# Sensitivity of Discrete Symmetry Tests in the Positronium System with the J-PET Detector

## Abstract

**:**

## 1. Introduction

## 2. The J-PET Detector

## 3. Methods of Searching for Discrete Symmetry Violations with Ortho-Positronium in J-PET

#### 3.1. Estimation of Positronium Spin

^{68}Ge or

^{22}Na are allowed to form positronia only in a limited volume which defines a range of allowed ${e}^{+}$ spin quantization axes. As the positron polarization statistically translates to the formed ortho-positronium in 2/3 of cases, this allows for obtaining an estimate of the o-Ps spin direction with a finite uncertainty determined by the ${\beta}^{+}$ emission average energy and the applied geometry of positronium formation medium. In the original implementation of this idea, the latter uncertainty accounted for a reduction of statistical polarization by 0.686, in addition to the average polarization of P ≈ 0.4 inherent to the method of producing ortho-positronium [7]. On the other hand, it evaded the need for a acceptance-limiting hardware setup which allowed for the first measurement of a true distribution of an angular correlation in o-Ps annihilation, although limited in resolution by the coarse detector granularity.

^{22}Na is installed in the center of the chamber, while its walls are coated with 3 mm of R60G porous silica, allowing practically all positrons reaching the chamber walls to thermalize and interact within this layer [47]. The chamber walls are made of 3 mm polycarbonate so as to minimize absorption and scattering of annihilation photons. The chamber mounted inside the J-PET detector is presented in the left panel of Figure 1. The right panel of the figure illustrates a future enhancement of the chamber geometry, i.e., replacement of the cylinder with a spherical vacuum chamber (with R = 10 cm), which allows for a more efficient utilization of positrons from the ${\beta}^{+}$ source for positronium formation, increases o-Ps$\to 3\gamma $ registration efficiency for extreme values of certain correlations and reduces spurious asymmetries as demonstrated in the next sections.

#### 3.2. The Correlation between o-Ps Spin and Annihilation Plane

^{22}Na source in the setup described in Section 3.1. The efficiency is presented for two geometries of the annihilation chamber: cylindrical (presently used) and spherical (in preparation). In each case, three values of the energy deposition threshold for a single annihilation photon were considered: 40 keV, 100 keV and 140 keV. Results of the simulation show that lowering this photon registration threshold is vital for the total efficiency and each increase of the threshold by about 50 keV results in a reduction of the $3\gamma $ registration efficiency by an order of magnitude.

^{22}Na source. It is visible that the $\overrightarrow{S}\xb7(\overrightarrow{{k}_{1}}\times \overrightarrow{{k}_{2}})$ angular correlation is not sensitive to the geometry of the positronium annihilation region. Not only are the asymmetries detected using the cylindrical and spherical chambers in good agreement, but also the $A({\mathcal{O}}_{CPT})$ distribution obtained in absence of simulated CPT violation does not reveal signs of a false asymmetry in any of the cases.

#### 3.3. The Correlation between o-Ps Spin and Most Energetic Photon

## 4. Perspectives for J-PET Sensitivity to the Cpt Violation Effects

^{22}Na source amounts to about 0.4. Assuming that the MC-simulated events required for the ${C}_{CPT}$ extraction procedure described in Section 3.2 can be generated in ample statistics, the sensitivity to the CPT violation parameter is approximately described by the statistical uncertainty on the number N of recorded o-Ps$\to 3\gamma $ events and the analyzing power S as $\sigma ({C}_{CPT})\approx {N}^{-\frac{1}{2}}/S$. J-PET sets as its goal to reach the unprecedented sensitivity at the level beyond ${10}^{-3}$, which requires $N>6.3\times {10}^{6}$ of event candidates. With the expected rate estimated above, this goal can be achieved with about three months of measurement.

