P_1 \times N_{MIP}$, where $P_1$ is a constant parameter and $N_{MIP}$ is the number of MIPs.
• The timing integration process of the ADC signal is ignored, and we only simulate the digitization of the output analog voltage to obtain the ADC value ($ADC_{out}$). This process can be expressed by: $ADC_{out} = \mathcal{N}(\frac{V_{out}}{V_{ref}} \times 2^{N_b}, \sigma_V^2)$, where $\mathcal{N}([0], [1])$ represents Gaussian sampling with mean [0] and variance [1], $V_{ref}$ is the ADC reference voltage, $\sigma_V$ is the reference voltage noise, and $N_b$ is the ADC sampling depth.
• The noise of time information correlates with the ADC value [31], defined by: $\sigma_t = \frac{A}{ADC_{out}} \oplus C$, where $A$ and $C$ are noise-related parameters, $\oplus$ denotes sum in quadrature, and the readout timestamp is calculated by: $t_{out} = \mathcal{N}(t_{tru}, \sigma_t^2)$, where $t_{tru}$ is the true timestamp obtained using Equation 1.

The parameter $A$ in Equation 4 has a linear relationship with silicon layer thickness. Based on Refs. [30–35], for a 5 × 5 mm² silicon pixel cell with 0.5 mm thickness under 600 V bias voltage, the parameters are listed in [TABLE:2]. This paper assumes the silicon pixel layer is adequately cooled; therefore, thermal noise affecting output signal strength is not considered. Additionally, shot noise and other noises caused by material defects are also not addressed.

B. Calibration of the silicon pixel cell

Calibration of readout units aims to establish the relationship between readout signal magnitude and deposited energy within the unit. In the newly integrated silicon pixel units (including silicon pixel readout layer, PCB substrate, and cooling layer), most energy deposits occur in the cooling layer rather than the thin silicon layers. We therefore combine signals from both silicon pixel layers as the total signal, with energy deposited in silicon pixel units serving as the total energy. As expected, the linear dependence of output signal on deposited energy is explicitly illustrated in [FIGURE:7]. All silicon pixel units across layers are calibrated based on this relationship.

IV. Performance

The primary objective of integrating silicon pixel layers is to enhance both longitudinal and transverse granularity in electromagnetic calorimeter modules. Insertion of silicon pixel layers inevitably diverts a portion of energy originally deposited in SpaCal modules, thereby affecting downstream SpaCal readout unit performance. Simultaneously, optimizing silicon pixel layer placement requires reducing upstream SpaCal readout unit thickness, which also impacts their performance. The fundamental requirement for silicon layer integration is to improve granularity while minimizing degradation of the original module's resolution.

Following the layered reconstruction framework in Ref. [36], this section compares resolution performance between SpaCal-Silicon modules and standard SpaCal modules. The parameters of standard SpaCal modules are listed in [TABLE:3]. In comparative tests, using the PicoCal in LHCb Upgrade II [27, 37] as a concrete example, SpaCal-Silicon modules are installed in the PicoCal layout and completely replace baseline SpaCal modules (i.e., substituting W-GAGG modules with W-GAGG-Si hybrid modules). Throughout this analysis, "W-GAGG" and "Pb-Polystyrene" specifically denote standard SpaCal modules.

A. Energy resolution

For physics applications, preserving energy resolution is crucial because it directly impacts invariant mass reconstruction in channels such as π⁰ → γγ or η → γγ. The hybrid design ensures that while spatial and temporal resolutions are improved, the essential calorimetric role of precise energy measurement is not compromised. Although energy resolution degrades due to inclusion of inactive material (primarily cooling layers) and shortened upstream SpaCal, the addition of new active elements provides complementary information. Under these countervailing effects, the SpaCal-Silicon module achieves comparable energy resolution to the baseline. [FIGURE:8] compares energy resolution between two SpaCal-Silicon module configurations and baseline modules, demonstrating that the SpaCal-Silicon design meets preliminary resolution requirements.

B. Position resolution

Silicon pixel layers provide superior granularity compared to baseline SpaCal modules, and granularity is strongly correlated with position resolution. We therefore expect improved position resolution in SpaCal-Silicon modules versus baseline configurations. [FIGURE:9] compares position resolution between two SpaCal-Silicon module variants and baseline modules. As anticipated, integration of silicon pixel layers significantly enhances module position resolution. The improvement becomes increasingly pronounced at higher photon energies, where electromagnetic showers are more compact and better contained. Under these conditions, the fine segmentation of silicon pixels significantly reduces uncertainty in reconstructing the shower barycenter. This effect is particularly valuable for distinguishing nearby photon clusters originating from decays such as π⁰ → γγ. Such improvement directly enhances discrimination between π⁰ and isolated photons, thereby strengthening background rejection in analyses where multiple photon showers overlap spatially.

