vestifmИзвестия Национальной академии наук Беларуси. Серия физико-математических наукProceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series1561-24302524-2415The Republican Unitary Enterprise Publishing House "Belaruskaya Navuka"10.29235/1561-2430-2019-55-3-325-337vestifm-402Research ArticleФИЗИКАPHYSICSРаспады легких мезонов в релятивистской кварковой моделиDecays of light mesons in the relativistic quark modelhttps://orcid.org/0000-0003-0030-4971ГавришВ. Ю.HauryshV. Yu.

Гавриш Вадим Юрьевич – аспирант

пр. Октября, 48, 246746, г. Гомель, Республика Беларусь

Vadzim Y. Haurysh – Postgraduate Student

48, Oktyabrya Ave., 246746, Gomel, Republic of Belarus

mez0n@inbox.ruhttps://orcid.org/0000-0003-3314-7175АндреевВ. В.AndreevV. V.

Андреев Виктор Васильевич – доктор физико-математических наук, профессор

ул. Советская, 98, 246019, г. Гомель, Республика Беларусь

Viktor V. Andreev – Dr. Sc. (Physics and Mathematics), Professor

98, Sovetskaya Str., 246019, Gomel, Republic of Belarus

vik.andreev@gsu.byГомельский государственный технический университет им. П. О. СухогоSukhoi State Technical University of GomelГомельский государственный университет им. Ф. СкориныFrancisk Skorina Gomel State University201904102019553325337Copyright © Гавриш В.Ю., Андреев В.В., 20192019Гавриш В.Ю., Андреев В.В.Haurysh V.Y., Andreev V.V.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://vestifm.belnauka.by/jour/article/view/402

В рамках релятивисткой кварковой модели, основанной на точечной форме пуанкаре-инвариантной квантовой механики, проведена процедура фиксации параметров на основе использования интегральных представлений констант лептонных распадов псевдоскалярных и векторных мезонов, содержащих u-, d- и s-кварки. В результате численных расчетов с применением осцилляторной волновой функции получены базовые параметры модели с использованием константы псевдоскалярной плотности и токовых масс кварков. Анализ показал, что результаты вычислений в рамках полученной модели и экспериментальные данные по лептонным распадам адронов хорошо согласуются друг с другом. Как результат, методика расчета обобщена на случай адронных переходов с испусканием γ-кванта и последующим расчетом интегральных представлений констант радиационных распадов псевдоскалярных и векторных мезонов. Полученные значения аномальных магнитных моментов сопоставлены с барионными данными. В качестве проверки модели авторами исследовано поведение форм-факторов радиационных распадов векторных мезонов с последующим сопоставлением с современными экспериментальными данными в диапазоне q < 0,5 ГэВ, где резонансные эффекты незначительны. В результате получено самосогласованное описание лептонных и радиационных переходов в рамках предложенной авторами модели.

In the framework of the relativistic quark model based on the point form of the Poincaré-invariant quantum mechanics, the parameters were fixed using the integral representations of the lepton decay constants of pseudoscalar and vector mesons containing u-, d- and s-quarks. As a result of numerical calculations using the oscillator wave function, the basic parameters of the model are obtained using the pseudoscalar density constant and current quark masses. The analysis showed that the obtained calculation results in the framework of the model and the experimental data on the lepton decays of hadrons agree well with each other. As a result, the calculation method is generalized to the case of hadronic transitions with γ-quantum emission and a subsequent calculation of the integral representations of radiative decay constants of pseudoscalar and vector mesons. The obtained values of the anomalous magnetic moments are compared with the baryon data. As a test of the model, the authors studied the behavior of the form-factors of radiative decays of vector mesons with a subsequent comparison to the modern experimental data in the q < 0.5 GeV range where the resonance effects are insignificant. As a result, self-consistent descriptions of lepton and radiative transitions were obtained within the framework of the model proposed by the authors.

