Eighth-order QED contribution to the anomalous magnetic moment of the muon

T. Kinoshita; B. Nizic; Y. Okamoto

doi:10.1103/PhysRevD.41.593

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Eighth-order QED contribution to the anomalous magnetic moment of the muon

T. Kinoshita, B. Nizic^*, and Y. Okamoto^†

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

^*Present address: Physics Department, Institute R. Boskovic, 41001 Zagreb, Yugoslavia.
^†Present address: Physics Department, Nara Women's University, Nara 630, Japan.

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Phys. Rev. D 41, 593 – Published 15 January, 1990

DOI: https://doi.org/10.1103/PhysRevD.41.593

Abstract

We report a calculation of the eighth-order QED contribution to the muon anomalous magnetic moment $a_{μ}^{(8)}$ coming from 469 Feynman diagrams, all of which contain electron loops of vacuum-polarization type and/or light-by-light scattering type. Our result is $126.92 (41) {(\frac{α}{π})}^{4}$ . The error represents the estimated accuracy (90% confidence limit) of the required numerical integration. We also report an estimate of the tenth-order contribution to $a_{μ}$ . Combining these with the lower-order results and the latest theoretical value for the electron anomaly $a_{e}$ , we find that the QED contribution to the muon anomaly is given by $a_{μ}^{QED} = 1165846947 (46) (28) \times 10^{- 12}$ , where the first error is an estimate of theoretical uncertainty and the second reflects the measurement uncertainty in $α$ . Including the hadronic and electroweak contributions, the best theoretical prediction for $a_{μ}$ available at present is $a_{μ}^{theory} = 116591920 (191) \times 10^{- 11}$ , where the error comes predominantly from the hadronic contribution.

References (34)

T. Kinoshita, B. Nizic, and Y. Okamoto, Phys. Rev. Lett. 52, 717 (1984)
L. Lyons, in Prog. Part. Nucl. Phys. 10, 227 (1983) F. M. Renard, Phys. Lett. 116B, 264 (1982)
J. A. Grifols, A. Mendez, and J. Sola, Phys. Rev. Lett. 57, 2348 (1986)
T. Kinoshita, B. Nizic, and Y. Okamoto, Phys. Rev. D 31, 2108 (1985)
T. Kinoshita and W. B. Lindquist, Phys. Rev. Lett. 47, 1573 (1981) [16]
B. E. Lautrup and E. de Rafael, Phys. Rev. 174, 1835 (1968)
Particle Data Group, G. P. Yost et al., Phys. Lett. B 204, 1 (1988)
H. Suura and E. Wichmann, Phys. Rev. 105, 1930 (1957) A. Peterman, ibid. 105, 1931 (1957) H. H. Elend, Phys. Lett. 20, 682 (1966) ibid.21, 720 (1966) G. W. Erickson and H. H. T. Liu, Report No. UCD-CNL-81, 1968 (unpublished)
J. Calmet et al., Rev. Mod. Phys. 49, 21 (1977)
J. Aldins, S. Brodsky, A. Dufner, and T. Kinoshita, Phys. Rev. D 1, 2378 (1970)
G. P. Lepage, J. Comput. Phys. 27, 192 (1978)
T. Kinoshita, Phys. Rev. Lett. 61, 2898 (1988)
M. A. Samuel and C. Chlouber, Phys. Rev. Lett. 36, 442 (1976)
T. Kinoshita, Phys. Rev. D 40, 1323 (1989)
M. E. Cage et al., IEEE Trans. Instrum. Meas. 38, 284 (1989)
T. Kinoshita, Metrologia 25, 233 (1988) T. Kinoshita and W. B. Lindquist (unpublished)
J. A. Casas, C. Lopez, and F. J. Yndurain, Phys. Rev. D 32, 736 (1985) L. M. Kurdadze et al., Yad. Fiz. 40, 451 (1984) [Sov. J. Nucl. Phys. 40, 286 (1984)]
R. Jackiw and S. Weinberg, Phys. Rev. D 5, 2473 (1972) I. Bars and M. Yoshimura, ibid. 6, 374 (1972) K. Fujikawa, B. W. Lee, and A. I. Sanda, ibid. 6, 2923 (1972) W. A. Bardeen, R. Gastmans, and B. E. Lautrup, Nucl. Phys. B46, 319 (1972)
J. Lee-Franzini, in Proceedings of the XXIV International Conference on High Energy Physics, Munich, West Germany, 1988, edited by R. Kotthaus and J. H. Kühn (Springer, Berlin, 1989), pp. 1432-1440
J. Bailey et al., Phys. Lett. 68B, 191 (1977) F. J. M. Farley and E. Picasso, Annu. Rev. Nucl. Sci. 29, 243 (1979)
V. W. Hughes and T. Kinoshita, Comments Nucl. Part. Phys. 14, 341 (1985) M. Greco, Frascati Report No. LNF-88/24(P), 1988 (unpublished)
T. Kinoshita and W. B. Lindquist, Phys. Rev. D 27, 867 (1983)
B. E. Lautrup, in Proceedings of the Second Colloquium in Advanced Computer Methods in Theoretical Physics, Marseille, France, 1971, edited by A. Visconti (University of Marseille, Marseille, 1971)
T. Kinoshita and W. B. Lindquist, Phys. Rev. D 27, 853 (1983)
[27] [22,26] Cornell Report No. CLNS 88/894 (unpublished)
T. Kinoshita and W. B. Lindquist, Phys. Rev. D 27, 877 (1983)
T. Kinoshita and W. B. Lindquist, Phys. Rev. D 27, 886 (1983)
[29]
T. Kinoshita and W. B. Lindquist, Phys. Rev. D 39, 2407 (1989)
T. Kinoshita, Nuovo Cimento B51, 140 (1967)
B. E. Lautrup and E. de Rafael, Nucl. Phys. B70, 317 (1974) ibid.B78, 576(E) (1974)
E. de Rafael and J. L. Rosner, Ann. Phys. (N.Y.) 82, 369 (1974)
B. E. Lautrup and E. de Rafael, Phys. Rev. 174, 1835 (1968) R. Barbieri and E. Remiddi, Nucl. Phys. B90, 233 (1975)
S. L. Adler, Phys. Rev. D 5, 3021 (1972)

