Двухфотонный распад псевдоскалярного мезона в релятивистской кварковой модели

В релятивистской кварковой модели, основанной на точечной форме пуанкаре-инвариантной квантовой механики, получено интегральное представление форм-фактора псевдоскалярного P⁰(π⁰,η,η′)-мезона распада P⁰ (qq̅)→γγ с учетом аномальных магнитных моментов u-, d- и s-кварков. В развитом формализме вычислены значения конституентных масс кварков и параметров волновых функций с использованием константы f_P^±  лептонного распада P^±(qQ̅ ) → ℓ^±ν_ℓ±  и константы псевдоскалярной плотности g_P±.  Показано, что учет глюонной компоненты в η/η′-мезонах и использование структурных функций кварков легкого сектора приводит к согласующемуся с современными экспериментальными данными поведению форм-факторов псевдоскалярных π⁰-, η- и η′-мезонов в области малых переданных лептонной паре импульсов.

1. Measurement of the Dalitz decay π0 → e+e–γ at the Mainz Microtron / P. Adlarson [et al.]; (A2 collaboration at MAMI) // Phys. Rev. C. – 2017. – Vol. 95, № 2. – P. 025202. https://doi.org/10.1103/physrevc.95.025202

2. Measurement of the π0 electromagnetic transition form factor slope / C. Lazzeroni [et al.]; (NA62 collaboration) // Phys. Let. B. – 2017. – Vol. 768. – P. 38–45. https://doi.org/10.1016/j.physletb.2017.02.042

3. 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 / P. Aguar-Bartolome [et al.]; (A2 collaboration at MAMI) // Phys. Rev. C. – 2014. – Vol. 89, № 4. – P. 044608. https://doi.org/10.1103/PhysRevC.89.044608

4. Observation of the Dalitz decay η′ → e+e–γ / M. Ablikim [et al.]; (BESIII collaboration) // Phys. Rev. D. – 2015. – Vol. 92, № 1. – P. 012001. https://doi.org/10.1103/physrevd.92.012001

5. Review of Particle Physics / R. L. Walkman [et al.] // Prog. Theor. Exp. Phys. – 2022. – Vol. 2022, № 8. https://doi.org/10.1093/ptep/ptac097

6. Feldman, T. Quark structure of pseudoscalar mesons / T. Feldman // Int. J. Mod. Phys. A. – 2000. – Vol. 15, № 02. – P. 159–207. https://doi.org/10.1142/s0217751x00000082

7. Escribano, R. The η transition form factor from spaceand time-like experimental data / R. Escribano, P. Masjuan, P. Sanchez-Puertas // Eur. Phys. J. C. – 2015. – Vol. 75. – P. 414. https://doi.org/10.1140/epjc/s10052-015-3642-z

8. Radiative decays, nonet symmetry, and SU(3) breaking / M. Benayoun [et al.] // Phys. Rev. D. – 1999. – Vol. 59, № 11. – P. 114027. https://doi.org/10.1103/PhysRevD.59.114027

9. Thomas, C. E. Composition of the pseudoscalar η and η′ mesons / C. E. Thomas // JHEP. – 2007. – Vol. 10. – P. 026. https://doi.org/10.1088/1126-6708/2007/10/026

10. Escribano, R. On the gluon content of the η and η′ mesons / R. Escribano, J. Nadal // JHEP. – 2007. – Vol. 05. – P. 006. https://doi.org/10.1088/1126-6708/2007/05/006

11. Measurement of the pseudoscalar mixing angle and η′ gluonium content with KLOE detector / F. Ambrosino [et al.] // Phys. Lett. B. – 2007. – Vol. 648, № 4. – P. 267–273. https://doi.org/10.1016/j.physletb.2007.03.032

12. Bartelski, J. Radiative decays of mesons and the η–η′–g mixing / J. Bartelski, S. Tatur // Phys. Lett. B. – 1992. – Vol. 289, № 3–4. – P. 429–434. https://doi.org/10.1016/0370-2693(92)91244-4

13. Keister, B. D. Relativistic Hamiltonian dynamics in nuclear and particle physics / B. D. Keister, W. N. Polyzou // Adv. Nucl. Phys. – 1991. – Vol. 20. – P. 225–479.

