Description of radiative decays of $V \to P \gamma^{*}$ in different forms of Poincar\'e-invariant quantum mechanics

A. F. Krutov ; R. G. Polezhaev

Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 19 (2015) no. 2, pp. 259-269.

Résumé

The description of the radiative decays of $V \to P \gamma^*$ in different forms Poincaré invariant quantum mechanics (PIQM) is considered. To construct the matrix element of the electromagnetic current we use the non-diagonal parametrization procedure. The obtained matrix element of the current satisfies the conditions of the Lorentz covariance and conservation. To illustrate this approach in a modified relativistic impulse approximation the description of the radiative transition $\rho \to \pi \gamma^{*}$ is performed. An analytic expression for the transition form factor $F_{\pi \rho}(Q^2)$, matching all forms PIQM, is obtained. Numerical calculations of the transition form factor are made with different model wave functions.

Détail

Keywords: Poincaré invariant quantum mechanics, radiative decays, electromagnetic current
Mots-clés : transition formfactor.

Bibliographie

[1] Krutov A. F., Polezhaev R. G., “Description of radiative decays of $V \to P \gamma^{*}$ in different forms of Poincare-invariant quantum mechanics”, The 4nd International Conference “Mathematical Physics and its Applications”, Book of Abstracts and Conference Materials, eds. I. V. Volovich; V. P. Radchenko, Samara State Technical Univ., Samara, 2014, 210–211 (In Russian)

[2] Arnaldi R. (et.al. NA60 Collaboration), “Study of the electromagnetic transition form-factors in $\eta\to \mu^{+}\mu^{-}\gamma$ and $\omega\to \mu^{+}\mu^{-}\pi^{0}$ decays with NA60”, Phys. Lett. B, 677:5 (2009), 260–266, arXiv: [hep-ph] 0902.2547 | DOI

[3] Usai G. (et.al. NA60 Collaboration), “Low mass dimuon production in proton-nucleus collisions at 400 GeV/c”, Nucl. Phys. A, 855:1 (2011), 918–196 | DOI | MR

[4] Uras A. (et.al. NA60 Collaboration), “Measurement of the $\eta$ and $\omega$ Dalitz decays transition form factors in p-A collisions at 400 GeV/c with the NA60 apparatus”, J. Phys.: Conf. Ser., 270:1 (2011), 012038, arXiv: [hep-ex] 1108.0968 | DOI

[5] Archilli F. (et.al. KLOE-2 Collaboration), “Search for a vector gauge boson in $\phi$ meson decays with the KLOE detector”, Phys. Lett. B, 706:4–5 (2012), 251–255, arXiv: [hep-ph] 1110.0411 | DOI

[6] Amsler C. (et.al. Particle Data Group), “Review of particle physics”, Phys. Lett. B, 667:1–5 (2008), 1–6 | DOI

[7] Krutov A. F., Troitsky V. E., “Instant form of Poincaré-invariant quantum mechanics and description of the structure of composite systems”, Physics of Particles and Nuclei, 40:2 (2009), 136–161 | DOI

[8] Maris P., Tandy P.C., “Electromagnetic transition form factors of light mesons”, Phys. Rev. C, 65:4 (2002), 045211, arXiv: nucl-th/0201017 | DOI | MR

[9] Yu J., Xiao B.-W., Ma B.-Q., “Space-like and time-like pion–rho transition form factors in the light-cone formalism”, J. Phys. G: Nucl. Part. Phys., 34:7 (2007), 1845–1860, arXiv: [hep-ph] 0706.2018 | DOI

[10] Desplanques B., “RQM description of the charge form factor of the pion and its asymptotic behavior”, Eur. Phys. J. A, 42:2 (2009), 219–236, arXiv: [nucl-th] 0906.1889 | DOI

[11] Ivashyn S.A., “Vector to pseudoscalar meson radiative transition in chiral theory with resonances”, Problems of Atomic Science and Technology. No. 1, Nuclear Physics Investigations, 57, 2012, 179–182, arXiv: [hep-ph] 1111.1291

[12] Bierrat E. P., Schweiger W., “Electromagnetic $\rho$-meson form factors in point-form relativistic quantum mechanics”, Phys. Rev. C, 89:5 (2014), 055205, arXiv: [hep-ph] 1404.2440 | DOI

[13] Krutov A. F., Troitsky V. E., Tsirova N. A., “Nonperturbative relativistic approach to pion form factor: predictions for future JLab experiments”, Phys. Rev. C, 80:5 (2009), 055210, arXiv: [nucl-th] 0910.3604 | DOI

[14] Krutov A. F., Polezhaev R. G., “Description of the electromagnetic structure of the pion in the various forms of the Poincaré-invariant quantum mechanics”, Iadernaia fizika i inzhiniring [Nuclear Physics and Engineering], 4:9–10 (2013), 848–852 (In Russian) | DOI

[15] Cheshkov A. A., Shirokov Yu. M., “Invariant parametrization of local operators”, Soviet Physics JETP, 17 (1963), 1333–1339 | DOI | MR | MR

[16] Zare R. N., Angular Momentum: Understanding Spatial Aspects in Chemistry and Physics, Wiley, New York, 1988, xi+349 pp.

[17] Edmonds A. R., Angular Momentum in Quantum Mechanics, Investigations in Physics, 4, Princeton University Press, Princeton, New Jersey, 1957, viii+146 pp. | MR | Zbl

[18] Cardarelli F., Grach I. L., Narodetskii I. M., Salmé G., Simula S., “Radiative $\pi\rho$ and $\pi\omega$ transition form factor in a light-front constituent quark model”, Phys. Lett. B, 359:1–2 (1995), 1–7, arXiv: nucl-th/9509004 | DOI

[19] Andreev V. V., Krutov A. F., “Electromagnetic form factors of mesons”, Problemy fiziki, matematiki i tekhniki, 2011, no. 1(6), 7–19 (In Russian)

[20] Krutov A. F., Troitsky V. E., “Relativistic effects in the electromagnetic structure of the $\rho$-meson”, Vestnik SamGU. Estestvenno-Nauchnaya Ser., 2003, Second Special Issue, 95–111 (In Russian)

[21] Gerasimov S. B., “Magnetic moments of baryons and strange content of the nucleon”, Phys. Lett. B, 357:4 (1995), 666–670 | DOI

[22] Cardarelli F., Grach I. L., Narodetskii I. M., Pace E., Salme G., Simula S., “Hard Constituent Quarks and Electroweak Properties of Pseudoscalar Mesons”, Phys. Lett. B, 332:1–2 (1994), 1–7, arXiv: nucl-th/9405014 | DOI