Feasibility of H Annihilation-Vertex Reconstruction with Modular J-PET: A Simulation-Based Study

The Antihydrogen Experiment: gravity, Interferometry, Spectroscopy at CERN aims to measure the gravitational acceleration of antihydrogen (H) atoms to test the weak equivalence principle for antimatter systems. In the proposed approach, a pulsed H beam, produced via charge exchange between Rydberg positronium and antiprotons, traverses a moiré deflectometer comprising two equally spaced gratings followed by a position-sensitive detector. As the beam traverses the moiré setup, H may annihilate on the gratings or nearby structures, producing high-energy pions, or continue towards the position-sensitive detector. For a high-accuracy gravity measurement, precise knowledge of the beam profile and annihilation points is essential. We present results from a feasibility study of vertex reconstruction using modular J-PET detectors spanning the full axial length of the moiré setup. The generated pions, being minimum-ionising particles, follow straight paths. The adapted method is based on the consecutive registration of each pion, defining individual tracks in a pair of modules placed 10 cm apart. The hit positions are used to reconstruct the track direction, which is then projected back to estimate the spatial coordinates of the H annihilation vertex. For this feasibility study, we developed a customised Geant4-based simulation package and an analysis algorithm that implements a track-and-extrapolate algorithm to image the annihilation vertices.