C. Time information and resolution

High-precision timing information is a critical parameter in high-luminosity collider physics experiments. Timing resolution is not only a detector performance metric but also a physics enabler. In HL-LHC environments, where pile-up leads to multiple simultaneous collisions per bunch crossing, the ability to assign precise timestamps to photons is essential for rejecting out-of-time background and improving vertex association. This section analyzes timing characteristics of silicon pixel layers and their impact on overall module time resolution. Positioning silicon layers near shower maximum ensures sufficient MIP flux at these locations, enabling high signal-to-noise ratio signals for improved timing precision. [FIGURE:10] shows time resolution of silicon layers in different module configurations.

In the low-energy region, silicon layers in the W-GAGG-Si module exhibit superior time resolution compared to those in the Pb-Polystyrene-Si module. The W-GAGG-Si module features a smaller Molière radius (dominated by SpaCal parts), resulting in higher MIP density per cell area compared to the Pb-Polystyrene-Si module. This increased MIP flux through individual silicon pixels ultimately enhances timing resolution.

Based on previous analysis, a key consideration for silicon pixel layers with cell sizes smaller than the Molière radius is whether to combine timing information from multiple readout cells (Cell2D). This approach does not rely solely on the seed time of the cluster and has the potential to further improve silicon pixel layer time resolution. In electromagnetic showers, transverse shower development occurs perpendicular to the particle momentum direction. Consequently, the first-hit cell (Cell2D), which typically has maximum energy, serves as the seed (Seed2D). As formalized in Equation 6, a basic model assigns the timestamp of neighboring Cell2D units as the Seed2D timestamp plus a drift time determined by the distance between Cell2D and Seed2D: $t_{Cell} = t_{Seed} + t_{Drift}$. The extrapolated Cell2D timestamp at Seed2D is calculated via: $t'{cell} = \frac{\sum \cdot t'}^{N_{Cell}} E_{cell_i{cell_i}}{\sum$.}^{N_{Cell}} E_{cell_i}}$. The merged time information is then noted as $t'_{cell

[FIGURE:10] compares time resolution between merged multi-Cell2D timing and exclusive Seed2D timing. It also presents combined time resolution from all silicon layers, where the blue curve represents the SpaCal-Silicon module with two silicon layers. [FIGURE:11] presents the overall time resolution (merged timing information from both SpaCal and silicon layers) of two SpaCal-Silicon modules compared to the baseline module.

D. Performance of physical channels

The primary purpose of electromagnetic calorimeters is to analyze final-state particles such as electrons, photons, π⁰ mesons, and their associated physical phenomena. It is crucial to emphasize that energy resolution metrics only indirectly reflect detector performance in specific physical analyses. Systematic investigations of concrete physical processes therefore provide more direct insights into operational efficacy. The simulation environment incorporates high-luminosity pp collision backgrounds with instantaneous luminosity of 1.5 × 10³⁴ cm⁻²s⁻¹.

1. Decay channels with high-energy photons in the final state

The B⁰ → K⁰γ decay channel is conventionally used in the LHCb experiment to validate calorimeter performance in high-energy photon detection. This channel features high-energy single photon emission, background interference, reconstructible K⁰ → K⁺π⁻ trajectories/vertices, and excellent Monte Carlo data consistency, making it ideal for benchmarking. [FIGURE:12] demonstrates signal significance of B⁰ → K⁰γ within the SpaCal region, comparing SpaCal-Silicon module configuration with standard SpaCal module. K⁰ candidates are reconstructed from K⁺π⁻ combinations with 10% energy smearing applied to each track. Results indicate that while energy resolution dominates performance in this high-energy regime, the fine granularity of silicon pixels still contributes marginally by improving vertex pointing of the photon. This effect helps reduce systematic biases in invariant mass reconstruction, which can otherwise smear resonance peaks. Importantly, the performance gain, though modest, demonstrates that the hybrid design introduces no detrimental effect even in regimes where silicon is not the primary performance driver.

