Method of calculation of electroweak characteristics of mesons in the Poincar\'e invariant quantum mechanics
Problemy fiziki, matematiki i tehniki, no. 1 (2018), pp. 7-19.

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On the basis of the point form of Poincaré-invariant quantum mechanics, a method for calculating the formsfactors and the decay constants of mesons, as relativistic coupled quark systems, is presented. As an example of the developed technique, an integral representation of the radiative decay constant of a vector meson $V\to P\gamma$ is obtained.
Keywords: quark, Poincaré-invariant quantum mechanics, form factor, decay constant.
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V. V. Andreev; V. Yu. Haurysh; A. F. Krutov. Method of calculation of electroweak characteristics of mesons in the Poincar\'e invariant quantum mechanics. Problemy fiziki, matematiki i tehniki, no. 1 (2018), pp. 7-19. http://geodesic.mathdoc.fr/item/PFMT_2018_1_a0/

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

[2] W. N. Polyzou et al., “Mini review of Poincare invariant quantum theory”, Few Body Syst., 49 (2011), 129–147 | DOI

[3] V.V. Andreev, “QCD coupling constant below 1 GeV in the Poincare-covariant model”, Physics of Particles and Nuclei Letters, 8:4 (2011), 347–355 | DOI | MR

[4] F. Coester, W.N. Polyzou, “Relativistic quantum mechanics of particles with direct interactions”, Phys. Rev., D26 (1982), 1348–1367 | MR

[5] W.N. Polyzou, “Relativistic two-body models”, Annals of Physics, 193:2 (1989), 367–418 | DOI | MR

[6] B. Bakamjian, L.H. Thomas, “Relativistic Particle Dynamics. II”, Phys. Rev., 92:5 (1953), 1300–1310 | DOI | MR | Zbl

[7] B. Bakamjian, “Relativistic Particle Dynamics”, Phys. Rev., 121:6 (1961), 1849–1851 | DOI | MR | Zbl

[8] S.N. Sokolov, “Relyativistskoe slozhenie pryamykh vazimodeistvii v tochechnoi forme dinamiki”, TMF, 36:2 (1978), 193–207

[9] B.D. Keister, W.N. Polyzou, “Relativistic Hamiltonian dynamics in nuclear and particle physics”, Adv. Nucl. Phys., 20 (1991), 225–479

[10] T. Lin, C. Elster, W.N. Polyzou, W. Glockle, “First Order Relativistic Three-Body Scattering”, Phys. Rev., C76 (2007), 014010

[11] V. V. Andreev, Elektroslabye kharakteristiki kvantovykh sistem v puankare-kovariantnykh modelyakh, Lap Lambert Academic Publishing, 2017, 320 pp.

[12] H.A. Bete, E.E. Salpeter, “A relativistic equation for bound-state problems”, Phys. Rev., 84:2 (1951), 1232–1242 | MR

[13] E.E. Salpeter, “Mass-corrections to the fine structure of Hydrogen-like atoms”, Phys. Rev., 87:2 (1952), 328–343 | DOI | Zbl

[14] A.A. Logunov, O.A. Khrustalev, “Veroyatnostnoe opisanie rasseyaniya pri vysokikh energiyakh i gladkii kvazipotentsial”, EChAYa, 1:1 (1970), 71–90

[15] V.G. Kadyshevskii, R.M. Mir-Kasimov, N.B. Skachkov, “Trekhmernaya formulirovka relyativistskoi problemy dvukh tel”, EChAYa, 2:3 (1972), 635–690

[16] E. Eichten et al., “Spectrum of Charmed Quark-Antiquark Bound States”, Phys. Rev. Lett., 34 (1975), 369–372 | DOI

[17] A.E. Dorokhov, “Spin effects in instanton model”, Czech. J. Phys., 52 (2002), C79–C89 | DOI

[18] M.D. Scadron, F. Kleefeld, G. Rupp, E. van Beveren, “Meson form-factors and the quark-based linear sigma model”, Fizika, B13 (2004), 43–56

[19] V.V. Andreev, Puankare-kovariantnye modeli dvukhchastichnykh sistem s kvantovopolevymi potentsialami, UO «Gomelskii gosudarstvennyi universitet im. F. Skoriny», Gomel, 2008, 294 pp.

[20] F. Cardarelli et al., “Hard constituent quarks and electroweak properties of pseudoscalar mesons”, Phys. Lett., B332 (1994), 1–7 | DOI

[21] P.L. Chung, F. Coester, W.N. Polyzou, “Charge form-factors of quark model pions”, Phys. Lett., B205 (1988), 545–548 | DOI

[22] F. Coester, W.N. Polyzou, “Charge form factors of quarkmodel pions”, Phys. Rev., C71 (2005), 028202

[23] F. Schlumpf, “Charge form-factors of pseudoscalar mesons”, Phys. Rev., D50 (1994), 6895–6898

[24] W. Jaus, “Relativistic constituent quark model of electroweak properties of light mesons”, Phys. Rev., D44 (1991), 2851–2859

[25] W. Jaus, “Semileptonic decays of B and D mesons in the light front formalism”, Phys. Rev., D41 (1990), 3394

[26] S. Simula, “Comparison among Hamiltonian light-front formalisms at q+ =0 and q+ not = 0: Space-like elastic form factors of pseudoscalar and vector mesons”, Phys. Rev., C66 (2002), 035201

[27] A.A. Cheshkov, Yu.M. Shirokov, “Invariantnaya parametrizatsiya lokalnykh operatorov”, ZhETF, 44:6 (1963), 1982–1992

