Apparatus-dependent contributions to <i>g-2</i>?

David G. Boulware; Lowell S. Brown; Taejin Lee

doi:10.1103/PhysRevD.32.729

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Apparatus-dependent contributions to g-2?

David G. Boulware, Lowell S. Brown, and Taejin Lee

Department of Physics, FM-15, University of Washington, Seattle, Washington 98195

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Phys. Rev. D 32, 729 – Published 1 August, 1985

DOI: https://doi.org/10.1103/PhysRevD.32.729

Abstract

The University of Washington g-2 experiments have progressed to the marvelous precision of $10^{12}$ in their measurement of the magnetic moment of the electron. A further improvement of a factor of 10 should occur in the near future. Concomitant with this accuracy is the necessity of understanding small corrections. These experiments employ a Penning trap whose electrodes behave as conducting walls for a microwave cavity. We investigate the effect of this cavity on the spin and cyclotron frequencies. Previous work, employing calculations that are not gauge invariant, implies that the present level of accuracy cannot be exceeded because of cavity effects on the spin-precession frequency. In contrast to this work, we find no significant correction to the spin-precession frequency, but we do find a correction to the cyclotron frequency which may be important.

References (9)

Reviews of this work are given by R. S. Van Dyck, Jr., P. B. Schwinberg, and H. G. Dehmelt, in New Frontiers in High Energy Physics, proceedings of Orbis Scientiae, Coral Gables, 1978, edited by A. Perlmutter and L. Scott (Plenum, New York, 1978); H. G. Dehmelt, in 1982/83 Yearbook of Science and Technology (McGraw-Hill, New York, 1983); in Atomic Physics 7, edited by D. K. Kleppner and F. M. Pipkin (Plenum, New York, 1981). An elementary account appears in P. Ekstrom and D. Wineland, Sci. Am. 243, 105 (1980). An exhaustive account of the theory of the experiment is given by L. S. Brown and G. Gabrielse (unpublished).
R. S. Van Dyck, Jr., P. B. Schwinberg, and H. G. Dehmelt, in Atomic Physics 9, edited by R. S. Van Dyck, Jr. and E. N. Fortson (World Scientific, Singapore, 1985).
E. Fischbach and N. Nakagawa, Phys. Rev. D 30, 2356 (1984).
G. Barton and H. Grotch, J. Phys. A 10, 1201 (1977).
(a) L. S. Brown, G. Gabrielse, K. Helmerson and J. Tan, Phys. Rev. Lett. 55, 44 (1985); (b) L. S. Brown, G. Gabrielse, K. Helmerson, and J. Tan (unpublished).
This has been seen experimentally by G. Gabrielse and H. G. Dehmelt [Phys. Rev. Lett. 55, 67 (1985)].
See, for example, G. W. Erickson and D. R. Yennie, Ann. Phys (N.Y.) 35, 271 (1965), Eq. (2.1).
See, for example, J. D. Jackson, Classical Electrodynamics, 2nd edition (Wiley, New York, 1975), Sec. 14.1, Eq. (14.14).
We neglect the radiative damping. It is not difficult to see that this damping, which shrinks the orbit but does not change the orientation of v vec (t) does not affect our result. The alteration of the cyclotron damping constant $γ_{c}$ caused by the plane can be computed in a similar way by taking the scalar product of Eq. (2.1) with v ${vec}_{0}$ (t) rather than with ρ ${vec}_{0}$ (t).

[c1] Reviews of this work are given by R. S. Van Dyck, Jr., P. B. Schwinberg, and H. G. Dehmelt, in New Frontiers in High Energy Physics, proceedings of Orbis Scientiae, Coral Gables, 1978, edited by A. Perlmutter and L. Scott (Plenum, New York, 1978); H. G. Dehmelt, in 1982/83 Yearbook of Science and Technology (McGraw-Hill, New York, 1983); in Atomic Physics 7, edited by D. K. Kleppner and F. M. Pipkin (Plenum, New York, 1981). An elementary account appears in P. Ekstrom and D. Wineland, Sci. Am. 243, 105 (1980). An exhaustive account of the theory of the experiment is given by L. S. Brown and G. Gabrielse (unpublished).

[c2] R. S. Van Dyck, Jr., P. B. Schwinberg, and H. G. Dehmelt, in Atomic Physics 9, edited by R. S. Van Dyck, Jr. and E. N. Fortson (World Scientific, Singapore, 1985).

[c3] E. Fischbach and N. Nakagawa, Phys. Rev. D 30, 2356 (1984).

[c4] G. Barton and H. Grotch, J. Phys. A 10, 1201 (1977).

[c5] (a) L. S. Brown, G. Gabrielse, K. Helmerson and J. Tan, Phys. Rev. Lett. 55, 44 (1985); (b) L. S. Brown, G. Gabrielse, K. Helmerson, and J. Tan (unpublished).

[c6] This has been seen experimentally by G. Gabrielse and H. G. Dehmelt [Phys. Rev. Lett. 55, 67 (1985)].

[c7] See, for example, G. W. Erickson and D. R. Yennie, Ann. Phys (N.Y.) 35, 271 (1965), Eq. (2.1).

[c8] See, for example, J. D. Jackson, Classical Electrodynamics, 2nd edition (Wiley, New York, 1975), Sec. 14.1, Eq. (14.14).

[c9] We neglect the radiative damping. It is not difficult to see that this damping, which shrinks the orbit but does not change the orientation of v vec (t) does not affect our result. The alteration of the cyclotron damping constant $γ_{c}$ caused by the plane can be computed in a similar way by taking the scalar product of Eq. (2.1) with v ${vec}_{0}$ (t) rather than with ρ ${vec}_{0}$ (t).

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Apparatus-dependent contributions to g-2?

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