Nucleon magnetic moments beyond the perturbative chiral regime

Derek B. Leinweber; Ding H. Lu; Anthony W. Thomas

doi:10.1103/PhysRevD.60.034014

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Nucleon magnetic moments beyond the perturbative chiral regime

Derek B. Leinweber, Ding H. Lu, and Anthony W. Thomas

Department of Physics and Mathematical Physics and Special Research Centre for the Subatomic Structure of Matter, University of Adelaide, Australia 5005

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Phys. Rev. D 60, 034014 – Published 7 July, 1999

DOI: https://doi.org/10.1103/PhysRevD.60.034014

Abstract

The quark mass dependence of nucleon magnetic moments is explored over a wide range. Quark masses currently accessible to lattice QCD, which lie beyond the regime of chiral perturbation theory $(χ PT)$ , are accessed via the cloudy bag model (CBM). The latter reproduces the leading nonanalytic behavior of $χ PT$ , while modeling the internal structure of the hadron under investigation. We find that the predictions of the CBM are succinctly described by the simple formula $μ_{N} {(m}_{π}) = μ_{N}^{(0)} / (1 + α m_{π} + β m_{π}^{2})$ , which reproduces the lattice data, as well as the leading nonanalytic behavior of $χ PT$ . As this form also incorporates the anticipated Dirac moment behavior in the limit $m_{π} \to \infty$ , it constitutes a powerful method for extrapolating lattice results to the physical mass regime.

References (28)

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D. B. Leinweber and T. D. Cohen, Phys. Rev. D 47, 2147 (1993); A. W. Thomas, Aust. J. Phys. 44, 173 (1991).
M. F. L. Golterman, Acta Phys. Pol. B 25, 1731 (1994).
J. N. Labrenz and S. R. Sharpe, Nucl. Phys. B (Proc. Suppl.) 34, 335 (1994).
C. Bernard and M. Golterman, Phys. Rev. D 46, 853 (1992).
S. R. Sharpe, Phys. Rev. D 46, 3146 (1992).
B. Holstein, in Future Directions in Quark Nuclear Physics, CSSM, Adelaide, SA, 1998, edited by K. Tsushima and A. W. Thomas (World Scientific, Singapore, 1998), nucl-th/9806037.
P. Langacker and H. Pagels, Phys. Rev. D 8, 4595 (1973).
S. Weinberg, Physica A 96, 327 (1979).
J. Gasser and H. Leutwyler, Ann. Phys. (N.Y.) 158, 142 (1984).
J. Gasser, M. E. Sainio, and A. Suarc, Nucl. Phys. B307, 779 (1988).
M. Butler, D. B. Leinweber, and R. Springer (unpublished).
E. Jenkins, M. Luke, A. V. Manohar, and M. J. Savage, Phys. Lett. B 302, 482 (1993); ibid.388, 866(E) (1996).
L. Durand and P. Ha, Phys. Rev. D 58, 013010 (1998).
D. B. Leinweber, R. M. Woloshyn, and T. Draper, Phys. Rev. D 43, 1659 (1991).
W. Wilcox, T. Draper, and K. F. Liu, Phys. Rev. D 46, 1109 (1992).
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A. W. Thomas, in Advances in Nuclear Physics, edited by J. Negle and E. Vogt (Plenum, New York, 1984), Vol. 13, p. 1; G. A. Miller, Int. Rev. Nucl. Phys. 2, 90 (1984).
Magnetic moment contributions from the coupling of the electromagnetic current directly to sea-quark loops are neglected in these simulations. However, the net effect from u, d, and s sea-quark loops is small due to approximate SU(3)-flavor symmetry where the net loop contribution vanishes.
S. Cabasino et al., Nucl. Phys. B (Proc. Suppl.) 20, 399 (1991).
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D. H. Lu, A. W. Thomas, and A. G. Williams, Phys. Rev. C 57, 2628 (1998).
S. Théberge and A. W. Thomas, Nucl. Phys. A393, 252 (1983).
S. Aoki et al., in Lattice ’97, Proceedings of XVth International Symposium on Lattice Field Theory, Edinburgh, UK, 1997, edited by C. T. H. Davies et al. [Nucl. Phys. B (Proc. Suppl.) 60A, 14 (1998)].
T. D. Cohen and D. B. Leinweber, Comments Nucl. Part. Phys. 21, 137 (1993).
This dependence on $χ PT$ will eventually be alleviated as better lattice data become available at smaller quark masses, allowing a three parameter fit of Eq. (4).

