Testing CPT symmetry in ortho-positronium decays with positronium annihilation tomography

The paper investigates CPT invariance in a purely leptonic bound system—the positronium atom—by testing for CPT-odd angular correlations in the three-photon decay of ortho-positronium (o-Ps→3γ). While CPT has withstood extensive tests in hadronic systems (e.g., neutral mesons) and atomic comparisons (hydrogen vs antihydrogen), charged lepton systems are mostly governed by QED, which is stringently verified. However, recent discrepancies in positronium fine-structure measurements and the potential for Lorentz/CPT tests within the Standard-Model Extension motivate new, model-independent searches. The authors target the CPT-odd operator O_CPT = S·(k1×k2)/|k1×k2| = cos θ, correlating the o-Ps spin with the orientation of the decay plane. Prior constraints reached sensitivity ~3×10−3; the goal here is to improve sensitivity by leveraging a PET-based apparatus that allows per-event spin estimation without external magnetic fields or polarized sources.

The study situates itself among several lines of CPT tests: (i) stringent tests in hadronic systems (neutral kaons and B mesons) and antihydrogen spectroscopy, which find no violation; (ii) neutrino oscillation experiments testing CPT by comparing neutrino/antineutrino parameters, currently consistent with CPT conservation; and (iii) positronium spectroscopy proposals within the SME framework for Lorentz/CPT tests. Prior positronium searches for CP/CPT violation targeted angular correlations in o-Ps→3γ using either polarized positron beams or external magnetic fields to polarize positronium, often limited to single-plane detection and requiring reconfiguration, which introduced systematic uncertainties. The most recent CPT search using the cos θ operator exploited the intrinsic positron polarization from β+ decay and constrained emission geometry with a hemispherical aerogel, enabling a first asymmetry search over cos θ but with effective polarization limited by geometry (factor ~0.686). Radiative corrections that could mimic CPT violation in o-Ps→3γ are expected only at ~10−9, leaving ample sensitivity headroom for geometric and instrumental improvements.

Experimental apparatus: The J-PET detector consists of three concentric sparse layers of 50 cm plastic scintillator strips arranged axially in a cylindrical geometry. Each strip is read out on both ends by vacuum-tube photomultipliers. Interaction times and longitudinal positions are reconstructed via timing of light propagation to both ends, with ~250 ps time resolution. System synchronization uses self-calibration based on time differences from 2γ annihilations and uncorrelated prompt photons from a 22Na source. Positronium production: A vacuum chamber (radius R = 12 cm) coated with porous silica/gypsum material (bulk density ~0.32 g/cm3; SBET = 252 m2/g; total pore volume 0.58 cm3/g; average pore width 6.6 nm) allows o-Ps formation on the walls. Vacuum ~10−3 Pa reduces positron scattering. Smearing due to positronium escape from pores is small relative to ~8 cm annihilation point resolution. Data taking: A 10 MBq 22Na source was run for 26 continuous days (August 2018), yielding 7.3×10^6 three-photon event candidates identified in a 2.5 ns coincidence window. Signal identification and reconstruction: Photon energy deposition is estimated via time-over-threshold (TOT) from leading/trailing edge timestamps at four thresholds per PMT. Candidates for o-Ps annihilation photons are selected with TOT in 15–55 ns to reject noise and minimize 2γ events near the Compton edge. Initial 3γ candidates are clusters of three photon interactions within 2.5 ns. Annihilation vertex and momenta: With plastic scintillators registering Compton interactions, the three photon momenta are reconstructed from the interaction points and the annihilation vertex reconstructed by trilateration using interaction times. High angular resolution (~1°) and exclusive 3γ registration allow inference of relative angles and thus photon energies from kinematic constraints. Event-by-event o-Ps spin axis is estimated from the reconstructed 3γ vertex and inferred positron flight direction; no restriction on e+ emission direction beyond the chamber boundaries is applied. Background rejection:

