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

Abstract

Charged lepton system symmetry under combined charge, parity, and time-reversal transformation (CPT) remains scarcely tested. Despite stringent quantum-electrodynamic limits, discrepancies in predictions for the electron-positron bound state (positronium atom) motivate further investigation, including fundamental symmetry tests. While CPT noninvariance effects could be manifested in non-vanishing angular correlations between final-state photons and spin of annihilating positronium, measurements were previously limited by knowledge of the latter. Here, we demonstrate tomographic reconstruction techniques applied to three-photon annihilations of ortho-positronium atoms to estimate their spin polarisation without magnetic field or polarised positronium source. We use a plastic-scintillator-based positron-emission-tomography scanner to record ortho-positronium (o-Ps) annihilations with single-event estimation of o-Ps spin and determine the complete spectrum of an angular correlation operator sensitive to CPT-violating effects. We find no violation at the precision level of 10^-4, with an over threefold improvement on the previous measurement.

Fig. 1. Methodology of the measurement of CPT-violation-sensitive angular correlation in three-photon annihilations of ortho-positronium.

a Photograph of the J-PET tomograph with the cylindrical positronium production chamber. Plastic scintillators (black strips) record photons produced in o-Ps → 3γ events (red arrows) and a prompt photon from β⁺ emitter de-excitation (green arrow). b Photograph of the interior of the positronium production chamber and a schematic view of the transverse cross section of the J-PET tomograph. Plastic scintillators (with rectangular cross sections (blue)) form three coaxial rings. Annihilating o-Ps atoms are produced by positrons from a ²²Na β⁺ source in the centre of a cylindrical vacuum chamber (grey), the walls of which are coated with porous silica, where positrons thermalise and form positronia. c Reconstructed spatial locations of the identified o-Ps → 3γ events obtained using three-photon annihilations, allowing us to reproduce a tomographic image of the vacuum chamber. The maximum density distribution is in a ring with a radius of 12 cm, equal to the radius of the positronium production chamber. d For every selected event, the o-Ps spin axis is reconstructed, allowing calculation of the cosine of the angle between the spin (S) and annihilation plane orientation (n = k₁ × k₂), the distribution of which is sensitive to CPT-violating asymmetries. The histogram presents the determined $\cos \theta$ distribution for 1.9 × 10⁶ identified o-Ps → 3γ events.

Fig. 2. Measurement of deposited γ energy with time-over-thresholds (TOT).

a Photomultiplier electric signals in J-PET sampled at four predefined voltage thresholds (ν₁, …, ν₄), yielding four timestamps for the leading ($t_i^{\mathrm{L}}$) and trailing ($t_i^{\mathrm{T}}$) edges of the signal. The total TOT of a signal is calculated as ${\sum }_{i=1}^4\left(t_i^{\mathrm{T}}-t_i^{\mathrm{L}}\right)$. b Distribution of total TOTs from both photomultiplier signals in J-PET detection modules, used as a measure of photon energy deposited in Compton scattering. The hatched red region is used to identify o-Ps annihilation photon candidates, whereas candidates for prompt photons from ²²Ne* de-excitation are found in the green dotted region.

Fig. 3. Schematic presentation of signal (o-Ps → 3γ) and background events in the transverse view of the J-PET detector.

The grey rectangles represent photon detection modules of plastic scintillators (only one layer is shown for readability). The modules in which photons were recorded are marked white. The annihilations take place in the wall of the vacuum chamber (grey band). In a signal event a, all three photons from an ortho-positronium annihilation are recorded and the angles between their momenta, labelled according to ascending magnitude (θ₁ < θ₂ < θ₃), obey θ₁ + θ₂ > 180^∘. The background is dominated by direct e⁺e⁻ → 2γ annihilations, where the third recorded photon comes from secondary Compton scattering in the detector b, resulting in the identification of a spurious primary photon marked with a dashed arrow. Three-photon events may also be caused by two subsequent secondary scatterings in the case where one of the direct annihilation photons is not detected c, and by two-photon annihilations originating in the β⁺ source setup (grey circle) accompanied by a prompt ²²Ne^* de-excitation photon depositing low energy in Compton scattering d.

Fig. 4. Rejection of secondary Compton scatterings.

Distribution of the minimal discrepancy between the travelled path and time of flight among all hypothetical secondary scattered photons considered in a single 3γ event candidate. Events with ${\delta }_{\min }<15$ cm (marked with the red line) are discarded as containing secondary Compton scatterings in the detector modules.

Fig. 5. Effect of secondary Compton scatterings’ rejection.

Relative distribution of the sum and difference of the two smallest angles between photon momenta (see Fig. 3) in the identified 3γ events before (a) and after (b) rejection of the secondary scattered photons. The θ₁ + θ₂ > 180^∘ limit results from momentum conservation in o-Ps → 3γ annihilations. o-Ps annihilation events are expected in the right corner of the populated region, whereas the topmost region is specifically for secondary scattered photon events.

Fig. 6. Separation of ortho-positronium annihilations from direct two-photon events.

Distribution of distance between the β⁺ source location and the closest hypothetical 2γ annihilation point on a line of response between two recorded photon interactions vs. the sum of the two smallest angles between azimuthal coordinates of the recorded γ interaction points. Events located in the signal-specific upper right region of the distribution (marked with dashed black line) are retained for the analysis in order to discriminate background events from 2γ annihilations (see Fig. 3b–d).