пуанкаре-инвариантная квантовая механикаточечная форма динамикикваркмезонмагнитный моментрадиационный распадформ-факторанализ экспериментальных данныхPoincaré-invariant quantum mechanicspoint form of dynamicsquarkmesonmagnetic momentradiative decayform-factoranalysis of experimental dataReferencesStudy of the Dalitz decay e e + − ϕ → η with the KLOE detector / D. Babusci [et al.] // Phys. Lett. B. – 2015. – Vol. 742. – P. 1–6. https://doi.org/10.1016/j.physletb.2015.01.011Babusci D., Balwierz-Pytko I., Bencivenni G., Bloise C., Bossi F., Branchini P. [et al.]. Study of the Dalitz decay e e + − ϕ → η with the KLOE detector. Physical Review Letters B, 2015, vol. 742, pp. 1–6. https://doi.org/10.1016/j.physletb.2015.01.011Adlarson, P. Measurement of the 0 e e + − ω → π and e e + − η → Dalitz decays with the A2 setup at MAMI / P. Adlarson (A2 collaboration), F. Afzal, A. Bartolome // Phys. Rev. C. – 2017. – Vol. 95. – P. 035208. https://doi.org/10.1103/ PhysRevC.95.035208Adlarson P., Afzal F., Aguar-Bartolomé P., Ahmed Z., Annand J. R. M., Arends H. J. [et al.]. Measurement of the 0 e e + − ω → π and e e + − η → Dalitz decays with the A2 setup at MAMI. Physical Review C, 2017, vol. 95, pp. 035208. https://doi.org/10.1103/PhysRevC.95.035208Study of the Dalitz decay e e + − ϕ → η with the KLOE detector / A. Anastasi (KLOE collaboration) [et al.] // Phys. Lett. B. – 2016. – Vol. 757. – P. 362–367. https://doi.org/10.1016/j.physletb.2016.04.015Anastasi A., Babusci D., Bencivenni G., Berlowski M., Bloise C., Bossi F. [et al.]. Measurement of the e e + − ϕ → η transition form factor with the KLOE detector. Physical Review Letter B, 2016, vol. 752, pp. 362–367. https://doi.org/10.1016/j.physletb.2016.04.015Amelino-Camelia, G. (KLOE collaboration). Physics with the KLOE-2 experiment at the upgraded DAFNE / G. Amelino-Camelia // Eur. Phys. J. – 2010. – Vol. C65. – P. 619–681. https://doi.org/10.1140/epjc/s10052-010-1351-1Amelino-Camelia G., Archilli F., Babusci D., Badoni D., Bencivenni G., Bernabeu J. [et al.]. Physics with the KLOE-2 experiment at the upgraded DAFNE. European Physics Journal, 2010, vol. 68, pp. 619–681. https://doi.org/10.1140/epjc/s10052-010-1351-1Dirac, P. A. M. Forms of Relativistic Dynamics / P. A. M. Dirac // Rev. Mod. Phys. – 1949. – Vol. 21. – P. 392–399. https://doi.org/10.1103/RevModPhys.21.392Dirac P. A. M. Forms of Relativistic Dynamics. Review Modern Physics, 1949, vol. 21, pp. 392–399. https://doi.org/10.1103/RevModPhys.21.392Keister, 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.Keister B. D., Polyzou W. N. Relativistic Hamiltonian dynamics in nuclear and particle physics. Advanced Nuclear Physics, 1991, vol. 20, pp. 225–479.Jaus, W. Relativistic constituent quark model of electroweak properties of light mesons / W. Jaus // Phys. Rev. D. – 1991. – Vol. 44. – P. 2851–2859. https://doi.org/10.1103/PhysRevD.44.2851Jaus W. Relativistic constituent quark model of electroweak properties of light mesons. Physical Review D, 1991, vol. 44, pp. 2851–2859. https://doi.org/10.1103/PhysRevD.44.2851Jaus, W. Consistent treatment of spin 1 mesons in the light front quark model / W. Jaus // Phys. Rev. D. – 2003. – Vol. 67. – P. 094010. https://doi.org/10.1103/PhysRevD.67.094010Jaus W. Consistent treatment of spin 1 mesons in the light front quark model. Physical Review D, 2003, vol. 67, pp. 094010. https://doi.org/10.1103/PhysRevD.67.094010Choi, H. M. Decay constants and radiative decays of heavy mesons in light-front quark model / H. M. Choi // Phys. Rev. D. – 2007. – Vol. 75. – P. 073016. https://doi.org/10.1103/PhysRevD.75.073016Choi Ho-Meoyng. Decay constants and radiative decays of heavy mesons in light-front quark model. Physical Review D, 2007, vol. 75, pp. 094010. https://doi.org/10.1103/PhysRevD.75.073016Zhang, W. M. Light front dynamics and light front QCD / W. M. Zhang // Chin. J. Phys. – 1994. – Vol. 32. – P. 717–808.Zhang W. M. Light front dynamics and light front QCD. Chinese Journal of Physics, 1994, vol. 32. pp. 717–808.Krutov, A. F. Relativistic instant form approach to the structure of two-body composite systems / A. F. Krutov, V. E. Troitsky // Phys. Rev. C. – 2002. – Vol. 65. – P. 045501. https://doi.org/10.1103/PhysRevC.65.045501Krutov A. F., Troitsky V. E. Relativistic instant form approach to the structure of two-body composite systems. Physical Review C, 2002, vol. 65, pp. 045501. https://doi.org/10.1103/PhysRevC.65.045501Krutov, 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. – P. 033007. https://doi.org/10.1103/PhysRevD.97.033007Krutov 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, pp. 033007. https://doi.org/10.1103/PhysRevD.97.033007Krutov, 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/201713802007Krutov 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/201713802007Klink, W. H. Point form relativistic quantum mechanics and electromagnetic form factors / W. H. Klink // Phys. Rev. C. – 1998. – Vol. 58. – P. 3587–3604. https://doi.org/10.1103/PhysRevC.58.3587Klink W. H. Point form relativistic quantum mechanics and electromagnetic form factors. Physical Review C, 1998, vol. 58, pp. 3587–3604. https://doi.org/10.1103/PhysRevC.58.3587Desplanques, B. Dirac’s inspired point form and hadron form-factors / B. Desplanques // Nucl. Phys. A. – 2005. – Vol. 755. – P. 303–306. https://doi.org/10.1016/j.nuclphysa.2005.03.032Desplanques B. Dirac’s inspired point form and hadron form-factors. Nuclear Physics A, 2005, vol. 755, pp. 303–306. https://doi.org/10.1016/j.nuclphysa.2005.03.032Biernat, E. P. Point-form quantum field theory / E. P. Biernat, W. H. Klink, W. Schweiger // Ann. Phys. – 2008. – Vol. 323. – P. 1361–1383. https://doi.org/10.1016/j.aop.2007.09.004Biernat E. P., Klink W. H., Schweiger W., Zelzer S. Point-form quantum field theory. Annals of Physics, 2008, vol. 323, pp. 1361–1383. https://doi.org/10.1016/j.aop.2007.09.004Gomez-Rocha, M. Semileptonic meson decays in point-form relativistic quantum mechanics: unambiguous extraction of weak form factors / M. Gomes-Rocha // Phys. Rev. D. – 1998. – Vol. 90. – P. 076003. https://doi.org/10.1103/PhysRevD.90.076003Gomez-Rocha M. Semileptonic meson decays in point– form relativistic quantum mechanics: unambiguous extraction of weak form factors. Physical Review D, 2014, vol. 7, pp. 076003. https://doi.org/10.1103/PhysRevD.90.076003Allen, T. W. Point-form analysis of elastic deuteron form factors / T. W. Allen, W. H. Klink, W. N. Polyzou // Phys. Rev. C. –2001. – Vol. 63. – P. 034002. https://doi.org/10.1103/PhysRevC.63.034002Allen T. W., Klink W. H., Polyzou W. N. Point-form analysis of elastic deuteron form factors. Physical Review C, 2001, vol. 63, pp. 034002. https://doi.org/10.1103/PhysRevC.63.034002Andreev, V. V. QCD coupling constant below 1 GeV in the Poincare-covariant model / V. V. Andreev // Physics of Particles and Nuclei Let. – 2011. – Vol. 8. – P. 347–355. https://doi.org/10.1134/S1547477111040030Andreev V. V. QCD coupling constant below 1 GeV in the Poincare-covariant model. Physics of Particles and Nuclei Letters, 2011, vol. 8, pp. 347–355. https://doi.org/10.1134/S1547477111040030Andreev, V. V. Constituent quark masses in Poincaré-invariant quantum mechanics / V. V. Andreev, V. Yu. Haurysh // J. Phys. Conf. Ser. – 2017. – Vol .938. – P. 012030. https://doi.org/10.1088/1742-6596/938/1/012030Andreev V. V., Haurysh V. Yu. Constituent quark masses in Poincaré-invariant quantum mechanics. Journal of Physics: Conference Series, 2017, vol. 938, pp. 1–5. https://doi.org/10.1088/1742-6596/938/1/012030Andreev, V. V. Radiative decays of light vector mesons in Poincare-invariant quantum mechanics / V. V. Andreev, V. Yu. Haurysh // J. Phys. Conf. Ser. – 2016. – Vol. 678. – P. 012041. https://doi.org/10.1088/1742-6596/678/1/012041Andreev V. V., Haurysh V. Yu. Radiative decays of light vector mesons in Poincare– invariant quantum mechanics. Journal of Physics: Conference Series, 2016, vol. 678, pp. 1–5. https://doi.org/10.1088/1742-6596/678/1/012041Андреев, В. В. Методика вычисления электрослабых характеристик мезонов в пуанкаре-инвариантной квантовой механике / В. В. Андреев, В. Ю. Гавриш, А. Ф. Крутов // Проблемы физики, математики и техники. – 2018. – T. 1. – С. 7–19.Andreev V. V., Haurush V. Yu., Krutov A. F. Method of calculation of electroweak characteristics of mesons in the Poincaré-invariant quantum mechanics. Problemy Fiziki, Matematiki i Tekhniki = Problems of Physics, Mathematics and Technics, 2018, vol. 1 (34), pp. 7–19. https://doi.org/mathnet.ru/pfmt545Review of Particle Physics / M. Tanabashi (PDG Group) [et al.] // Phys. Rev. D. –2019. – Vol. 98. – P. 030001. https://doi.org/10.1103/PhysRevD.98.030001Tanabashi M., Hagiwara K., Hikasa K., Nakamura K., Sumino Y., Takahashi F. [et al.]