[c1] Lattice ’98, Proceedings of the International Symposium, Boulder, Colorado, 1998, edited by T. DeGrand, C. DeTar, R. Sugar, and D. Toussaint, [Nucl. Phys. B (Proc. Suppl.), (in press)].

[c2] D. B. Leinweber and T. D. Cohen, Phys. Rev. D 47, 2147 (1993); A. W. Thomas, Aust. J. Phys. 44, 173 (1991).

[c3] M. F. L. Golterman, Acta Phys. Pol. B 25, 1731 (1994).

[c4] J. N. Labrenz and S. R. Sharpe, Nucl. Phys. B (Proc. Suppl.) 34, 335 (1994).

[c5] C. Bernard and M. Golterman, Phys. Rev. D 46, 853 (1992).

[c6] S. R. Sharpe, Phys. Rev. D 46, 3146 (1992).

[c7] B. Holstein, in Future Directions in Quark Nuclear Physics, CSSM, Adelaide, SA, 1998, edited by K. Tsushima and A. W. Thomas (World Scientific, Singapore, 1998), nucl-th/9806037.

[c8] P. Langacker and H. Pagels, Phys. Rev. D 8, 4595 (1973).

[c9] S. Weinberg, Physica A 96, 327 (1979).

[c10] J. Gasser and H. Leutwyler, Ann. Phys. (N.Y.) 158, 142 (1984).

[c11] J. Gasser, M. E. Sainio, and A. Suarc, Nucl. Phys. B307, 779 (1988).

[c12] M. Butler, D. B. Leinweber, and R. Springer (unpublished).

[c13] E. Jenkins, M. Luke, A. V. Manohar, and M. J. Savage, Phys. Lett. B 302, 482 (1993); ibid.388, 866(E) (1996).

[c14] L. Durand and P. Ha, Phys. Rev. D 58, 013010 (1998).

[c15] D. B. Leinweber, R. M. Woloshyn, and T. Draper, Phys. Rev. D 43, 1659 (1991).

[c16] W. Wilcox, T. Draper, and K. F. Liu, Phys. Rev. D 46, 1109 (1992).

[c17] S. J. Dong, K. F. Liu, and A. G. Williams, Phys. Rev. D 58, 074504 (1998).

[c18] S. Théberge, A. W. Thomas, and G. A. Miller, Phys. Rev. D 22, 2838 (1980); ibid.23, 2106(E) (1981).

[c19] A. W. Thomas, in Advances in Nuclear Physics, edited by J. Negle and E. Vogt (Plenum, New York, 1984), Vol. 13, p. 1; G. A. Miller, Int. Rev. Nucl. Phys. 2, 90 (1984).

[c20] Magnetic moment contributions from the coupling of the electromagnetic current directly to sea-quark loops are neglected in these simulations. However, the net effect from u, d, and s sea-quark loops is small due to approximate SU(3)-flavor symmetry where the net loop contribution vanishes.

[c21] S. Cabasino et al., Nucl. Phys. B (Proc. Suppl.) 20, 399 (1991).

[c22] B. Efron, SIAM (Soc. Ind. Appl. Math.) Rev. 21, 460 (1979).

[c23] A. Chodos et al., Phys. Rev. D 9, 3471 (1974); ibid., 10, 2599 (1974); ibid.T. A. DeGrand et al., 12, 2060 (1975).

[c24] D. H. Lu, A. W. Thomas, and A. G. Williams, Phys. Rev. C 57, 2628 (1998).

[c25] S. Théberge and A. W. Thomas, Nucl. Phys. A393, 252 (1983).

[c26] S. Aoki et al., in Lattice ’97, Proceedings of XVth International Symposium on Lattice Field Theory, Edinburgh, UK, 1997, edited by C. T. H. Davies et al. [Nucl. Phys. B (Proc. Suppl.) 60A, 14 (1998)].

[c27] T. D. Cohen and D. B. Leinweber, Comments Nucl. Part. Phys. 21, 137 (1993).

[c28] This dependence on $χ PT$ will eventually be alleviated as better lattice data become available at smaller quark masses, allowing a three parameter fit of Eq. (4).

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