## 5. Conclusions

## Funding

## Conflicts of Interest

## References

- Wu, C.S.; Ambler, E.; Hayward, R.W.; Hoppes, D.D.; Hudson, R.P. Experimental Test of Parity Conservation in Beta Decay. Phys. Rev.
**1957**, 105, 1413–1415. [Google Scholar] [CrossRef] - Christenson, J.H.; Cronin, J.W.; Fitch, V.L.; Turlay, R. Evidence for the 2π Decay of the ${K}_{0}^{2}$ Meson. Phys. Rev. Lett.
**1964**, 13, 138–140. [Google Scholar] [CrossRef] [Green Version] - Moskal, P.; Alfs, D.; Bednarski, T.; Białas, P.; Czerwiński, E.; Curceanu, C.; Gajos, A.; Głowacz, B.; Gorgol, M.; Hiesmayr, B.; et al. Potential of the J-PET detector for studies of discrete symmetries in decays of positronium atom—A purely leptonic system. Acta Phys. Polon.
**2016**, 47, 509. [Google Scholar] [CrossRef] [Green Version] - Mills, A.P.; Berko, S. Search for C Nonconservation in Electron-Positron Annihilation. Phys. Rev. Lett.
**1967**, 18, 420–425. [Google Scholar] [CrossRef] - Bernreuther, W.; Low, U.; Ma, J.P.; Nachtmann, O. How to Test CP, T and CPT Invariance in the Three Photon Decay of Polarized s Wave Triplet Positronium. Z. Phys.
**1988**, 41, 143–158. [Google Scholar] [CrossRef] - Yamazaki, T.; Namba, T.; Asai, S.; Kobayashi, T. Search for CP Violation in Positronium Decay. Phys. Rev. Lett.
**2010**, 104, 083401. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Vetter, P.A.; Freedman, S.J. Search for CPT-Odd Decays of Positronium. Phys. Rev. Lett.
**2003**, 91, 263401. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Vetter, P.A.; Freedman, S.J. Branching-ratio measurements of multiphoton decays of positronium. Phys. Rev. A
**2002**, 66, 052505. [Google Scholar] [CrossRef] [Green Version] - Matsumoto, T.; Chiba, M.; Hamatsu, R.; Hirose, T.; Yang, J.; Yu, J. Measurement of five-photon decay in orthopositronium. Phys. Rev. A
**1996**, 54, 1947–1951. [Google Scholar] [CrossRef] [PubMed] - Von Busch, H.; Thirolf, P.; Ender, C.; Habs, D.; Köck, F.; Schulze, T.; Schwalm, D. Measurement of the decay e
^{+}e^{-}→4γ at rest. Phys. Lett. B**1994**, 325, 300–307. [Google Scholar] [CrossRef] - Branco, G.C.; González Felipe, R.; Joaquim, F.R. Leptonic CP violation. Rev. Mod. Phys.
**2012**, 84, 515–565. [Google Scholar] [CrossRef] [Green Version] - Inami, K.; Abe, K.; Abe, K.; Abe, R.; Abe, T.; Adachi, I.; Aihara, H.; Akatsu, M.; Asano, Y.; Aso, T.; et al. Search for the electric dipole moment of the τ lepton. Phys. Lett. B
**2003**, 551, 16–26. [Google Scholar] [CrossRef] [Green Version] - Abe, K.; Akutsu, R.; Ali, A.; Amey, J.; Andreopoulos, C.; Anthony, L.; Antonova, M.; Aoki, S.; Ariga, A.; Ashida, Y.; et al. Search for CP Violation in Neutrino and Antineutrino Oscillations by the T2K Experiment with 2.2 × 10
^{21}Protons on Target. Phys. Rev. Lett.**2018**, 121, 171802. [Google Scholar] [CrossRef] [Green Version] - Acero, M.A.; Adamson, P.; Alion, L.A.T.; Allakhverdian, V.; Antoshkin, N.A.A.; Arrieta-Diaz, E.; Back, A.A.A.; Backhouse, C.; Balashov, M.B.N.; Bambah, B.A.; et al. New constraints on oscillation parameters from ν
_{e}appearance and ν_{μ}disappearance in the NOvA experiment. Phys. Rev. D**2018**, 98, 032012. [Google Scholar] [CrossRef] [Green Version] - Abe, K.; Akutsu, R.; Ali, A.; Alt, C.; Andreopoulos, C.; Anthony, L.; Antonova, M.; Aoki, S.; Ariga, A.; Asada, Y.; et al. Constraint on the matter–antimatter symmetry-violating phase in neutrino oscillations. Nature
