Мeson resonances in the relativistic quark model
https://doi.org/10.29235/1561-2430-2021-57-1-46-63
Abstract
In this paper, the relativistic quark model is developed for the study of mesons and resonances as quasi-bound quark states. A classic analogue of the spinless Salpeter equation is analyzed. It is shown that the potential for a conservative isolated two-particle system is the Lorentz-scalar function of the distance between quarks and can be included into the particle mass, which leads to the position-dependent quark mass. The funnel-type potential is modified with taking into account the dependence of the strong coupling αS on the distance. The concept of free motion of particles in a bound state is developed. The eigenvalue problem for the bound state is defined by the relativistic quasiclassical wave equation for the scalar potential. Two exact asymptotic solutions of the equation for the Coulomb and linear parts of the potential are obtained analytically; on this basis, the complex-mass formula for mesons and resonances is written. The efficiency of the model is demonstrated by
comparison of the calculation results with the data for the masses of ρ and D mesons.
About the Author
М. N. Sergeenko
Francisk Skorina Gomel State University
Russian Federation
Russian Federation
Mikhail N. Sergeenko – Dr. Sc. (Physics and Mathematics)
104, Sovetskaya Str., 246019, Gomel
References
1. Olive K. A. Review of Particle Physics. Chinese Physics C, 2014, vol. 38, no. 9. pp. 090001. https://doi.org/10.1088/1674- 1137/38/9/090001
2. Armstrong W. W., Burris W., Gingrich D. M. ATLAS: Technical proposal for a general-purpose pp experiment at the Large Hadron Collider at CERN, CERN-LHCC-94-43. December, 1994. 289 p.
3. Bhaduri R. K. Models of the Nucleon (From Quark to Soliton). Chap. 2. New York, Addison-Wesley, 1988.
4. Morpurgo G. Field theory and the nonrelativistic quark model: a parametrization of meson masses. Physical Review D, 1990, vol. 41, no. 9, pp. 2865–2870. https://doi.org/10.1103/physrevd.41.2865
5. Sergeenko M. N. An Interpolating mass formula and Regge trajectories for light and heavy quarkonia. Zeitschrift fur Physik C, 1994, vol. 64, no. 2, pp. 315–322. https://doi.org/10.1007/bf01557404
6. Eichten E., Godfrey S., Mahlke H., Rosner J. L. Quarkonia and their transitions. Reviews of Modern Physics, 2008, vol. 80, no. 3, pp. 1161–1193. https://doi.org/10.1103/revmodphys.80.1161
7. Ebert D., Faustov R. N., Galkin V. O. Spectroscopy and Regge trajectories of heavy quarkonia and Bc mesons. The European Physical Journal C, 2011, vol. 71, no. 12, pp. 1825. https://doi.org/10.1140/epjc/s10052-011-1825-9
8. Sergeenko M. N. Glueball masses and Regge trajectories for the QCD-inspired potential. The European Physical Journal C, 2012, vol. 72, no. 8, pp. 2128. https://doi.org/10.1140/epjc/s10052-012-2128-5
9. Sergeenko M. N. Masses and widths of Resonances for the Cornell Potential. Advances in High Energy Physics, 2013, vol. 2013, pp. 1–7. https://doi.org/10.1155/2013/325431
10. Collins P. D. B. An Introduction To Regge Theory & High Energy Physics. Moscow, Atomizdat Publ., 1980. 432 p. (in Russian).
