Two-loop polarization contributions to radiative-recoil corrections to hyperfine splitting in muonium

Michael I. Eides; Howard Grotch; Valery A. Shelyuto

doi:10.1103/PhysRevD.65.013003

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Two-loop polarization contributions to radiative-recoil corrections to hyperfine splitting in muonium

Michael I. Eides^*

Howard Grotch^†

Valery A. Shelyuto^‡

Department of Physics and Astronomy, University of Kentucky, Lexington, Kentucky 40506
Petersburg Nuclear Physics Institute, Gatchina, St. Petersburg 188350, Russia

Department of Physics and Astronomy, University of Kentucky, Lexington, Kentucky 40506

D. I. Mendeleev Institute of Metrology, St. Petersburg 198005, Russia

^*Email address: eides@pa.uky.edu, eides@thd.pnpi.spb.ru
^†Email address: asdean@pop.uky.edu
^‡Email address: shelyuto@vniim.ru

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Phys. Rev. D 65, 013003 – Published 7 December, 2001

DOI: https://doi.org/10.1103/PhysRevD.65.013003

Abstract

We calculate radiative-recoil corrections of order $α^{2} (Z α {) (m / M) E}_{F}$ to hyperfine splitting in muonium generated by the diagrams with electron and muon polarization loops. These corrections are enhanced by the large logarithm of the electron-muon mass ratio. The leading logarithm cubed and logarithm squared contributions were obtained a long time ago. The single-logarithmic and nonlogarithmic contributions calculated here improve the theory of hyperfine splitting, and affect the value of the electron-muon mass ratio extracted from the experimental data on the muonium hyperfine splitting.

References (17)

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G. Li, M. A. Samuel, and M. I. Eides, Phys. Rev. A 47, 876 (1993).
M. I. Eides, H. Grotch, and V. A. Shelyuto, Phys. Rep. 342, 63 (2001).
E. A. Terray and D. R. Yennie, Phys. Rev. Lett. 48, 1803 (1982).
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M. I. Eides, S. G. Karshenboim, and V. A. Shelyuto, Phys. Lett. B 229, 285 (1989); Pis’ma Zh. Éksp. Teor. Fiz. 50, 3 (1989) [JETP Lett. 50, 1 (1989)]; Yad. Fiz. 50, 1636 (1989) [Sov. J. Nucl. Phys. 50, 1015 (1989)].
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[c1] M. I. Eides and V. A. Shelyuto, Phys. Lett. 146B, 241 (1984).

[c2] M. I. Eides, S. G. Karshenboim, and V. A. Shelyuto, Phys. Lett. B 216, 405 (1989); Yad. Fiz. 49, 493 (1989) [Sov. J. Nucl. Phys. 49, 309 (1989)].

[c3] S. G. Karshenboim, M. I. Eides, and V. A. Shelyuto, Yad. Fiz. 52, 1066 (1990) [Sov. J. Nucl. Phys. 52, 679 (1990)].

[c4] S. L. Adler, Phys. Rev. 177, 2426 (1969).

[c5] G. Li, M. A. Samuel, and M. I. Eides, Phys. Rev. A 47, 876 (1993).

[c6] M. I. Eides, H. Grotch, and V. A. Shelyuto, Phys. Rep. 342, 63 (2001).

[c7] E. A. Terray and D. R. Yennie, Phys. Rev. Lett. 48, 1803 (1982).

[c8] J. R. Sapirstein, E. A. Terray, and D. R. Yennie, Phys. Rev. D 29, 2290 (1984).

[c9] M. I. Eides, S. G. Karshenboim, and V. A. Shelyuto, Phys. Lett. B 229, 285 (1989); Pis’ma Zh. Éksp. Teor. Fiz. 50, 3 (1989) [JETP Lett. 50, 1 (1989)]; Yad. Fiz. 50, 1636 (1989) [Sov. J. Nucl. Phys. 50, 1015 (1989)].

[c10] M. I. Eides, H. Grotch, and V. A. Shelyuto, Phys. Rev. D 58, 013008 (1998).

[c11] G. Kallen and A. Sabry, K. Dan. Vidensk. Selsk. Mat. Fys. Medd. 29, 17 (1955).

[c12] J. Schwinger, Particles, Sources and Fields (Addison-Wesley, Reading, MA, 1973), Vol. 2.

[c13] W. E. Caswell and G. P. Lepage, Phys. Rev. Lett. 41, 1092 (1978).

[c14] K. Melnikov and A. Yelkhovsky, Phys. Rev. Lett. 86, 1498 (2001).

[c15] R. J. Hill, Phys. Rev. Lett. 86, 3280 (2001).

[c16] W. Liu et al., Phys. Rev. Lett. 82, 711 (1999).

[c17] P. J. Mohr and B. N. Taylor, Rev. Mod. Phys. 72, 351 (2000).

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Two-loop polarization contributions to radiative-recoil corrections to hyperfine splitting in muonium

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