**2020**, 580, 339–344. [Google Scholar] [CrossRef] [Green Version] - Kostelecký, V.A.; Vargas, A.J. Lorentz and CPT tests with hydrogen, antihydrogen, and related systems. Phys. Rev.
**2015**, 92, 056002. [Google Scholar] [CrossRef] [Green Version] - Vargas, A.J. Overview of the Phenomenology of Lorentz and CPT Violation in Atomic Systems. Symmetry
**2019**, 11, 1433. [Google Scholar] [CrossRef] [Green Version] - Moskal, P.; Moskal, P.; Niedźwiecki, S.; Bednarski, T.; Czerwiński, E.; Kubicz, E.; Moskal, I.; Pawlik-Niedźwieckaa, M.; Sharmaa, N.G.; Silarski, M.; et al. Test of a single module of the J-PET scanner based on plastic scintillators. Nucl. Instrum. Meth.
**2014**, 764, 317–321. [Google Scholar] [CrossRef] [Green Version] - Moskal, P.; Zoń, N.; Bednarski, T.; Białas, P.; Czerwiński, E.; Gajos, A.; Kamińska, D.; Kapłon, Ł.; Kochanowski, A.; Korcyl, G.; et al. A novel method for the line-of-response and time-of-flight reconstruction in TOF-PET detectors based on a library of synchronized model signals. Nucl. Instrum. Meth. A
**2015**, 775, 54–62. [Google Scholar] [CrossRef] [Green Version] - Niedźwiecki, S.; Białas, P.; Curceanu, C.; Czerwiński, E.; Dulski, K.; Gajos, A.; Głowacz, B.; Gorgol, M.; Hiesmayr, B.C.; Jasińska, B.; et al. J-PET: A new technology for the whole-body PET imaging. Acta Phys. Polon.
**2017**, 48, 1567. [Google Scholar] [CrossRef] - Kowalski, P.; Wiślicki, W.; Shopa, R.Y.; Raczyński, L.; Klimaszewski, K.; Curcenau, C.; Czerwiński, E.; Dulski, K.; Gajos, A.; Gorgol, M. Estimating the NEMA characteristics of the J-PET tomograph using the GATE package. Phys. Med. Biol.
**2018**, 63, 165008. [Google Scholar] [CrossRef] [PubMed] - Moskal, P. Towards total-body modular PET for positronium and quantum entanglement imaging. In Proceedings of the 2018 IEEE Nuclear Science Symposium and Medical Imaging Conference Proceedings (NSS/MIC), Sydney, Australia, 10–17 November 2018; pp. 1–4. [Google Scholar]
- Moskal, P.; Stępień, E.Ł. Prospects and clinical perspectives of total-body PET imaging using plastic scintillators. PET Clin.
**2020**, in press. [Google Scholar] - Moskal, P.; Kisielewska, D.; Curceanu, C.; Czerwiński, E.; Dulski, K.; Gajos, A.; Gorgol, M.; Hiesmayr, B.; Jasińska, B.; Kacprzak, K. Feasibility study of the positronium imaging with the J-PET tomograph. Phys. Med. Biol.
**2019**, 64, 055017. [Google Scholar] [CrossRef] [PubMed] - Moskal, P.; Jasińska, B.; Stępień, E.Ł.; Bass, S.D. Positronium in medicine and biology. Nat. Rev. Phys.
**2019**, 1, 527–529. [Google Scholar] [CrossRef] - Moskal, P.; Kisielewska, D.; Bura, Z.; Chhokar, C.; Curceanu, C.; Czerwiński, E.; Dadgar, M.; Dulski, K.; Gajewski, J.; Gajos, A.; et al. Performance assessment of the 2γ positronium imaging with the total-body PET scanners. EJNMMI Phys.
**2020**, 7, 44. [Google Scholar] [CrossRef] [PubMed] - Hiesmayr, B.; Moskal, P. Genuine Multipartite Entanglement in the 3-Photon Decay of Positronium. Sci. Rep.
