New Value of the <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>α</mi></mrow><mrow><mn>3</mn></mrow></msup></mrow></math></span> Electron Anomalous Magnetic Moment

Toichiro Kinoshita

doi:10.1103/PhysRevLett.75.4728

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New Value of the $α^{3}$ Electron Anomalous Magnetic Moment

Toichiro Kinoshita

Newman Laboratory, Cornell University, Ithaca, New York 14853

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Phys. Rev. Lett. 75, 4728 – Published 25 December, 1995

DOI: https://doi.org/10.1103/PhysRevLett.75.4728

Abstract

Highly accurate numerical evaluation of the sixth-order term of the electron anomalous magnetic moment $a_{e}$ has detected an error in the analytic value of a fourth-order infrared-divergent integral, which is needed to obtain the best estimate of the $α^{3}$ term as a combination of analytic values of 67 Feynman diagrams and numerical values of 5 diagrams for which no analytic results are known. Correction of this error leads to a small but significant revision of the $α^{3}$ term. As a consequence the fine structure constant $α$ determined from theory and experiment of $a_{e}$ is reduced by $55 \times 10^{- 9}$ .

References (15)

R. S. Van Dyck, Jr., P. B. Schwinberg, and H. G. Dehmelt, Phys. Rev. Lett. 59, 26 (1987).
R. S. Van Dyck, Jr., P. B. Schwinberg, and H. G. Dehmelt, in G. Gabrielse and J. TanThe Electron, D. Hestenes and A. Weingartshofer ( P. BermanKluwer Academic Publishers, Netherlands,1991); , in Cavity Quantum Electrodynamics, edited by (Academic, New York,1992).
T. Kinoshita, in Quantum Electrodynamics, T. Kinoshita (World Scientific, Singapore,1990), pp. 218–321.
For a review of earlier analytic results, see R. Z. Roskies, E. Remiddi, and M. J. Levine, in Quantum Electrodynamics, T. Kinoshita (World Scientific, Singapore,1990), pp. 162–217.
E. Remiddi and S. Laporta, Phys. Lett. B 265, 182 (1991) S. Laporta, Phys. Rev. D 47, 4793 (1993) Phys. Lett. B 343, 421 (1995).
J. A. Mignaco and E. Remiddi, Nuovo Cimento 60A, 519 (1969) R. Barbieri and E. Remiddi, Nucl. Phys. B90, 233 (1975) R. Barbieri, M. Caffo, and E. Remiddi, Phys. Lett. 57B, 460 (1975).
G. P. Lepage, J. Comput. Phys. 27, 192 (1978).
P. Cvitanovic and T. Kinoshita, Phys. Rev. D 10, 4007 (1974).
Unpublished calculation by J. Sapirstein, 1975.
M. E. Cage et al., IEEE Trans. Instrum. Meas. 38, 284 (1989).
E. R. Williams et al., IEEE Trans. Instrum. Meas. 38, 233 (1989).
E. Krueger, W. Nistler, and W. Weirauch, Metrologia 32, 117 (1995).
The $\ln λ$ terms of $I_{4 x}, I_{4 l}, I_{4 c},$ and $I_{4 s}$ are derived from A, B, C, D in Table 2 of the paper by R. Z. Roskies, E. Remiddi, and M. J. Levine quoted in [[4]].
J. Sapirstein (private communication).
T. Kinoshita, IEEE Trans. Instrum. Meas. 44, 498 (1995).

[c1] R. S. Van Dyck, Jr., P. B. Schwinberg, and H. G. Dehmelt, Phys. Rev. Lett. 59, 26 (1987).

[c2] R. S. Van Dyck, Jr., P. B. Schwinberg, and H. G. Dehmelt, in G. Gabrielse and J. TanThe Electron, D. Hestenes and A. Weingartshofer ( P. BermanKluwer Academic Publishers, Netherlands,1991); , in Cavity Quantum Electrodynamics, edited by (Academic, New York,1992).

[c3] T. Kinoshita, in Quantum Electrodynamics, T. Kinoshita (World Scientific, Singapore,1990), pp. 218–321.

[c4] For a review of earlier analytic results, see R. Z. Roskies, E. Remiddi, and M. J. Levine, in Quantum Electrodynamics, T. Kinoshita (World Scientific, Singapore,1990), pp. 162–217.

[c5] E. Remiddi and S. Laporta, Phys. Lett. B 265, 182 (1991) S. Laporta, Phys. Rev. D 47, 4793 (1993) Phys. Lett. B 343, 421 (1995).

[c6] J. A. Mignaco and E. Remiddi, Nuovo Cimento 60A, 519 (1969) R. Barbieri and E. Remiddi, Nucl. Phys. B90, 233 (1975) R. Barbieri, M. Caffo, and E. Remiddi, Phys. Lett. 57B, 460 (1975).

[c7] G. P. Lepage, J. Comput. Phys. 27, 192 (1978).

[c8] P. Cvitanovic and T. Kinoshita, Phys. Rev. D 10, 4007 (1974).

[c9] Unpublished calculation by J. Sapirstein, 1975.

[c10] M. E. Cage et al., IEEE Trans. Instrum. Meas. 38, 284 (1989).

[c11] E. R. Williams et al., IEEE Trans. Instrum. Meas. 38, 233 (1989).

[c12] E. Krueger, W. Nistler, and W. Weirauch, Metrologia 32, 117 (1995).

[c13] The $\ln λ$ terms of $I_{4 x}, I_{4 l}, I_{4 c},$ and $I_{4 s}$ are derived from A, B, C, D in Table 2 of the paper by R. Z. Roskies, E. Remiddi, and M. J. Levine quoted in [[4]].

[c14] J. Sapirstein (private communication).

[c15] T. Kinoshita, IEEE Trans. Instrum. Meas. 44, 498 (1995).

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New Value of the $α^{3}$ Electron Anomalous Magnetic Moment

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New Value of the α3 Electron Anomalous Magnetic Moment

Abstract

References (15)

New Value of the $α^{3}$ Electron Anomalous Magnetic Moment