Two-photon decay of the pseudoscalar meson in the relativistic quark model
https://doi.org/10.29235/1561-2430-2023-59-4-315-327
Abstract
In the relativistic quark model, based on the point form of Poincaré-invariant quantum mechanics, an integral representation of the form-factor of the pseudoscalar P0(π0,η,η′) meson of P0 (qq̅)→γγ decay is obtained taking into account the anomalous magnetic moments of u-, d- and s-quarks. IIn the developed formalism the values of the constituent quark masses and the parameters of the wave functions are calculated using the lepton decay P±(qQ̅ ) → ℓ±νℓ± constant fP± and the pseudoscalar density constant gP±. It is shown that taking into account the gluonium component in η/η′-mesons and using the structure functions of light sector quarks lead to the behavior of the form factors of pseudoscalar π0-, η-, η′-mesons in the area of a small transferred momentum to the lepton pair, which is consistent with the modern experimental data
About the Authors
V. Y. Haurysh
Sukhoi State Technical University of Gomel
Belarus
Belarus
Vadzim Y. Haurysh – Ph. D. (Physics and Mathematics
48, Oktyabrya Ave., 246746, Gomel, Republic of Belarus
V. V. Andreev
Francisk Skorina Gomel State University
Belarus
Belarus
Viktor V. Andreev – Dr. Sc. (Physics and Mathematics), Professor
98, Sovetskaya Str., 246028, Gomel, Republic of Belarus
References
1. Adlarson P., Afzal F., Aguar-Bartolomé P., Ahmed Z., Akondi C. S., Annand J. R. M., Arends H. J. [et al.]; (A2 collaboration at MAMI). Measurement of the Dalitz decay π0 → e+e–γ at the Mainz Microtron. Physical Review C, 2017, vol. 95, no. 2, pp. 025202. https://doi.org/10.1103/physrevc.95.025202
2. Lazzeroni C., Lurkin N., Romano A., Blazek T., Koval M., Ceccucci A., Danielsson H. [et al.]; (NA62 collaboration). Measurement of the π0 electromagnetic transition form factor slope. Physical Lettres B, 2017, vol. 768, pp. 025202. https://doi.org/10.1016/j.physletb.2017.02.042
3. Aguar-Bartolomé P. J. R., Annand M., Arends H. J., Bantawa K., Beck R., Bekrenev V., Berghäuser H. [et al.]; (A2 collaboration at MAMI). New determination of the η transition form factor in the Dalitz decay η → e+e–γ with the Crystal Ball/TAPS detectors at the Mainz Microtron. Physical Review C, 2014, vol. 89, no. 4, pp. 044608. https://doi.org/10.1103/PhysRevC.89.044608
4. Ablikim M., Achasov M. N., Ai X. C., Albayrak O., Albrecht M., Ambrose D. J., Amoroso A. [et al.]; (BESIII collaboration). Observation of the Dalitz decay η′ → e+e–γ. Physical Review D, 2015, vol. 92, no. 1, pp. 012001. https://doi.org/10.1103/physrevd.92.012001
5. Workman R. L., Burkert V. D., Crede V., Klempt E., Thoma U., Tiator L. [et al.]. Review of Particle Physics. Progress of Theoretical and Experimental Physics, 2022, vol. 2022, no. 8. https://doi.org/10.1093/ptep/ptac097
6. Feldman T. Quark structure of pseudoscalar mesons. International Journal of Modern Physics A, 2000, vol. 15, no. 02, pp. 159–207. https://doi.org/10.1142/s0217751x00000082
7. Escribano R., Masjuan P., Sanchez-Puertas P. The η transition form factor from spaceand time-like experimental data. The European Physical Journal C, 2015, vol. 75, pp. 414. https://doi.org/10.1140/epjc/s10052-015-3642-z
8. Benayoun M., DelBuono L., Eidelman S., Ivanchenko, V. N., O’Connell, H. B. Radiative decays, nonet symmetry, and SU(3) breaking. Physical Review D, 1999, vol. 59, no. 11, pp. 114027. https://doi.org/10.1103/PhysRevD.59.114027
9. Thomas C. E. Composition of the pseudoscalar η and η′ mesons. Journal of High Energy Physics, 2007, vol. 10, pp. 026. https://doi.org/10.1088/1126-6708/2007/10/026
10. Escribano R., Nadal J. On the gluon content of the η and η′ mesons. Journal of High Energy Physics, 2007, vol. 05, pp. 006. https://doi.org/10.1088/1126-6708/2007/05/006
11. Ambrosino F., Antonelli A., Antonelli M., Bacci C., Beltrame P., Bencivenni G., Bertolucci S. [et al.]. Measurement of the pseudoscalar mixing angle and η′ gluonium content with KLOE detector. Physical Letters B, 2007, vol. 648, no. 4, pp. 267–273. https://doi.org/10.1016/j.physletb.2007.03.032
12. Bartelski J., Tatur S. Radiative decays of mesons and the η–η′–g mixing. Physical Lettres B, 1992, vol. 289, no. 3–4, pp. 429–434. https://doi.org/10.1016/0370-2693(92)91244-4
13. Keister B. D., Polyzou W. N. Relativistic Hamiltonian dynamics in nuclear and particle physics. Advanced Nuclear Physics, 1991, vol. 20, pp. 225–479.