**2017**, 7, 15349. [Google Scholar] [CrossRef] [Green Version] - Moskal, P.; Krawczyk, N.; Hiesmayr, B.C.; Bała, M.; Curceanu, C.; Czerwiński, E.; Dulski, K.; Gajos, A.; Gorgol, M.; Grande, R.D.; et al. Feasibility studies of the polarization of photons beyond the optical wavelength regime with the J-PET detector. Eur. Phys. J. C
**2018**, 78, 970. [Google Scholar] [CrossRef] - Hiesmayr, B.C.; Moskal, P. Witnessing Entanglement In Compton Scattering Processes Via Mutually Unbiased Bases. Sci. Rep.
**2019**, 9, 8166. [Google Scholar] [CrossRef] - Pałka, M.; Strzempek, P.; Korcyl, G.; Bednarski, T.; Niedźwiecki, S.; Białas, P.; Czerwiński, E.; Dulski, K.; Gajos, A.; Głowacz, B.; et al. Multichannel FPGA based MVT system for high precision time (20 ps RMS) and charge measurement. JINST
**2017**, 12, P08001. [Google Scholar] [CrossRef] - Pałka, M.; Bednarski, T.; Białas, P.; Czerwiński, E.; Kapłon, L.; Kochanowski, A.; Korcyl, G.; Kowal, J.; Kowalski, P.; Kozik, T.; et al. A novel method based solely on FPGA units enabling measurement of time and charge of analog signals in Positron Emission Tomography. Bio-Algorithms Med-Syst.
**2014**, 10, 41–45. [Google Scholar] [CrossRef] [Green Version] - Korcyl, G.; Alfs, D.; Bednarski, T.; Białas, P.; Czerwiński, E.; Dulski, K.; Gajos, A.; Głowacz, B.; Jasińska, B.; Kamińska, D.; et al. Sampling FEE and Trigger-less DAQ for the J-PET Scanner. Acta Phys. Polon.
**2016**, 47, 491. [Google Scholar] [CrossRef] - Korcyl, G.; Białas, P.; Curceanu, C.; Czerwiński, E.; Dulski, K.; Flak, B.; Gajos, A.; Głowacz, B.; Gorgol, M.; Hiesmayr, B.C.; et al. Evaluation of Single-Chip, Real-Time Tomographic Data Processing on FPGA SoC Devices. IEEE Trans. Med. Imaging
**2018**, 37, 2526–2535. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Sharma, S. Time Over Threshold as a measure of energy response of plastic scintillators used in the J-PET detector. EPJ Web Conf.
**2019**, 199, 05014. [Google Scholar] [CrossRef] [Green Version] - Sharma, S.; Chhokar, J.; Curceanu, C.; Czerwinski, E.; Dadgar, M.; Dulski, K.; Gajewski, J.; Gajos, A.; Gorgol, M.; Gupta-Sharma, N.; et al. Estimating relationship between the Time Over Threshold and energy loss by photons in plastic scintillators used in the J-PET scanner. EJNMMI Phys.
**2020**, 7, 39. [Google Scholar] [CrossRef] [PubMed] - Gajos, A.; Curceanu, C.; Czerwiński, E.; Dulski, K.; Gorgol, M.; Gupta-Sharma, N.; Hiesmayr, B.C.; Jasińska, B.; Kacprzak, K.; Kapłon, Ł.; et al. Feasibility Study of the Time Reversal Symmetry Tests in Decay of Metastable Positronium Atoms with the J-PET Detector. Adv. High Energy Phys.
**2018**, 2018, 8271280. [Google Scholar] [CrossRef] [Green Version] - Korcyl, G.; Moskal, P.; Bednarski, T.; Białas, P.; Czerwiński, E.; Kapłon, L.; Kochanowski, A.; Kowal, J.; Kowalski, P.; Kozik, T.; et al. Trigger-less and reconfigurable data acquisition system for positron emission tomography. Bio-Algorithms Med-Syst.
**2014**, 10, 37–40. [Google Scholar] [CrossRef] - Krzemień, W.; Gajos, A.; Gruntowski, A.; Stola, K.; Trybek, D.; Bednarski, T.; Białas, P.; Czerwiński, E.; Kamińska, D.; Kapłon, L.; et al. Analysis framework for the J-PET scanner. Acta Phys. Polon. A
**2015**, 127, 1491–1494. [Google Scholar] [CrossRef] - Krzemień, W.; Alfs, D.; Bialas, P.; Czerwinski, E.; Gajos, A.; Glowacz, B.; Jasinska, B.; Kaminska, D.; Korcyl, G.; Kowalski, P.; et al. Overview of the software architecture and data flow for the J-PET tomography device. Acta Phys. Polon. B
**2016**, 47, 561. [Google Scholar] [CrossRef] - Krzemien, W.; Gajos, A.; Kacprzak, K.; Rakoczy, K.; Korcyl, G. J-PET Framework: Software platform for PET tomography data reconstruction and analysis. SoftwareX
**2020**, 11, 100487. [Google Scholar] [CrossRef] - Moskal, P.; Rundel, O.; Alfs, D.; Bednarski, T.; Białas, P.; Czerwiński, E.; Gajos, A.; Giergiel, K.; Gorgol, M.; Jasińska, B.; et al. Time resolution of the plastic scintillator strips with matrix photomultiplier readout for J-PET tomograph. Phys. Med. Biol.