. Review of Particle Physics. Physical Review D, 2018, vol. 98, pp. 030001. https://doi.org/10.1103/PhysRevD.98.030001Physics at KLOE / F. Ambrosino [et al.] // PoS. – 2009. – Vol. CD09. – P. 045. https://doi.org/10.22323/1.086.0045Ambrosino F., Antonelli A., Anton M., Archilli F., Beltrame P., Bencivenni G. [et al.]. Physics at KLOE. Proceedings of Science, 2009, vol. CD09, pp. 45. https://doi.org/10.22323/1.086.0045Feldmann, T. Mixing and decay constants of pseudoscalar mesons: The Sequel / T. Feldmann, P. Kroll, B. Stech // Phys. Lett. B. – 1999. – Vol. 449. – P. 339–346. https://doi.org/10.1016/S0370-2693(99)00085-4Feldmann T., Kroll P., Stech B. Mixing and decay constants of pseudoscalar mesons: The Sequel. Physics Letters B, 1999, vol. 448, pp. 339–346. https://doi.org/10.1016/S0370-2693(99)00085-4Kokkedee, J. The quark model / J. Kokkede. – New York; Amsterdam: W. A. Benjamin Inc., 1969. – 239 p.Kokkedee J. The Quark Model. New York, Amsterdam, W. A. Benjamin Inc., 1969. 239 p.Haurysh, V. Electroweak decays of unflavored mesons in Poincare covariant quark model / V. Haurysh, V. V. Andreev // Turk. J. Phys. – 2019. – Vol. 43. – P. 167–177. https://doi.org/10.3906/fiz-1810-24Andreev V. V, Haurysh, V. Yu. Electroweak decays of unflavored mesons in Poincare covariant quark model. Turkish Journal of Physics, 2019, vol. 43, pp. 167–177. https://doi.org/10.3906/fiz-1810-24Petronzio, R. Possible evidence of extended objects inside the proton / R. Petronzio, S. Simula, G. Ricco // Phys. Rev. D. – 2003. – Vol. 67. – P. 094994. https://doi.org/10.1103/PhysRevD.67.094004Petronzio R., Simula S., Ricco G. Possible evidence of extended objects inside the proton. Physical Review D, 2003, vol. 67, pp. 094994. https://doi.org/10.1103/PhysRevD.67.094004Ito, H. Flavor SU(3) symmetty in the anomalous magnetic moments of constituent quarks / H. Ito // Phys. Lett. B. – 1995. – Vol. 353. – P. 13–19. https://doi.org/10.1016/0370-2693(95)00443-OIto H. Flavor SU(3) symmetty in the anomalous magnetic moments of constituent quarks. Physics Letters B, 1995, vol. 353, pp. 13–19. https://doi.org/10.1016/0370-2693(95)00443-OFayazbakhsh, 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. – P. 105030. https://doi.org/10.1103/PhysRevD.90.105030Fayazbakhsh Sh., Sadooghi N. Anomalous magnetic moment of hot quarks, inverse magnetic catalysis, and reentrance of the chiral symmetry broken phase. Physical Review D, 2014, vol. 90, pp. 105030. https://doi.org/10.1103/PhysRevD.90.105030Qian, W. Vector meson ω–φ mixing and their form factors in the light– cone quark model / W. Qian, B.-Q. Ma // Phys. Rev. D. – 2008. – Vol. 78. – P. 074002. https://doi.org/10.1103/PhysRevD.78.074002Qian W., Ma B.-Q. Vector meson ω–φ mixing and their form factors in the light-cone quark model. Physical Review D, 2008, vol. 78, pp. 074002. https://doi.org/10.1103/PhysRevD.78.074002Schneider, S. P. ω → π 0 γ* Transition form factors in dispersion theory / S. P. Schneider, B. Kibus, N. Frans // Phys. Rev. D. – 2012. – Vol. 86. – P. 054013. https://doi.org/10.1103/PhysRevD.91.094029Schneider S. P., Kibus B., Frans N. ω → π 0 γ* Transition form factors in dispersion theory. Physical Review D, 2012, vol. 86, pp. 054013. https://doi.org/10.1103/PhysRevD.91.094029Charge form– factor of π ± and K ± mesons / F. Cardarelli [et al.] // Phys. Rev. D. – 1996. – Vol. 53. – P. 6682–6685. https://doi.org/10.1103/PhysRevD.53.6682Cardarelli F., Grach I. L., Narodetsky I. M., Pace E., Salme G., Simula S. Charge form-factor of π ± and K ± mesons. Physical Review D, 1996, vol. 53, pp. 6682–6685. https://doi.org/10.1103/PhysRevD.53.6682

The authors declare that there are no conflicts of interest present.