[c1] T. Kinoshita, B. Nizic, and Y. Okamoto, Phys. Rev. Lett. 52, 717 (1984)

[c2] L. Lyons, in Prog. Part. Nucl. Phys. 10, 227 (1983) F. M. Renard, Phys. Lett. 116B, 264 (1982)

[c3] J. A. Grifols, A. Mendez, and J. Sola, Phys. Rev. Lett. 57, 2348 (1986)

[c4] T. Kinoshita, B. Nizic, and Y. Okamoto, Phys. Rev. D 31, 2108 (1985)

[c5] T. Kinoshita and W. B. Lindquist, Phys. Rev. Lett. 47, 1573 (1981) [16]

[c6] B. E. Lautrup and E. de Rafael, Phys. Rev. 174, 1835 (1968)

[c7] Particle Data Group, G. P. Yost et al., Phys. Lett. B 204, 1 (1988)

[c8] H. Suura and E. Wichmann, Phys. Rev. 105, 1930 (1957) A. Peterman, ibid. 105, 1931 (1957) H. H. Elend, Phys. Lett. 20, 682 (1966) ibid.21, 720 (1966) G. W. Erickson and H. H. T. Liu, Report No. UCD-CNL-81, 1968 (unpublished)

[c9] J. Calmet et al., Rev. Mod. Phys. 49, 21 (1977)

[c10] J. Aldins, S. Brodsky, A. Dufner, and T. Kinoshita, Phys. Rev. D 1, 2378 (1970)

[c11] G. P. Lepage, J. Comput. Phys. 27, 192 (1978)

[c12] T. Kinoshita, Phys. Rev. Lett. 61, 2898 (1988)

[c13] M. A. Samuel and C. Chlouber, Phys. Rev. Lett. 36, 442 (1976)

[c14] T. Kinoshita, Phys. Rev. D 40, 1323 (1989)

[c15] M. E. Cage et al., IEEE Trans. Instrum. Meas. 38, 284 (1989)

[c16] T. Kinoshita, Metrologia 25, 233 (1988) T. Kinoshita and W. B. Lindquist (unpublished)

[c17] J. A. Casas, C. Lopez, and F. J. Yndurain, Phys. Rev. D 32, 736 (1985) L. M. Kurdadze et al., Yad. Fiz. 40, 451 (1984) [Sov. J. Nucl. Phys. 40, 286 (1984)]

[c18] R. Jackiw and S. Weinberg, Phys. Rev. D 5, 2473 (1972) I. Bars and M. Yoshimura, ibid. 6, 374 (1972) K. Fujikawa, B. W. Lee, and A. I. Sanda, ibid. 6, 2923 (1972) W. A. Bardeen, R. Gastmans, and B. E. Lautrup, Nucl. Phys. B46, 319 (1972)

[c19] J. Lee-Franzini, in Proceedings of the XXIV International Conference on High Energy Physics, Munich, West Germany, 1988, edited by R. Kotthaus and J. H. Kühn (Springer, Berlin, 1989), pp. 1432-1440

[c20] J. Bailey et al., Phys. Lett. 68B, 191 (1977) F. J. M. Farley and E. Picasso, Annu. Rev. Nucl. Sci. 29, 243 (1979)

[c21] V. W. Hughes and T. Kinoshita, Comments Nucl. Part. Phys. 14, 341 (1985) M. Greco, Frascati Report No. LNF-88/24(P), 1988 (unpublished)

[c22] T. Kinoshita and W. B. Lindquist, Phys. Rev. D 27, 867 (1983)

[c23] B. E. Lautrup, in Proceedings of the Second Colloquium in Advanced Computer Methods in Theoretical Physics, Marseille, France, 1971, edited by A. Visconti (University of Marseille, Marseille, 1971)

[c24] T. Kinoshita and W. B. Lindquist, Phys. Rev. D 27, 853 (1983)

[c25] [27] [22,26] Cornell Report No. CLNS 88/894 (unpublished)

[c26] T. Kinoshita and W. B. Lindquist, Phys. Rev. D 27, 877 (1983)

[c27] T. Kinoshita and W. B. Lindquist, Phys. Rev. D 27, 886 (1983)

[c28] [29]

[c29] T. Kinoshita and W. B. Lindquist, Phys. Rev. D 39, 2407 (1989)

[c30] T. Kinoshita, Nuovo Cimento B51, 140 (1967)

[c31] B. E. Lautrup and E. de Rafael, Nucl. Phys. B70, 317 (1974) ibid.B78, 576(E) (1974)

[c32] E. de Rafael and J. L. Rosner, Ann. Phys. (N.Y.) 82, 369 (1974)

[c33] B. E. Lautrup and E. de Rafael, Phys. Rev. 174, 1835 (1968) R. Barbieri and E. Remiddi, Nucl. Phys. B90, 233 (1975)

[c34] S. L. Adler, Phys. Rev. D 5, 3021 (1972)

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Eighth-order QED contribution to the anomalous magnetic moment of the muon

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