11. Sergeenko M. N. Semiclassical wave equation and exactness of the WKB method. Physical Review A, 1996, vol. 53, no. 6, pp. 3798–3804. https://doi.org/10.1103/physreva.53.3798
12. Sergeenko M. N. Relativistic semiclassical wave equation and its solution. Modern Physics Letters A, 1997, vol. 12, no. 37, pp. 2859–2871. https://doi.org/10.1142/s0217732397002983
13. Salpeter E. E., Bethe H. A. A Relativistic Equation for Bound-State Problems. Physical Review, 1951, vol. 84, no. 6, pp. 1232–1241. https://doi.org/10.1103/physrev.84.1232
14. Salpeter E. E. A Mass Corrections to the Fine Structure of Hydrogen-Like Atoms. Physical Review, 1952, vol. 87, no. 2, pp. 328–343. https://doi.org/10.1103/physrev.87.328
15. Todorov I. T. Dynamics of Relativistic Point Particles as a Problem with Constraints. Annalesdel’ Institut Henri Poincaré D, 1978, vol. A28, pp. 207
16. Lucha W., Schoberl F. F. Instantaneous Bethe-Salpeter Kernel for the Lightest Pseuoscalar Mesons. Physical Review D, 2016, vol. 93, no. 9, pp. 096005–096014. https://doi.org/10.1103/physrevd.93.096005
17. Crater H. W., Schiermeyer J., Whitney J., Cheuk-Yin Wong. Applications of Two Body Dirac Equations to Hadron and Positronium Spectroscopy Proceedings of CST-MISC Joint Symposium on Particle Physics — from Spacetime Dynamics to Phenomenology. Tokyo, 2014. https://doi.org/10.7566/jpscp.7.010002
18. Crater H. W., Van Alstine P. Relativistic calculation of the meson spectrum: A fully covariant treatment versus stan dard treatments. Physical Review D, 2004, vol. 70, no. 3, pp. 034026. https://doi.org/10.1103/physrevd.70.034026
19. Crater H. W., Schiermeyer J. Applications of two-body Dirac equations to the meson spectrum with three versus two covariant interactions, SU(3) mixing, and comparison to a quasipotential approach. Physical Review D, 2010, vol. 82, no. 9, pp. 094020. https://doi.org/10.1103/physrevd.82.094020
20. Longhi G., Lusanna L. (eds.) Constraint’s Theory and Relativistic Dynamics. Proceedings of the Firenze Workshop. Singapore, World Scientific, 1987. 351 p.
21. Bijtbier J. 3D reduction of the three-fermion Bethe-Salpeter equation. Few-Body Problems in Physics ’98. Springer, 1999, pp. 127–130. https://doi.org/10.1007/978-3-7091-6798-4_22
22. Bijtbier J. Bound state equation for 4 or more relativistic particles. Nuclear Physics A, 2002, vol. 703, no. 1–2, pp. 327–345.https://doi.org/10.1016/s0375-9474(01)01341-0
23. Nakanishi N. A General Survey of the Theory of the Bethe-Salpeter Equation. Progress of Theoretical Physics Supplement, 1969, vol. 43, pp. 1–81. https://doi.org/10.1143/ptps.43.1
24. Jallouli H., Sazdjian H. Relativistic effects in the pionium lifetime. Physical Review D, 1998, vol. 58, no. 1, pp. 014011. https://doi.org/10.1103/physrevd.58.014011
25. Hara O., Ishida S., Naka S. Extended Objects and Bound Systems; From Relativistic Description to Phenomenological Application. Extended Objects and Bound Systems. 1993. https://doi.org/10.1142/9789814536226
26. Brau F., Semay C. A mass formula for light mesons from a potential model. Journal of Physics G: Nuclear and Particle Physics, 2002, vol. 28, no. 11, pp. 2771–2781. https://doi.org/10.1088/0954-3899/28/11/303
27. Brau F., Semay C. Light meson spectra and instanton-induced forces. Physical Review D, 1998, vol. 58, no. 3, pp. 034015. https://doi.org/10.1103/physrevd.58.034015
28. Alba D., Crater H. W., Lusanna L. Relativistic quantum mechanics and relativistic entanglement in the rest-frame instant form of dynamics. Journal of Mathematics and Physics, 2011, vol. 52, no. 6, pp. 062301. https://doi.org/10.1063/1.3591131