**2016**, 61, 2025. [Google Scholar] [CrossRef] [Green Version] - Skalsey, M.; Van House, J. First test of CP invariance in the decay of positronium. Phys. Rev. Lett.
**1991**, 67, 1993–1996. [Google Scholar] [CrossRef] [PubMed] - Arbic, B.K.; Hatamian, S.; Skalsey, M.; Van House, J.; Zheng, W. Angular Correlation Test of CPT in Polarized Positronium. Phys. Rev.
**1988**, 37, 3189–3194. [Google Scholar] [CrossRef] [PubMed] - Bernreuther, W.; Low, U.; Nachtmann, O. Possible tests of CP invariance with polarized positronium. Hyperfine Interact.
**1989**, 44, 139–145. [Google Scholar] [CrossRef] - Mohammed, M.; Białas, P.; Curceanu, C.; Czerwiński, E.; Dulski, K.; Gajos, A.; Głowacz, B.; Gorgol, M.; Hiesmayr, B.C.; Jasinska, B.; et al. A method to produce linearly polarized positrons and positronium atoms with the J-PET detector. Acta Phys. Polon.
**2017**, 132, 1486–1489. [Google Scholar] [CrossRef] - Gajos, A.; Kamińska, D.; Czerwiński, E.; Alfs, D.; Bednarski, T.; Białas, P.; Głowacz, B.; Gorgol, M.; Jasińska, B.; Kapłon, L.; et al. Trilateration-based reconstruction of ortho-positronium decays into three photons with the J-PET detector. Nucl. Instrum. Meth.
**2016**, 819, 54–59. [Google Scholar] [CrossRef] [Green Version] - Gajos, A. Studies of Ortho-Positronium Decays into Three Photons with the J-PET Detector. Acta Phys. Polon.
**2020**, 137, 126–129. [Google Scholar] [CrossRef] - Abe, K.; Abt, I.; Ahn, C.J.; Akagi, T.; Allen, N.J.; Ash, W.W.; Aston, D.; Baird, K.G.; Baltay, C.; Band, H.R.; et al. First Measurement of the T-Odd Correlation between the Z
^{0}Spin and the Three-Jet Plane Orientation in Polarized Z^{0}Decays into Three Jets. Phys. Rev. Lett.**1995**, 75, 4173–4177. [Google Scholar] [CrossRef] [Green Version] - Berestetskii, V.B.; Lifshitz, E.M.; Pitaevskii, L.P. Relativistic Quantum Theory, 1st ed.; Pergamon Press: Oxford, UK; New York, NY, USA, 1971. [Google Scholar]
- Kamińska, D.; Gajos, A.; Czerwiński, E.; Alfs, D.; Bednarski, T.; Białas, P.; Curceanu, C.; Dulski, K.; Głowacz, B.; Gupta-Sharma, N.; et al. A feasibility study of ortho-positronium decays measurement with the J-PET scanner based on plastic scintillators. Eur. Phys. J.
**2016**, 76, 1–14. [Google Scholar] [CrossRef] [Green Version] - Raj, J.; Gajos, A.; Curceanu, C.; Czerwiński, E.; Dulski, K.; Gorgol, M.; Gupta-Sharma, N.; Hiesmayr, B.C.; Jasińska, B.; Kacprzak, K.; et al. A feasibility study of the time reversal violation test based on polarization of annihilation photons from the decay of ortho-Positronium with the J-PET detector. Hyperfine Interact.
**2018**, 239, 56. [Google Scholar] [CrossRef] [Green Version] - Raj, J.; Kisielewska, D.; Czerwiński, E. J-PET Monte Carlo Simulations for Time-Reversal Symmetry Test in Ortho-Positronium Decay. Acta Phys. Polon.
**2020**, 137, 137–139. [Google Scholar] [CrossRef]