[28] A.F. Krutov, V.E. Troitsky, “Relativistic instant-form approach to the structure of two-body composite systems”, Phys. Rev. C, 2002, 045501 | DOI

[29] A.F. Krutov, V.E. Troitsky, “Relativistic properties of spin and pion electromagnetic structure”, J. High Energy Physics, 10 (1999), 028 | DOI

[30] A.F. Krutov, “Elektroslabye svoistva legkikh mezonov v relyativistskoi modeli sostavnykh kvarkov”, YaF, 60:8 (1997), 1442–1450

[31] A.F. Krutov, V.E. Troitskii, “Postroenie formfaktorov sostavnykh sistem s pomoschyu obobschennoi teoremy Vignera–Ekkarta dlya gruppy Puankare”, Teoreticheskaya i matematicheskaya fizika, 143:2 (2005), 258–277 | DOI | Zbl

[32] B. Desplanques, L. Theussl, “Form factors in the ‘point form’ of relativistic quantum mechanics: Single and two-particle currents”, Eur. Phys. J., A21 (2004), 93 | DOI

[33] B. Desplanques, L. Theussl, S. Noguera, “Effective boost and ‘pointform’ approach”, Phys. Rev., C65 (2002), 038202

[34] L. Theussl, A. Amghar, B. Desplanques, S. Noguera, “Comparison of different boost transformations for the calculation of form factors in relativistic quantum mechanics”, Few Body Syst. Suppl., 14 (2003), 393 | DOI

[35] A. Amghar, B. Desplanques, L. Theussl, “The form factor of the pion in ‘point-form’ of relativistic dynamics revisited”, Phys. Lett., B574 (2003), 201–209 | DOI

[36] B. Desplanques, “Dirac's inspired point form and hadron form factors”, Nucl. Phys., A755 (2005), 303–306 | DOI

[37] B. Desplanques, “Nucleon and pion form factors in different forms of relativistic quantum mechanics”, Int. J. Mod. Phys., A20 (2005), 1601–1606 | DOI

[38] B. Desplanques, “Relativistic quantum mechanics: A Dirac's point-form inspired approach”, Nucl. Phys., A748 (2005), 139–167 | DOI

[39] M.B. Menskii, Metod indutsirovannykh predstavlenii. Prostranstvo-vremya i kontseptsiya chastits, Nauka, 1976, 145 pp.

[40] Yu.V. Novozhilov, Vvedenie v teoriyu elementarnykh chastits, Nauka, M., 1972, 472 pp.

[41] F.I. Fedorov, Gruppa Lorentsa, Nauka, M., 1979, 384 pp.

[42] P.A.M. Dirac, “Forms of relativistic dynamics”, Rev. of Modern Phys., 21 (1949), 392–399 | DOI | MR | Zbl

[43] H.-C. Pauli, “On the effective Hamiltonian for QCD: An overview and status report”, Nucl. Phys. Proc. Suppl., 108 (2002), 273–280 | DOI | Zbl

[44] V.B. Berestetskii, M.V. Terentev, “Dinamika svetovogo fronta i nuklony iz relyativistskikh kvarkov”, Yadernaya fizika, 24:5 (1977), 1044–1057

[45] L.A. Kondratyuk, M.V. Terentev, “Zadacha rasseyaniya dlya relyativistskikh sistem s fiksirovannym chislom chastits v dinamike na svetovom fronte”, Yadernaya fizika, 31:4 (1980), 1087–1106

[46] M.V. Terentev, “O strukture volnovykh funktsii mezonov kak svyazannykh sostoyanii relyativistskikh kvarkov”, Yadernaya fizika, 25:1 (1976), 207–213

[47] T.W. Allen, W.H. Klink, “Pion charge form factor in point form relativistic dynamics”, Phys. Rev., C58 (1998), 3670–3673

[48] V.V. Andreev, “Opisanie leptonnykh raspadov v ramkakh puankare-kovariantnoi kvarkovoi modeli”, Vestsi NAH Belarusi. Ser. fiz.-mat. navuk, 2000, no. 2, 93–98

[49] W.H. Klink, Point form electrodynamics and the construction of conserved current operators, 2000, arXiv: (Date of access: 14.01.2008) nucl-th/0012033

[50] B.D. Keister, “Heavy quark symmetry and Dirac's point form dynamics”, Phys. Rev., D46 (1992), 3188–3194

[51] W.H. Klink, “Constructing Point Form Mass Operators from Interaction Lagrangians”, Nucl. Phys., A716 (2003), 123–135 | DOI | Zbl

[52] S.M. Bilenkii, Vvedenie v diagrammy Feinmana i fiziku elektroslabogo vzaimodeistviya, Energoatomizdat, M., 1990, 327 pp.

[53] W. Lucha, H. Rupprecht, F.F. Schoberl, “Relativistic treatment of fermion anti-fermion bound states”, Phys. Rev., D44 (1991), 242–249

[54] D. Ebert, R. Faustov, V. Galkin, “Radiative M1 decays of heavy light mesons in the relativistic quark model”, Phys. Lett., B537 (2002), 241–248 | DOI

[55] D.-S. Hwang, G.-H. Kim, “Decay constants of B, B* and D, D* mesons in relativistic mock meson model”, Phys. Rev., D55 (1997), 6944–6951

[56] H. Negash, S. Bhatnagar, “Radiative decay widths of ground and excited states of vector charmonium and bottomonium”, Adv. High Energy Phys., 2017 (2017), 7306825 | DOI

[57] V.V. Andreev, A.F. Krutov, “Elektromagnitnye form-faktory mezonov”, Problemy fiziki, matematiki i tekhniki, 2011, no. 1(6), 7–19