14. Dirac P. A. M. Forms of Relativistic Dynamics. Reviews of Modern Physics, 1949, vol. 21, no. 3, pp. 392–399. https://doi.org/10.1103/revmodphys.21.392
15. Choi H.-M., Ryu H.-Y., Ch.-R. Ji. Spacelike and timelike form factors for the (π0,η,η′) → γ* transitions in the lightfront quark model. Physical Review D, 2017, vol. 96, no. 5, pp. 056008. https://doi.org/10.1103/PhysRevD.96.056008
16. Jaus W. Relativistic constituent-quark model of electroweak properties of light mesons. Physical Review D, 1991, vol. 44, no. 9, pp. 2851–2859. https://doi.org/10.1103/PhysRevD.44.2851
17. Krutov A. F., Polezhaev R. G., Troitsky V. E. Electroweak properties of ρ-meson in the instant form of relativistic quantum mechanics. EPJ Web Conference, 2017, vol. 138, pp. 02007. https://doi.org/10.1051/epjconf/201713802007
18. Krutov A. F., Polezhaev R. G., Troitsky V. E. Magnetic moment of the ρ meson in instant-form relativistic quantum mechanics. Physical Review D, 2018, vol. 97, no. 3, pp. 033007. https://doi.org/10.1103/PhysRevD.97.033007
19. Biernat E. P., Klink W. H., Schweiger W., Zelzer S. Point-form quantum field theory. Annals of Physics, 2008, vol. 323, no. 6, pp. 1361–1383. https://doi.org/10.1016/j.aop.2007.09.004
20. Biernat E. P. Electromagnetic properties of few-body systems within a point-form approach. Arxiv [Preprint], 2011. Available at: https://arxiv.org/abs/1110.3180. https://doi.org/10.48550/arXiv.1110.3180
21. Godfrey S., Isgur N. Mesons in a relativized quark model with chromodynamics. Physical Review D, 1985, vol. 32, no. 1, pp. 189–231. https://doi.org/10.1103/PhysRevD.32.189
22. Celmaster W., Georgi H., Georgi. M. Potential model of meson masses. Physical Review D, 1978, vol. 17, no. 3, pp. 879–885. https://doi.org/10.1103/PhysRevD.17.879
23. Cardarelli F., Grach I. L., Narodetsky I. M., Pace E., Salme G., Simula S. Charge form-factor of π and K mesons mesons. Physical Review D, 1996, vol. 53, no. 1, pp. 6682–6685. https://doi.org/10.1103/PhysRevD.53.6682
24. Jaus W. Consistent treatment of spin-1 mesons in the light-front quark model. Physical Review D, 2003, vol. 67, no. 9, pp. 094010. https://doi.org/10.1103/PhysRevD.67.094010
25. Petronzio R., Simula S., Ricco G. Possible evidence of extended objects inside the proton. Physical Review D, 2003, vol. 67, no. 9, pp. 094994. https://doi.org/10.1103/PhysRevD.67.094004
26. Fayazbakhsh Sh., Sadooghi N. Anomalous magnetic moment of hot quarks, inverse magnetic catalysis, and reentrance of the chiral symmetry broken phase. Physical Review D, 2003, vol. 90, no. 10, pp. 105030. https://doi.org/10.1103/ PhysRevD.90.105030
27. Polyzou W. N., Elster C., Glöckle W. [et al.]. Mini review of Poincaré invariant quantum theory. Few-Body Systems, 2011, vol. 49, pp. 129–147. https://doi.org/10.1007/s00601-010-0149-x
28. Haurysh V. Yu., Andreev V. V. ρ-Meson form-factors in point form of Poincaré-invariant quantum mechanics. FewBody Systems. 2021, vol. 62, art. ID 29. https://doi.org/10.1007/s00601-021-01610-7
29. Haurysh V. Yu., Andreev V. V. Constituent quark masses in Poincaré-invariant quantum mechanics. Journal of Physics: Conference Series, 2017, vol. 938, pp. 012030. https://doi.org/10.1088/1742-6596/938/1/012030
30. Haurysh V. Yu., Andreev V. V. Radiative decays of light vector mesons in Poincare invariant quantum mechanics. Journal of Physics: Conference Series, 2016, vol. 678, pp. 012041. https://doi.org/10.1088/1742-6596/678/1/012041
31. Haurysh V. Yu., Andreev V. V. Electroweak decays of unflavored mesons in Poincaré covariant quark model. Turkish Journal of Physics, 2019, vol. 43, no. 2, pp. 167–177. https://doi.org/10.3906/fiz-1810-24
32. Haurysh V. Yu., Andreev V. V. Poincaré-covariant quark model of electroweak light mesons decays. EPJ Web of Conferences, 2019, vol. 204, pp. 08006. https://doi.org/10.1051/epjconf/201920408006
Review
Views: 154
Email this article 