Relativistic quantum model of confinement and the current quark masses

L. D. Soloviev

doi:10.1103/PhysRevD.58.035005

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Relativistic quantum model of confinement and the current quark masses

L. D. Soloviev

Department of Physics, University of Michigan, Ann Arbor, Michigan 48109-1120
Institute for High Energy Physics, 142284, Protvino, Russia

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Phys. Rev. D 58, 035005 – Published 30 June, 1998

DOI: https://doi.org/10.1103/PhysRevD.58.035005

Abstract

We consider a relativistic quantum model of confined massive spinning quarks and antiquarks which describes the leading Regge trajectories of mesons. The quarks are described by the Dirac equations and the gluon contribution is approximated by the Nambu-Goto straight-line string. The string tension and the current quark masses are the main parameters of the model. Additional parameters are phenomenological constants which approximate nonstring short-range contributions. A comparison of the measured meson masses with the model predictions allows one to determine the current quark masses (in MeV) to be $m_{s} = 227 \pm 5, m_{c} = 1440 \pm 10,$ and $m_{b} = 4715 \pm 20.$ The chiral ${SU}_{3}$ model makes it possible to estimate from here the $u$ - and $d$ -quark masses to be $m_{u} = 6.2 \pm 0.2 Mev$ and $m_{d} = 11.1 \pm 0.4 Mev .$

References (24)

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[c1] M. Green, J. Schwartz, and E. Witten, Superstring Theory (Cambrige University Press, Cambridge, England, 1987).

[c2] G. P. Pron’ko and A. V. Razumov, Theor. Math. Phys. 56, 192 (1983).

[c3] V. I. Borodulin et al., Theor. Math. Phys. 65, 119 (1985).

[c4] A. Chodos and C. B. Thorn, Nucl. Phys. B72, 509 (1974).

[c5] P. Frampton, Phys. Rev. D 12, 538 (1975).

[c6] I. Bars, Phys. Rev. Lett. 36, 1521 (1976).

[c7] I. Bars and A. Hanson, Phys. Rev. D 13, 1744 (1976).

[c8] R. C. Giles and S.-H. H. Tye, Phys. Rev. D 16, 1079 (1977).

[c9] K. Kikkawa and M. Sato, Phys. Rev. Lett. 38, 1309 (1977); K. Kikkawa, T. Kotani, and M. Sato, Phys. Rev. D 18, 2606 (1978).

[c10] M. Ida, Prog. Theor. Phys. 59, 1661 (1978).

[c11] K. Johnson and C. Nohl, Phys. Rev. D 19, 291 (1979).

[c12] F. Lizzi and C. Rosenzweig, Phys. Rev. D 31, 1685 (1985).

[c13] I. Yu. Kobzarev, B. V. Martemianov, and M. G. Shchepkin, Yad. Fiz. 44, 475 (1986); ibid.I. Yu. Kobzarev, N. A. Kondratiuk, B. V. Martemianov, and M. G. Shchepkin, 46, 1552 (1987).

[c14] A. V. Batunin and O. L. Zorin, IHEP Report No. 89-87, Serpukhov, 1989.

[c15] B. M. Barbashov, Report No. JINR E2-94-444, Dubna, 1994; Strong Interactions at Long Distances, Proceedings of the Conference, edited by L. Jenkovsky (Hadronic, Palm Harbor, FL, 1995), p. 257.

[c16] V. V. Nesterenko, Z. Phys. C 47, 111 (1990). In this paper the conclusion about absence of the radial quark motion on a straight-line string in the three-dimensional Minkowski space was also made.

[c17] S. Godfrey and N. Isgur, Phys. Rev. D 32, 189 (1985).

[c18] N. Mukunda, H. van Dam, and L. C. Biedenharn, Phys. Rev. D 22, 193 (1980).

[c19] R. R. Aldinger et al., Phys. Rev. D 29, 2828 (1984).

[c20] F. A. Berezin and M. S. Marinov, Ann. Phys. (N.Y.) 104, 336 (1977).

[c21] L. D. Soloviev, “Problems of Quantum Field Theory,” 10th International Conference (JINR E-2-96-369, Dubna, 1996), p. 75.

[c22] L. D. Soloviev, IHEP Report No. 96-67, Protvino, 1996.

[c23] S. Weinberg, Trans. NY Acad. Sci. 38, 185 (1977).

[c24] Particle Data Group, R. M. Barnett et al., Phys. Rev. D 54, 1 (1996).

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Relativistic quantum model of confinement and the current quark masses

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