• Secondary Compton scatterings: For each pair of interactions (i,j), compute δij = ||ri−rj|| − c|ti−tj|. Secondary scattering pairs yield δ≈0. Events with δmin < 15 cm are rejected. This purifies the θ1+θ2 versus θ2−θ1 distribution, moving backgrounds away from the o-Ps→3γ-allowed region (θ1+θ2 > 180° with small difference).
• 2γ annihilations plus prompt 1275 keV de-excitation photon: Identify events where two interactions are ~180° apart in azimuth and where a hypothetical line-of-response (LOR) annihilation point from any pair lies close to the β+ source (minimal d_LOR small). Retain events in the signal-dominated region with large d_LOR and θXY+θ′XY > 180°. Spin analyzing power and selection for O_CPT: To ensure precise spin reconstruction, interaction times were varied within uncertainties to align the reconstructed annihilation radius p = √(X^2+Y^2) with the chamber radius R = 12 cm; events with a χ2-like measure ≤ 0.5 (2 dof) were kept. About 2 million events passed selection. Analyzing power (effective polarization P): Components are (i) longitudinal positron polarization from 22Na, Pe+B ≈ 0.67; (ii) transfer to positronium, factor 2/3; (iii) ~8% polarization loss during thermalization; (iv) ~9% geometrical uncertainty of estimated e+ emission direction. Combined effective polarization P = 37.4%. Systematic checks: A CPT-even, CP-odd operator O_γ = (S·k1)(S·(k1×k2)) was evaluated to probe detector geometry-induced asymmetries; mean (1.3 ± 1.4)×10−4 indicates negligible geometry bias at 10−4 level. Cosmic-ray-only runs indicate contamination ≤ 3.9×10−5 of the final sample. Cut variations within multiple experimental resolutions showed only the upper TOT cut impacted ⟨O_CPT⟩ significantly; a 1 ns variation changed ⟨O_CPT⟩ by 1.26×10−4, included in systematics.

• First tomographic reconstruction and imaging of o-Ps→3γ annihilations in an extended medium, enabling per-event spin-axis estimation without magnetic fields.
• Dataset: 26 days, 10 MBq 22Na source, 7.3×10^6 3γ candidates; ~2×10^6 high-purity events after selections (χ2≤0.5, δmin≥15 cm, d_LOR/azimuthal cuts).
• Effective polarization (analyzing power) P = 37.4% (from Pe+B≈0.67, 2/3 transfer, ~8% loss, ~9% geometrical uncertainty).
• Measured expectation value over full domain: ⟨O_CPT⟩ = 0.00025 ± 0.00036, consistent with zero (statistical uncertainty 0.00033 dominates).
• CPT-violation parameter: C_CPT = ⟨O_CPT⟩/P = 0.00067 ± 0.00095.
• Sensitivity at the 10−4 level, improving the previous best constraint by more than a factor of three.
• Systematic controls: O_γ mean (1.3 ± 1.4)×10−4 (no significant detector asymmetry); cosmic rays ≤3.9×10−5 of final sample; main analysis-cut sensitivity from TOT upper bound (±1.26×10−4 per 1 ns change).

By reconstructing the annihilation vertex and photon directions for o-Ps→3γ in a PET-like detector, the authors infer the o-Ps spin axis statistically from positron emission directions without external fields. This enables measurement of the CPT-odd correlation O_CPT = cos θ across its full spectrum rather than limited asymmetries. The null result at 10−4 precision indicates no observable CPT-violating angular correlation in o-Ps decays and significantly tightens constraints compared to prior experiments. The methodology minimizes geometric biases by using a correlation defined by event geometry and by simultaneously covering many decay planes. Systematic checks confirm negligible detector-geometry-induced asymmetries and small cosmic-ray contamination. The approach opens broader applicability: imaging positronium properties in large volumes and enabling future tests of other symmetry-odd operators previously infeasible due to geometric limitations.

The work introduces a tomographic reconstruction approach for o-Ps→3γ decays that allows per-event spin-axis estimation without magnetic fields, providing a robust platform for discrete symmetry tests in positronium. The measured ⟨O_CPT⟩ is consistent with zero at 10−4 precision, improving previous limits by over a factor of three. Future upgrades—adding a dense digital readout layer to increase single-photon registration up to fourfold (overall o-Ps→3γ detection efficiency by ~64×) and a spherical annihilation chamber to enhance o-Ps formation (~1.5×) and reduce geometry-induced asymmetries—are expected to push CPT sensitivity to the 10−5 level. The methodology also paves the way for exploring additional operators (e.g., S·k1) and for novel positronium-based imaging modalities.

The measurement is primarily statistics-limited, with the uncertainty on ⟨O_CPT⟩ dominated by counting statistics. Effective polarization is reduced by thermalization losses (~8%) and geometrical uncertainty (~9%) in positron emission direction, lowering analyzing power. Event selection sensitivity to the TOT upper bound introduces a systematic component (1.26×10−4 per 1 ns variation). The annihilation vertex resolution (~8 cm) limits spin-axis precision, though it remains sufficient relative to pore-induced smearing. Without an external magnetic field, only vector polarization is available, restricting sensitivity to some CP-odd operators that require tensor polarization. Residual backgrounds from secondary Compton scattering and 2γ plus prompt photons are mitigated but require careful cuts; cosmic-ray contamination is negligible but nonzero.