29. Semay C., Baye D., Hesse M., Silvestre-Brac B. Semirelativistic Lagrange mesh calculations. Physical Review E, 2001, vol. 64.no. 1, pp. 016703. https://doi.org/10.1103/physreve.64.016703
30. Brau F., Semay C. The 3-dimensional Fourier grid Hamiltonian method. Journal of Computational Physics, 1998, vol. 139, no. 1, pp. 127–136. https://doi.org/10.1006/jcph.1997.5866
31. Fulcher L. P. Matrix representation of the nonlocal kinetic energy operator, the spinless Salpeter equation and the Cornell potential. Physical Review D, 1994, vol. 50, no. 1, pp. 447–453. https://doi.org/10.1103/physrevd.50.447
32. Hall R. L., Lucha W., Schoberl F. F. Discrete Spectra of Semirelativistic Hamiltonians. International Journal of Modern Physics A, 2003, vol. 18, no. 15, pp. 2657–2680. https://doi.org/10.1142/s0217751x0301406x
33. Semay C. An upper bound for asymmetrical spinless Salpeter equations. Physics Letters A, 2012, vol. 376, no. 33, pp. 2217–2221. https://doi.org/10.1016/j.physleta.2012.05.046
34. Currie D. G., Jordan T. F., Sudarshan E. C. G. Relativistic Invariance and Hamiltonian Theories of Interacting Particles. Reviews of Modern Physics, 1963, vol. 35, no. 4, pp. 1032. https://doi.org/10.1103/revmodphys.35.1032.2
35. Alba D., Crater H. W., Lusanna L. Hamiltonian relativistic two-body problem: center of mass and orbit reconstruction. Journal of Physics A, 2007, vol. 40, no. 31, pp. 9585–9607. https://doi.org/10.1088/1751-8113/40/31/029
36. 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
37. Silenko A. Ya., Teriayev O. V. Phenomenological Description of Relativistic Quarks with the Help of Dirac equation for the Cornell Potential. Yadernaya Fizika = Nuclear Physics, 2017, vol. 80, no. 5, pp. 573–580 (in Russian). https://doi. org/10.7868/s0044002717050233
38. Huang Y.-S. Schredinger-Like Relativistic Wave Equation of Motion for the Lorentz-Scalar Potential. Foundations of Physics, 2001, vol. 31, no. 9, pp. 1287–1298. doihttps://doi.org/10.1023/a:1012270110871
39. Bhaduri R. K. Models of the Nucleon (From Quark to Soliton). Chap. 2. NewYork, Addison-Wesley, 1988.
40. Tomil’chik L. M. Effects of Quark Confinement in Conformally flat background metric. Kovariantnye metody v teoeticheskoy fizike – fizika elementarnykhc hastist i teoriya otnositel’nosti [Covariant Methods in Theoretical Physics – Physics of Elementary Particles and Theory of Relativity]. Minsk, 2001, iss. 5, pp. 155–161 (in Russian).
41. Gorbatsevich A. K., Tomil’chik L. M. Equation of Particle Motion in Conformally Flat Space and Quark Confinement. Problemy fiziki vysokikh energiy v teorii polia, Protvino, 7–13 iyulya 1986 g. [Problems of high-energy physics in field theory, Protvino, July 7–13, 1986]. Moscow, 1987, pp. 378–383 (in Russian).
42. Sergeenko M. N. Relativistic model of mesons with the coordinate-dependent quark mass. Doklady Natsional’noi akademii nauk Belarusi = Doklady of the National Academy of Sciences of Belarus, 2017, vol. 61, no. 4, pp. 39–45 (in Russian).
43. Sergeenko M. N. Complex Masses of Mesons and Resonances in Relativistic Quantum Mechanics. Nonlinear Dynamisc and Applications, 2017, vol. 23, pp. 239–247.
44. Sergeenko M. N. Light and Heavy Mesons in The Complex Mass Scheme. Nonlinear Dynamisc and Applications, 2019, vol. 25, pp. 209–216.
45. Byckling E., KajantieK. Particle Kinematics. London, John Wiley & Sons, 1972, pp. 20–27.
Review
Views: 754
Email this article 