Nonperturbative self-consistent unitary loop corrections to Skyrmion masses

Louis A. P. Balázs

doi:10.1103/PhysRevD.41.1702

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Nonperturbative self-consistent unitary loop corrections to Skyrmion masses

Louis A. P. Balázs

Department of Physics, Purdue University, West Lafayette, Indiana 47907

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Phys. Rev. D 41, 1702 – Published 1 March, 1990

DOI: https://doi.org/10.1103/PhysRevD.41.1702

Abstract

Quantum chromodynamics (QCD) effectively reduces to a nonlinear meson theory in the color-number $N_{c} \to \infty$ limit. The nucleon and $Δ$ masses arising as solitons from such a theory usually turn out to be too large if phenomenological values are used for the meson parameters. Within a static-baryon approximation, however, we find that soft nonperturbative self-consistent unitary hadron-loop corrections (corresponding to quark-loop higher- $\frac{1}{N_{c}}$ orders in QCD) can lower these masses by the kind of magnitude needed to make them consistent with experiment, whereas a first-order $\frac{1}{N_{c}}$ correction is much smaller.

References (11)

T. H. R. Skyrme, Proc. R. Soc. London A260, 127 (1961) A. P. Balachandran, V. P. Nair, S. G. Rajeev, and A. Stern, Phys. Rev. Lett. 49, 1124 (1982)
E. Witten, Nucl. Phys. B223, 422 (1983) ibid.B223, 433 (1983) G. Adkins, C. Nappi, and E. Witten, ibid. B228, 552 (1983)
M. Mashaal, T. N. Pham, and Tran N. Truong, Phys. Rev. Lett. 56, 436 (1986) Ulf-G. Meissner, A. Kaiser, A. Wirzba, and W. Weise, ibid. 57, 1676 (1986)
M. Lacombe, B. Loiseau, R. Vinh Mau, and W. N. Cottingham, Phys. Rev. D 38, 1491 (1988)
A. Patel, R. Gupta, G. W. Kilcup, and S. R. Sharpe, Phys. Lett. B 225, 398 (1989)
L. A. P. Balázs, Phys. Rev. D 34, 2876 (1986) ibid.39, 1002 (1989)
S. N. Biswas and L. Balázs, Phys. Rev. 156, 1511 (1967)
L. A. P. Balázs, and J. M. Cornwall, Phys. Rev. 160, 1313 (1967)
P. Jain, J. Schechter, and R. Sorkin, Phys. Rev. D 39, 998 (1989)
P. H. Frampton, Dual Resonance Models and Superstrings (World Scientific, Singapore, 1986), pp. 22-28
R. Eden, P. Landshoff, D. Olive, and J. C. Polkinghorne, The Analytic S-Matrix (Cambridge University Press, Cambridge, England, 1980), pp. 132-136

[c1] T. H. R. Skyrme, Proc. R. Soc. London A260, 127 (1961) A. P. Balachandran, V. P. Nair, S. G. Rajeev, and A. Stern, Phys. Rev. Lett. 49, 1124 (1982)

[c2] E. Witten, Nucl. Phys. B223, 422 (1983) ibid.B223, 433 (1983) G. Adkins, C. Nappi, and E. Witten, ibid. B228, 552 (1983)

[c3] M. Mashaal, T. N. Pham, and Tran N. Truong, Phys. Rev. Lett. 56, 436 (1986) Ulf-G. Meissner, A. Kaiser, A. Wirzba, and W. Weise, ibid. 57, 1676 (1986)

[c4] M. Lacombe, B. Loiseau, R. Vinh Mau, and W. N. Cottingham, Phys. Rev. D 38, 1491 (1988)

[c5] A. Patel, R. Gupta, G. W. Kilcup, and S. R. Sharpe, Phys. Lett. B 225, 398 (1989)

[c6] L. A. P. Balázs, Phys. Rev. D 34, 2876 (1986) ibid.39, 1002 (1989)

[c7] S. N. Biswas and L. Balázs, Phys. Rev. 156, 1511 (1967)

[c8] L. A. P. Balázs, and J. M. Cornwall, Phys. Rev. 160, 1313 (1967)

[c9] P. Jain, J. Schechter, and R. Sorkin, Phys. Rev. D 39, 998 (1989)

[c10] P. H. Frampton, Dual Resonance Models and Superstrings (World Scientific, Singapore, 1986), pp. 22-28

[c11] R. Eden, P. Landshoff, D. Olive, and J. C. Polkinghorne, The Analytic S-Matrix (Cambridge University Press, Cambridge, England, 1980), pp. 132-136

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Nonperturbative self-consistent unitary loop corrections to Skyrmion masses

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