Charge sharing and alignment performance of bent ALPIDEs measured with low-energy protons

Technical Summary: Charge Sharing and Alignment Performance of Bent ALPIDEs Measured with Low-Energy Protons

Problem Statement
The ALICE experiment at the LHC is planning an upgrade to its Inner Tracking System (ITS3), which involves replacing the innermost detection layers with bent, wafer-scale CMOS Monolithic Active Pixel Sensors (MAPS). While previous studies have confirmed that thin silicon sensors can be bent to radii as small as 18 mm without mechanical failure, there was a lack of experimental data regarding the sensor's performance under high-energy loss conditions typical of low-momentum particle tracking. Specifically, it was unknown whether bending induces changes in charge sharing and cluster formation properties, which are critical for Particle Identification (PID). Furthermore, aligning cylindrical detector geometries with limited track sampling (few layers) to the multiple-scattering limit without external reference detectors remained an untested challenge.

Methodology
To address these questions, the authors conducted a fixed-target experiment at the Cyclotron Center Bronowice using proton beams of 80 MeV, 120 MeV, and 200 MeV.

• Detector Setup: The setup utilized five bent ALPIDE chips (the sensor type used in ALICE ITS2) mounted on 3D-printed cylindrical supports with bending radii of 18 mm, 24 mm, and 30 mm. The sensors were arranged in a two-arm telescope geometry pointing toward a target.
• Target: The target consisted of an array of eleven polypropylene fibers arranged in a hexagonal grid to facilitate the reconstruction of elastic proton-proton ($p,p$) scattering events.
• Trigger and Readout: Events were triggered by two CsI(Tl) scintillators positioned behind the tracker arms to ensure the selection of elastic scattering events. Data was acquired using the EUDAQ2 framework and processed with the Corryvreckan analysis framework.
• Analysis Strategy:
  • Charge Sharing: Cluster sizes were analyzed across different beam energies and bending radii. The raw cluster sizes were normalized by the cosine of the track impact angle to account for path length variations. A phenomenological model assuming a 2D Gaussian charge diffusion profile was fitted to the data to describe cluster size scaling with energy deposition.
  • Alignment: Due to the loss of one sensor arm (leaving only two sensors on the left arm), standard track-residual minimization was impossible. Instead, the authors developed custom alignment algorithms:
    1. Pre-alignment: Utilized the kinematic constraint of elastic $p,p$ scattering (coplanarity of outgoing tracks with the beam axis) to correct azimuthal degrees of freedom.
    2. Minimization: A bisection-based algorithm minimized the median Distance of Closest Approach (DCA) between the two reconstructed proton tracks to optimize translational and rotational degrees of freedom.
  • Validation: Experimental results were compared against Geant4 simulations that included multiple scattering effects and realistic sensor resolution smearing.

Key Contributions

• High-Energy Loss Characterization: This study provides the first experimental investigation of bent MAPS sensors under high-energy loss conditions (low-energy protons), extending beyond previous Minimum Ionizing Particle (MIP) studies.
• Alignment Strategy for Sparse Cylindrical Geometries: The paper demonstrates a viable method for aligning cylindrical detector arrays with limited layer counts (2–3 layers per arm) without external reference detectors, relying solely on kinematic constraints and DCA minimization.
• Phenomenological Modeling: A parameterized model for cluster size scaling with energy deposition in bent sensors was developed and validated against data.

Results

• Charge Sharing and Clustering: No statistically significant dependence of cluster size or charge sharing on the bending radius (18 mm, 24 mm, 30 mm) was observed. The cluster size distributions for high-energy loss events followed the same trends as those observed for MIPs in flat configurations. The threshold dependence of cluster size remained consistent across all radii.
• Alignment Performance: The custom alignment procedure successfully reduced the systematic misalignment. For the 200 MeV beam data, the reconstructed vertex DCA width was measured at $(80.5 \pm 4.6)$ $\mu$m.
• Comparison with Simulation: The measured DCA width agreed with the Geant4 simulation of the multiple-scattering limit, which predicted $(80.5 \pm 1.6)$ $\mu$m. The difference of 0.04 $\mu$m is well within the combined statistical uncertainty, indicating that the achieved resolution is limited by physics (multiple scattering) rather than residual misalignment or sensor defects.
• Angular Resolution: The measured opening angles of scattered protons matched simulated expectations within 1 mrad, confirming the angular precision of the bent geometry.

Significance
The paper concludes that bending ALPIDE sensors to radii relevant for the ITS3 upgrade (down to 18 mm) does not degrade charge sharing or clustering performance, even under high-energy deposition conditions. Furthermore, the successful alignment of the bent detector to the multiple-scattering limit demonstrates that cylindrical MAPS geometries can achieve high-precision vertexing without external reference detectors. These findings support the feasibility of using bent wafer-scale CMOS MAPS sensors for future high-energy and nuclear physics experiments, particularly those requiring low material budgets and high impact parameter resolution, such as the ITS3 upgrade and inverse kinematic heavy-ion experiments like R3B and Samurai.