The boxed data in [FIGURE:12] show selection criteria, significance value, and efficiency when signal significance is maximized, where Δt is defined as: $\Delta t = |t'\gamma - t^{K⁰}|$. In this formula, $t_{Gen}^{K⁰}$ represents the time of the K⁰ production vertex, and $t'_\gamma$ represents the photon time extrapolated to the K⁰ production vertex using time-of-flight information. The SpaCal-Silicon module demonstrates slightly improved performance compared to standard SpaCal in hard-photon decay channels, as performance in these channels is predominantly governed by energy resolution. [FIGURE:13] shows the K*⁰γ invariant mass distribution corresponding to maximum signal significance in [FIGURE:12].

2. Decay channels with low-energy photons in the final state

The B⁻ → D⁰π⁻ → (D⁰, γ)π⁻ decay is a key channel for probing the Standard Model and exploring new physics. As shown in [FIGURE:14], the photon from this channel has very low transverse momentum. Therefore, the precise time and position information provided by the SpaCal-Silicon module is expected to contribute to signal selection and enhance signal significance for this decay. D⁰ candidates are reconstructed by combining K⁻π⁺ signal pairs with 10% Gaussian energy smearing applied to the K⁻/π⁺ mesons. [FIGURE:15] illustrates the relationship between signal significance and signal efficiency for the process B⁻ → D⁰(→ D⁰γ)π⁻ with D*⁰ → D⁰γ. Selection criteria follow definitions provided in the previous subsection.

Owing to superior time and position resolution, the SpaCal-Silicon module demonstrates enhanced performance in soft-photon decay channels. [FIGURE:16] shows the D⁰γ invariant mass distribution corresponding to maximum signal significance. This result highlights the physics relevance of the hybrid approach: while high-energy channels benefit only modestly, the low-energy photon regime critical for rare B decays and CP violation studies gains disproportionately from improved granularity and timing. Such improvements could directly translate into new physics discovery potential at both HL-LHC and next-generation e⁺e⁻ colliders.

V. Conclusion

This paper proposes a hybrid design integrating silicon pixel layers into SpaCal modules to meet performance enhancement needs for electromagnetic calorimeters in high-luminosity collider experiments. Feasibility and performance benefits are verified through systematic simulation studies. The hybrid SpaCal-silicon module design embeds silicon pixel layers into longitudinally segmented SpaCal modules, with optimized silicon layer positioning. Experimental validation shows best performance is achieved by placing silicon pixel layers at approximately 5–8 X₀ (radiation lengths). Simultaneously, the silicon pixel layer geometry is configured as 5×5 mm² to achieve higher granularity (smaller cell size) than the scintillator portion. Additionally, the two silicon layers share a single cooling layer, ensuring efficient energy deposition in the active material by minimizing material insertion.

To support simulation studies of this hybrid module, a simplified silicon pixel layer simulation model was developed based on minimum ionizing particle counts to establish a parametric relationship between energy deposition and voltage signals. A time noise model and drift time correction method are also proposed to enable accurate simulation of silicon pixel layer signal characteristics.

In terms of performance enhancement, the hybrid module significantly optimizes position resolution while maintaining energy resolution comparable to standard SpaCal modules. For example, in the Pb-Polystyrene-Si configuration, position resolution improves by more than 56%, while time resolution improves by approximately 14% and 26% in the W-GAGG-Si and Pb-Polystyrene-Si systems, respectively, demonstrating superior characteristics compared to standard SpaCal modules.

In decay channel benchmarking, the hybrid module significantly improves signal significance (S/√(S+B)) for D⁰ from the low-energy photon channel B⁻ → D⁰(→ D⁰γ)π⁻ by about 16%, while also showing modest performance improvement in hard-photon channels compared to standard SpaCal modules.

In summary, the hybrid calorimeter module design with embedded silicon pixel layers not only retains the advantages of traditional scintillator modules but also significantly improves multidimensional detection capability, providing a new technical solution for high-precision measurements in high-luminosity collider experiments and offering key reference for future hybrid calorimeter development.

VI. Acknowledgments

We express gratitude to colleagues from the LHCb Upgrade R&D group at CERN, Peking University, and Tsinghua University for helpful suggestions. In particular, Marco Pizzichemi, Loris Martinazzoli, and Philipp Gerhard Roloff developed the simulation software, while Zhenwei Yang, Liming Zhang, and Zehua Xu provided insightful references that greatly inspired this study. Additionally, we thank the developers and maintainers of the Gauss software in LHCb, which we used for event generation. Numerical calculations were performed using a supercomputing system at the Supercomputing Center of Wuhan University. This work is partially supported by the National Natural Science Foundation of China under Grant No. W2443007.

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