Hyperfine splittings in heavy-quark systems

W. Buchmüller; Yee Jack Ng; S. -H. H. Tye

doi:10.1103/PhysRevD.24.3003

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Hyperfine splittings in heavy-quark systems

W. Buchmüller

Yee Jack Ng

S. -H. H. Tye

Fermi National Accelerator Laboratory, P. O. Box 500, Batavia, Illinois 60510

Institute of Field Physics, Department of Physics and Astronomy, University of North Carolina, Chapel Hill, North Carolina 27514

Newman Laboratory of Nuclear Studies, Cornell University, Ithaca, New York 14853

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Phys. Rev. D 24, 3003(R) – Published 1 December, 1981

DOI: https://doi.org/10.1103/PhysRevD.24.3003

Abstract

The hyperfine splittings in heavy-quark systems are calculated to fourth order in the strong coupling constant. The $ψ - η_{c}$ mass difference gives $Λ_{\overset{―}{MS}} = 0.16 \pm 0.02 \pm 0.07$ GeV ( $\overset{―}{MS}$ refers to the modified minimal-subtraction scheme) where the first uncertainty is experimental and the second is a crude estimate of the uncertainty arising from scheme dependence. From the $ϒ - η_{b}$ mass difference we expect a more reliable and accurate determination of $Λ$ .

References (16)

R. Barbieri, G. Curci, E. d'Emilio, and E. Remiddi, Nucl. Phys. B154, 535 (1979) R. Barbieri, M. Caffo, R. Gatto, and E. Remiddi, Phys. Lett. 95B, 93 (1980) K. Hagiwara, C. B. Kim, and T. Yoshino, Nucl. Phys. B. 177, 461 (1981)
W. Buchmüller and S.-H. H. Tye, Phys. Rev. D 24, 132 (1981)
P. Mackenzie and P. Lepage, Phys. Rev. Lett. 47, 1244 (1981)
E. Eichten and F. Feinberg, Phys. Rev. D 23, 2724 (1981) A. Duncan, ibid. 13, 2866 (1976)
E. Eichten, K. Gottfried, T. Kinoshita, K. D. Lane, and T. M. Yan, Phys. Rev. D 17, 3090 (1978) ibid.21, 203 (1980) C. Quigg and J. L. Rosner, ibid. 23, 2625 (1981)
G.'t Hooft, Nucl. Phys. B61, 455 (1973) G.'t Hooft and M. Veltman, ibid. B44, 189 (1972)
W. A. Bardeen, A. J. Buras, D. W. Duke, and T. Muta, Phys. Rev. D 18, 3998 (1978) A. J. Buras, Rev. Mod. Phys. 52, 199 (1980) W. Celmaster and R. J. Gonsalves, Phys. Rev. D 20, 1420 (1979)
M. Dine, Yale University thesis, 1978 (unpublished) Phys. Lett. 81B, 339 (1979)
H. J. Schnitzer, Phys. Rev. D 19, 1566 (1979)
J.-M. Richard and D. P. Sidhu, Phys. Lett. 83B, 362 (1979)
C. G. Callan, R. Dashen, D. J. Gross, F. Wilczek, and A. Zee, Phys. Rev. D 18, 4684 (1978) [4] M. Shifman et al., Phys. Lett. 77B, 80 (1978)
Omitted endnote
[2]
[2], Appendix B [1]
K. Berkelman, in High Energy Physics—1980, proceedings of the XXth International Conference, Madison, Wisconsin, edited by L. Durand and L. G. Pondrom (AIP, New York, 1981)
G. Grunberg, Phys. Lett. 95B, 70 (1980) P. M. Stevenson, Phys. Rev. D 23, 2916 (1981)

[c1] R. Barbieri, G. Curci, E. d'Emilio, and E. Remiddi, Nucl. Phys. B154, 535 (1979) R. Barbieri, M. Caffo, R. Gatto, and E. Remiddi, Phys. Lett. 95B, 93 (1980) K. Hagiwara, C. B. Kim, and T. Yoshino, Nucl. Phys. B. 177, 461 (1981)

[c2] W. Buchmüller and S.-H. H. Tye, Phys. Rev. D 24, 132 (1981)

[c3] P. Mackenzie and P. Lepage, Phys. Rev. Lett. 47, 1244 (1981)

[c4] E. Eichten and F. Feinberg, Phys. Rev. D 23, 2724 (1981) A. Duncan, ibid. 13, 2866 (1976)

[c5] E. Eichten, K. Gottfried, T. Kinoshita, K. D. Lane, and T. M. Yan, Phys. Rev. D 17, 3090 (1978) ibid.21, 203 (1980) C. Quigg and J. L. Rosner, ibid. 23, 2625 (1981)

[c6] G.'t Hooft, Nucl. Phys. B61, 455 (1973) G.'t Hooft and M. Veltman, ibid. B44, 189 (1972)

[c7] W. A. Bardeen, A. J. Buras, D. W. Duke, and T. Muta, Phys. Rev. D 18, 3998 (1978) A. J. Buras, Rev. Mod. Phys. 52, 199 (1980) W. Celmaster and R. J. Gonsalves, Phys. Rev. D 20, 1420 (1979)

[c8] M. Dine, Yale University thesis, 1978 (unpublished) Phys. Lett. 81B, 339 (1979)

[c9] H. J. Schnitzer, Phys. Rev. D 19, 1566 (1979)

[c10] J.-M. Richard and D. P. Sidhu, Phys. Lett. 83B, 362 (1979)

[c11] C. G. Callan, R. Dashen, D. J. Gross, F. Wilczek, and A. Zee, Phys. Rev. D 18, 4684 (1978) [4] M. Shifman et al., Phys. Lett. 77B, 80 (1978)

[c12] Omitted endnote

[c13] [2]

[c14] [2], Appendix B [1]

[c15] K. Berkelman, in High Energy Physics—1980, proceedings of the XXth International Conference, Madison, Wisconsin, edited by L. Durand and L. G. Pondrom (AIP, New York, 1981)

[c16] G. Grunberg, Phys. Lett. 95B, 70 (1980) P. M. Stevenson, Phys. Rev. D 23, 2916 (1981)

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Hyperfine splittings in heavy-quark systems

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