Bag-inspired gluonic and relativistic effects in a harmonic-oscillator model

Avinash Sharma; Manmohan Gupta

doi:10.1103/PhysRevD.27.2182

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Bag-inspired gluonic and relativistic effects in a harmonic-oscillator model

Avinash Sharma and Manmohan Gupta

Department of Physics, Panjab University, Chandigarh-160014, India

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Phys. Rev. D 27, 2182 – Published 1 May, 1983

DOI: https://doi.org/10.1103/PhysRevD.27.2182

Abstract

The harmonic-oscillator (HO) quark model, wherein Pauli spinors are replaced by Dirac spinors and quark masses are less than $\frac{1}{3}$ of the nucleon mass, is studied in the spirit of the bag model. In particular, we have calculated $\frac{G_{A}}{G_{V}}$ and the magnetic moment and charge radius of the proton; the variation of these quantities with quark mass and spring constant is also investigated. In the case of the magnetic moment we find that the relativistic correction is of the right order of magnitude, while in the case of charge radius the result is better than the nonrelativistic HO value. For $\frac{G_{A}}{G_{V}}$ we find that the relativistic corrections bring the nonrelativistic value of 1.667 down to ∼ 1.50 only; reasons for this less-than-anticipated fall are investigated in detail. Furthermore, we have calculated certain gluon probability integrals; the trend of our results is the same as those of Golowich and of Close and Horgan.

References (27)

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[c1] M. Gell-Mann, Phys. Lett. 8, 214 (1964) G. Zwieg, CERN Report No. 8479-Th-412, 1964 (unpublished)

[c2] H. D. Politzer, Phys. Rep. 14C, (1974) W. Marciano and H. Pagels, ibid. 36C, (1978)

[c3] K. Wilson, Phys. Rev. D 10, 2445 (1974)

[c4] M. Creutz, Phys. Rev. D 21, 1006 (1978) ibid.21, 2308 (1978) Phys. Rev. Lett. 43, 553 (1979)

[c5] T. DeGrand, R. Jaffe, K. Johnson, and J. Kiskis, Phys. Rev. D 12, 2060 (1975) A. Chodos, R. L. Jaffe, K. Johnson, and C. B. Thorn, ibid. 10, 2599 (1974)

[c6] T. D. Lee, Phys. Rev. D 19, 1802 (1979)

[c7] W. Bardeen, M. Chanowitz, S. Drell, M. Weinstein, and T. M. Yen, Phys. Rev. D 11, 1094 (1975)

[c8] E. Golowich, Phys. Rev. D 12, 2108 (1975)

[c9] E. Golowich, Phys. Rev. D 18, 927 (1978)

[c10] F. E. Close and R. Horgan, Nucl. Phys. B164, 413 (1980)

[c11] C. Deter, Phys. Rev. D 17, 302 (1978) ibid.17, 323 (1978) P. Hasenfratz and J. Kuti, Phys. Rep. 40C, 75 (1978) P. Hasenfratz, R. Horgan, J. Kuti, and J. M. Richard, CERN Report Nos. TH. 3837 and 3838, 1978 (unpublished) W. Haxton and L. Heller, Los Alamos Report No. LA-UR-80-855, 1980 (unpublished)

[c12] T. DeGrand, in Baryon 1980, proceedings of IVth International Conference on Baryon Resonances, Toronto, edited by N. Isgur (Univ. of Toronto Press, Toronto, 1981), p. 209

[c13] O. W. Greenberg, Phys. Rev. Lett. 13, 598 (1964) R. H. Dalitz, in Proceedings of the XIIIth International Conference on High Energy Physics, Berkeley, 1966 (Univ. of California Press, Berkeley, 1967) H. Harari, in Proceedings of the Fourteenth International Conference on High Energy Physics, Vienna, 1968, edited by J. Prentki and J. Steinberger (CERN, Geneva, 1968) J. Rosner, in Proceedings of the XVIIth International Conference on High Energy Physics, London, 1974, edited by J. R. Smith (Rutherford Laboratory, Chilton, Didcot, Berkshire, England, 1974) R. P. Feynman, M. Kisslinger, and F. Ravndal, Phys. Rev. D 3, 2706 (1971) D. Faiman and A. W. Hendry, Phys. Rev. 173, 1720 (1968) ibid.180, 1572 (1969)

[c14] A. De Rújula, H. Georgi, and S. L. Glashow, Phys. Rev. D 12, 147 (1975)

[c15] N. Isgur and G. Karl, Phys. Rev. D 18, 4187 (1978) ibid.19, 2653 (1979) Roman Koniuk and N. Isgur, 21, 1868 (1980)

[c16] A. Le Yaouanc, L. Oliver, O. Pene, and J. C. Raynal, Phys. Rev. D 15, 844 (1977)

[c17] H. J. Lipkin, in Baryon 1980 ([12]), p. 461

[c18] P. L. Ferreira and N. Zagury, Lett. Nuovo Cimento 20, 511 (1977) P. L. Ferreira, J. A. Helayel, and N. Zagury, Nuovo Cimento 55A, 215 (1980) F. Ravndal, Phys. Lett. B113, 57 (1982)

[c19] A. N. Mitra and M. Ross, Phys. Rev. 158, 1630 (1967)

[c20] P. N. Bogoliubov, Ann. Inst. Henri Poincaré 8, 163 (1968)

[c21] A. N. Mitra and S. Sen, Lett. Nuovo Cimento 10, 685 (1974) J. L. Cortes and J. Sanchez Guilten, Phys. Rev. D 22, 1775 (1980)

[c22] Omitted endnote

[c23] M. Bohm, R. Huerta, and A. Zepeda, Phys. Rev. D 25, 223 (1982)

[c24] N. Isgur and G. Karl, Phys. Rev. D 21, 3175 (1980)

[c25] Particle Data Group, Rev. Mod. Phys. 45, S1 (1973)

[c26] N. Isgur, Phys. Rev. D 20, 1191 (1979)

[c27] F. Borkowski et al., Nucl. Phys. A222, 269 (1974)

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Bag-inspired gluonic and relativistic effects in a harmonic-oscillator model

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