**Figure 1.**(

**a**): View of the Jagiellonian Positron Emission Tomography (J-PET) detector with a cylindrical vacuum chamber for positronium production and annihilation mounted in its center. (

**b**): Schematic view of two future extensions of the experimental setup: (i) the current three layers of sparsely-arranged scintillator strips (blue) will be complemented by a layer of 24 modules containing 13 densely-packed scintillator strips each (red); (ii) the cylindrical annihilation chamber will be replaced by a spherical one (gray).

**Figure 2.**Distributions of the ${\mathcal{O}}_{CPT}$ operator resulting from toy Monte Carlo simulations of ${10}^{13}$ positron interactions in J-PET with the cylindrical positronium production chamber in case of no CPT violation assumed in the simulation (hatched blue histogram) and extreme violation (hollow red histogram).

**Figure 3.**(

**a**): Total efficiency of registration ortho-positronium (o-Ps)$\to 3\gamma $ events in J-PET as a function of the $\overrightarrow{S}\xb7(\overrightarrow{{k}_{1}}\times \overrightarrow{{k}_{2}})$ angular correlation obtained in a MC simulation. The curves present efficiencies in the case of two different geometries of the positronium production chamber: cylindrical and spherical as well as for three values of energy deposition threshold for single $\gamma $ detection. (

**b**): Asymmetry of the $\overrightarrow{S}\xb7(\overrightarrow{{k}_{1}}\times \overrightarrow{{k}_{2}})$ distribution for the two chamber geometries in cases of no CPT violation and an exaggerated violation at the 10% level assumed in the simulations.

**Figure 4.**(

**a**): Total efficiency of registration o-Ps$\to 3\gamma $ events in J-PET as a function of the $\overrightarrow{S}\xb7\overrightarrow{{k}_{1}}$ angular correlation obtained in a MC simulation. The curves present efficiencies in case of two different geometries of the positronium production chamber: cylindrical and spherical as well as for three values of energy deposition threshold for single $\gamma $ detection. (

**b**): Asymmetry of the $\overrightarrow{S}\xb7\overrightarrow{{k}_{1}}$ distribution for the two chamber geometries in cases of no CPT violation and an exaggerated violation at the 10% level assumed in the simulations.

**Table 1.**Angular correlation operators constructed with observables of ortho-positronium annihilations into three photons: positronium spin $\overrightarrow{S}$ and momenta of the annihilation photons ordered by their magnitude: $|{\overrightarrow{k}}_{1}|>|{\overrightarrow{k}}_{2}|>|{\overrightarrow{k}}_{3}|$. Each of these operators is either even (+) or odd (–) with respect to the basic symmetry transformations and their combinations as marked in the table. While measurement of operators 1 and 2 only requires non-zero vector polarization of ortho-positronium, operator 3 is sensitive to CP violation in the presence of a specific tensor polarization [5,44] produced e.g., by an external magnetic field [42].

No. | Operator | C | P | T | CP | CPT |
---|---|---|---|---|---|---|

1 | $\overrightarrow{S}\xb7\overrightarrow{{k}_{1}}$ | + | – | + | – | – |

2 | $\overrightarrow{S}\xb7(\overrightarrow{{k}_{1}}\times \overrightarrow{{k}_{2}})$ | + | + | – | + | – |

3 | $(\overrightarrow{S}\xb7\overrightarrow{{k}_{1}})(\overrightarrow{S}\xb7(\overrightarrow{{k}_{1}}\times \overrightarrow{{k}_{2}}))$ | + | – | – | – | + |

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Gajos, A.
Sensitivity of Discrete Symmetry Tests in the Positronium System with the J-PET Detector. *Symmetry* **2020**, *12*, 1268.
https://doi.org/10.3390/sym12081268

**AMA Style**

Gajos A.
Sensitivity of Discrete Symmetry Tests in the Positronium System with the J-PET Detector. *Symmetry*. 2020; 12(8):1268.
https://doi.org/10.3390/sym12081268

**Chicago/Turabian Style**

Gajos, Aleksander.
2020. "Sensitivity of Discrete Symmetry Tests in the Positronium System with the J-PET Detector" *Symmetry* 12, no. 8: 1268.
https://doi.org/10.3390/sym12081268