The $\mathsf{\mu }$PPET [mu($\mathsf{\mu }$)on Probe with J-PET] project aims to investigate the “Muon Puzzle” seen in cosmic ray air showers. This puzzle arises from the observation of a significantly larger number of muons on Earth’s surface than that predicted by the current theoretical models. The investigated hypothesis is based on recently observed asymmetries in the parameters for the strong interaction cross-section and trajectory of an outgoing particle due to projectile–target polarization. The measurements require detailed information about muons at the ground level, including their track and charge distributions. To achieve this, the two PET scanners developed at the Jagiellonian University in Krakow (Poland), the J-PET detectors, will be employed, taking advantage of their well-known resolution and convenient location for detecting muons that reach long depths in the atmosphere. One station will be used as a muon tracker, while the second will reconstruct the core of the air shower. In parallel, the existing hadronic interaction models will be modified and fine-tuned based on the experimental results. In this work, we present the conceptualization and preliminary designs of $\mathsf{\mu }$PPET.

The main aim of this research is to test the charge–parity discrete symmetry in the ortho-positronium (o-Ps) atom decay using the modular Jagiellonian positron emission tomography (J-PET) detector. The J-PET is distinguished by its ability to determine the polarization plane of photons emitted during positronium annihilation. The J-PET detector can investigate discrete symmetry by examining the non-zero expectation values of the symmetry-odd operators constructed from the momentum and direction of polarization plane of gamma (γ) quanta coming from o-Ps annihilation. In positronium decay, the photon–photon interactions in the final state due to vacuum polarization may mimic a charge–parity symmetry violation at the level of 10-9, according to the Standard Model prediction. Currently, with the help of the 192-strip J-PET detector, the experimental limits on charge–parity symmetry violation in o-Ps decay are set at a precision value of 0.0005 ± 0.0007. Using the modular J-PET detector, we aim to improve this value by at least an order of magnitude. This article focuses on developing analysis criteria towards improving the sensitivity level for charge–parity-discrete symmetry studies in o-Ps decay using the modular J-PET detector.