14. Dirac, P. A. M. Forms of Relativistic Dynamics / P. A. M. Dirac // Rev. Mod. Phys. – 1949. – Vol. 21, № 3. – P. 392–199. https://doi.org/10.1103/revmodphys.21.392

15. Choi, H.-M. Spacelike and timelike form factors for the (π0,η,η′) → γ* transitions in the light-front quark model / H.-M. Choi, H.-Y. Ryu, Ch.-R. Ji // Phys. Rev. D. – 2017. – Vol. 96, № 5. – P. 056008. https://doi.org/10.1103/PhysRevD.96.056008

16. Jaus, W. Relativistic constituent quark model of electroweak properties of light mesons / W. Jaus // Phys. Rev. D. – 1991. – Vol. 44, № 9. – P. 2851–2859. https://doi.org/10.1103/PhysRevD.44.2851

17. Krutov, A. F. Electroweak properties of ρ-meson in the instant form of relativistic quantum mechanics / A. F. Krutov, R. G. Polezhaev, V. E. Troitsky // EPJ Web Conf. – 2017. – Vol. 138. – P. 02007. https://doi.org/10.1051/epjconf/201713802007

18. Krutov, A. F. Magnetic moment of the ρ meson in instant-form relativistic quantum mechanics / A. F. Krutov, R. G. Polezhaev, V. E. Troitsky // Phys. Rev. D. – 2018. – Vol. 97, № 3. – P. 033007. https://doi.org/10.1103/PhysRevD.97.033007

19. Point-form quantum field theory / E. P. Biernat [et al.] // Ann. Phys. – 2008. – Vol. 323, № 6. – P. 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 [Electronic resource] / E. P. Biernat // Arxiv [Preprint]. – 2011. – Mode of access: https://arxiv.org/abs/1110.3180

21. Godfrey, S. Mesons in a relativized quark model with chromodynamics / S. Godfrey, N. Isgur // Phys. Rev. D. – 1985. – Vol. 32, № 1. – P. 189–231. https://doi.org/10.1103/PhysRevD.32.189

22. Celmaster, W. Potential model of meson masses / W. Celmaster, H. Georgi, M. Georgi. // Phys. Rev. D. – 1978. – Vol. 17, № 3. – P. 879–885. https://doi.org/10.1103/PhysRevD.17.879

23. Charge form-factor of π and K mesons / F. Cardarelli [et al.] // Phys. Rev. D. – 1996. – Vol. 53, № 11. – P. 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 / W. Jaus // Phys. Rev. D. – 2003. – Vol. 67, № 9. – P. 094010. https://doi.org/10.1103/PhysRevD.67.094010

25. Petronzio, R. Possible evidence of extended objects inside the proton / R. Petronzio, S. Simula, G. Ricco // Phys. Rev. D. – 2003. – Vol. 67, № 9. – P. 094994. https://doi.org/10.1103/PhysRevD.67.094004

26. Fayazbakhsh, Sh. Anomalous magnetic moment of hot quarks, inverse magnetic catalysis, and reentrance of the chiral symmetry broken phase / Sh. Fayazbakhsh, N. Sadooghi // Phys. Rev. D. – 2014. – Vol. 90, № 10. – P. 105030. https://doi.org/10.1103/PhysRevD.90.105030

27. Mini review of Poincare invariant quantum theory / W. N. Polyzou [et al.] // Few-Body Syst. – 2011. – Vol. 49. – P. 129–147. https://doi.org/10.1007/s00601-010-0149-x

28. Haurysh, V. Yu. ρ-Meson form-factors in point form of Poincaré-invariant quantum mechanics / V. Yu. Haurysh, V. V. Andreev // Few-Body Syst. – 2021. – Vol. 62. – Art. ID 29. https://doi.org/10.1007/s00601-021-01610-7

29. Haurysh, V. Yu. Constituent quark masses in Poincaré-invariant quantum mechanics / V. Yu. Haurysh, V. V. Andreev // J. Phys.: Conf. Ser. – 2017. – Vol. 938. – P. 012030. https://doi.org/10.1088/1742-6596/938/1/012030

30. Haurysh, V. Yu. Radiative decays of light vector mesons in Poincare invariant quantum mechanics / V. Yu. Haurysh, V. V. Andreev // J. Phys.: Conf. Ser. – 2016. – Vol. 678. – P. 012041. https://doi.org/10.1088/1742-6596/678/1/012041

31. Haurysh, V. Yu. Electroweak decays of unflavored mesons in Poincaré covariant quark model / V. Yu. Haurysh, V. V. Andreev // Turk. J. Phys. – 2019. – Vol. 43, № 2. – P. 167–177. https://doi.org/10.3906/fiz-1810-24

32. Haurysh, V. Yu. Poincaré-covariant quark model of electroweak light mesons decays / V. Yu. Haurysh, V. V. Andreev // EPJ Web Conf. – 2019. – Vol. 204. – P. 08006. https://doi.org/10.1051/epjconf/201920408006