Mass spectrum of low-lying baryons in the ground state in a relativistic potential model of independent quarks with chiral symmetry

N. Barik; B. K. Dash

doi:10.1103/PhysRevD.33.1925

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Mass spectrum of low-lying baryons in the ground state in a relativistic potential model of independent quarks with chiral symmetry

N. Barik and B. K. Dash

Department of Physics, Utkal University, Bhubaneswar 751004, Orissa, India

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Phys. Rev. D 33, 1925 – Published 1 April, 1986

DOI: https://doi.org/10.1103/PhysRevD.33.1925

Abstract

Under the assumption that baryons are an assembly of independent quarks, confined in a first approximation by an effective potential U(r)=1/2(1+ $γ^{0}$ )( ${ar}^{2}$ + $V_{0}$ ) which presumably represents the nonperturbative gluon interactions, the mass spectrum of the low-lying ground-state baryons has been calculated by considering perturbatively the contributions of the residual quark-pion coupling arising out of the requirement of chiral symmetry and that of the quark-gluon coupling due to one-gluon exchange over and above the necessary center-of-mass correction. The physical masses of the baryons so obtained agree quite well with the corresponding experimental value. The strong coupling constant $α_{c}$ =0.58 required here to describe the QCD mass splittings is quite consistent with the idea of treating one-gluon-exchange effects in lowest-order perturbation theory.

References (16)

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[c1] N. Isgur and G. Karl, Phys. Rev. D 18, 4187 (1978); ibid. 20, 1191 (1979); Y. Nogami and N. Ohtsuka, ibid. 26, 261 (1982).

[c2] A. Chodos, R. L. Jaffe, K. Johnson, C. B. Thorn and V. F. Weisskopf, Phys. Rev. D 9, 3471 (1974).

[c3] A. Chodos, R. L. Jaffe, K. Johnson and C. B. Thorn, Phys. Rev. D 10, 2599 (1974).

[c4] T. DeGrand, R. L. Jaffe, K. Johnson and J. Kiskis, Phys. Rev. D 12, 2060 (1975).

[c5] A. W. Thomas, Adv. Nucl. Phys. 13, 1 (1983), and references cited therein.

[c6] T. J. Goldman and R. W. Haymaker, Phys. Lett. 100B, 276 (1981); Phys. Rev. D 24, 724 (1981).

[c7] R. Tegen, R. Brockmann and W. Weise, Z. Phys. A 307, 339 (1982); R. Tegen, M. Schedle and W. Weise, Phys. Lett. 125B, 9 (1983); R. Tegen and W. Weise, Z. Phys. A 314, 357 (1983).

[c8] Y. Nambu and G. Jona-Lasinio, Phys. Rev. 112, 345 (1961); ibid. 124, 246 (1961); R. Brockmann, W. Weise and E. Werner, Phys. Lett. 122B, 201 (1983).

[c9] N. Barik, B. K. Dash and M. Das, Phys. Rev. D 31, 1652 (1985); ibid. 32, 1725 (1985).

[c10] N. Barik and B. K. Dash, Pramana 24, 707 (1985).

[c11] A. Suzuki and R. K. Bhaduri, Phys. Lett. 125B, 347 (1983).

[c12] E. Peirels and J. Yoccoz, Proc. Phys. Soc. London 70, 381 (1957); J. F. Donoghue and K. Johnson, Phys. Rev. D 21, 1975 (1980); D. L. Hill and J. A. Wheeler, Phys. Rev. 89, 1102 (1953); C. W. Wong, Phys. Rep. 15C, 283 (1975).

[c13] C. W. Wong, Phys. Rev. D 24, 1416 (1981); I. Duck, Phys. Lett. 64B, 163 (1976); ibid. 77B, 223 (1978).

[c14] A. Chodos and C. B. Thorn, Phys. Rev. D 12, 2733 (1975); G. E. Brown, M. Rho and V. Vento, Phys. Lett. 84B, 383 (1979); G. E. Brown and M. Rho, ibid. 82B, 177 (1979); V. Vento, J. C. Jun, E. M. Nyman, M. Rho and G. E. Brown, Nucl. Phys. A345, 413 (1980); S. Théberge, A. W. Thomas and G. A. Miller, Phys. Rev. D 22, 2238 (1980); ibid. 23, 2106(E) (1981); A. W. Thomas, S. Théberge and G. A. Miller, ibid. 24, 216 (1981).

[c15] A. W. Thomas, Adv. Nucl. Phys. 13, 1 (1983).

[c16] S. Théberge, G. A. Miller and A. W. Thomas, Can. J. Phys. 60, 59 (1982).

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Mass spectrum of low-lying baryons in the ground state in a relativistic potential model of independent quarks with chiral symmetry

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