Analytical calculations of fifth-order electromagnetic corrections to the anomalous magnetic moment of leptons within the Mellin-Barnes representation
https://doi.org/10.29235/1561-2430-2023-59-4-338-351
Abstract
We investigate the explicit, analytical expressions for the fifth-order electromagnetic corrections in the fine structure constant α to the anomalous magnetic moment of leptons aL (L = e, μ, τ) from diagrams with insertions of the vacuum polarization operator consisting of pure lepton loops. Our approach is based on the consecutive application of dispersion relations for the polarization operator and the Mellin – Barnes transform for the propagators of massive particles. Exact analytical expressions for the corrections to aL from vacuum polarization by four identical loops are obtained. Asymptotic expansions are found in the limit of both small and large values of the lepton mass ratio (r = mℓ /mL), r≪ 1 and r→∞ The resulting expansions are compared with the corresponding expressions given in the literature.
Keywords
anomalous magnetic moment of the leptons,
higher-order quantum electromagnetic corrections,
Mellin – Barnes transform
Supporting agencies: This work was supported by the International Program of Cooperation between the Republic of Belarus and JINR.
About the Authors
O. P. Solovtsova
Sukhoi State Technical University of Gomel;
Joint Institute for Nuclear Research
Belarus
Belarus
Olga P. Solovtsova – Dr. Sc. (Physics and Mathematics), Chief Researcher of the Scientific Research Center, Sukhoi State Technical University of Gomel; Leading Researcher of the Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research
48, Octiabrya Ave., 246029, Gomel, Republic of Belarus;
6, Joliot-Curie Str., 141980, Dubna, Moscow Region, Russian Federation.
V. I. Lashkevich
Sukhoi State Technical University of Gomel
Belarus
Belarus
Vasil I. Lashkevich – Ph. D. (Physics and Mathematics), Associate Professor of the Higher Mathematics Department
48, Octiabrya Ave., 246029, Gomel, Republic of Belarus
L. P Kaptari
Joint Institute for Nuclear Research
Russian Federation
Russian Federation
Leonid P. Kaptari – Dr. Sc. (Physics and Mathematics), Professor, Leading Researcher of Bogoliubov Laboratory of Theoretical Physics,
6, Joliot-Curie Str., 141980, Dubna, Moscow Region, Russian Federation
References
1. Dirac P. A. M. The quantum theory of the electron. Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, 1972, vol. 117, no. 778, pp. 610–624. https://doi.org/10.1098/rspa.1928.0023
2. Jegerlehner F. The Anomalous Magnetic Moment of the Muon. Springer Tracts in Modern Physics. Springer Cham, 2017. 693 p. https://doi.org/10.1007/978-3-319-63577-4
3. Aoyama T., Asmussen N., Benayoun M., Bijnens J., Blum T., Bruno M. [et al.]. The anomalous magnetic moment of the muon in the Standard Model. Physics Reports, 2020, vol. 887, pp. 1–166. https://doi.org/10.1016/j.physrep.2020.07.006
4. Parker R. H., Chenghui Y., Zhong W., Estey B., Müller H. Measurement of the fine-structure constant as a test of the Standard Model. Science, 2018, vol. 360, no. 6385, pp. 191–195. https://doi.org/10.1126/science.aap7706
5. Morel L., Yao Z., Cladé P., Guellati-Khélifa S. Determination of the fine-structure constant with an accuracy of 81 parts per trillion. Nature, 2020, vol. 588, pp. 61–65. https://doi.org/10.1038/s41586-020-2964-7
6. Abi B., Albahri T., Al-Kilani S., Allspach D., Alonzi L. P., Anastasi A., Anisenkov A. [et al.]; (Muon g – 2 Collaboration). Measurement of the Positive Muon Anomalous Magnetic Moment to 0.46 ppm. Physical Review Letters, 2021, vol. 126, art. ID 141801. https://doi.org/10.1103/PhysRevLett.126.141801
7. Schwinger J. S. Quantum electrodynamics. III: The electromagnetic properties of the electron: radiative corrections to scattering. Physical Review, 1949, vol. 76, pp. 790–817. https://doi.org/10.1103/PhysRev.76.790
8. Petermann A. Fourth order magnetic moment of the electron. Nuclear Physics, 1958, vol. 5, pp. 667–683. https://doi. org/10.1016/0029-5582(58)90065-8
9. Sommerfield C. M. Magnetic dipole moment of the electron. Physical Review, 1957, vol. 107, pp. 328–329. https://doi. org/10.1103/PhysRev.107.328
10. Laporta S. High-precision calculation of the 4-loop contribution to the electron g − 2 in QED. Physics Letters B, 2017, vol. 772, no. 1, pp. 232–238. https://doi.org/10.1016/j.physletb.2017.06.056
11. Laporta S. High-precision calculation of the 4-loop QED contribution to the slope of the Dirac form factor. Physics Letters B, 2020, vol. 800, art. ID 135137. https://doi.org/10.1016/j.physletb.2019.135137
12. Laporta S. The analytical contribution of the sixth order graphs with vacuum polarization insertions to the muon (g–2) in QED. Il Nuovo Cimento A, 1993, vol. 106, pp. 675–683. https://doi.org/10.1007/bf02787236
13. Laporta S. The analytical contribution of some eighth order graphs containing vacuum polarization insertions to the muon (g−2) in QED. Physics Letters B, 1993, vol. 312, no. 4, pp. 495–500. https://doi.org/10.1016/0370-2693(93)90988-T
14. Friot S., Greynat D., Rafael E. Asymptotics of Feynman diagrams and the Mellin-Barnes representation. Physics Letters B, 2005, vol. 628, no. 1–2, pp. 73–84. https://doi.org/10.1016/j.physletb.2005.08.126
15. . Aguilar J. P., Greynat D., Rafael E. Muon anomaly from lepton vacuum polarization and the Mellin-Barnes representation. Physical Review D, 2008, vol. 77, no. 9, art. ID 093010. https://doi.org/10.1103/physrevd.77.093010
16. Solovtsova O. P., Lashkevich V. I., Kaptari L. P. Lepton anomaly from QED diagrams with vacuum polarization insertions within the Mellin–Barnes representation. European Physical Journal Plus, 2023, vol. 138, art. ID 212. https://doi. org/10.1140/epjp/s13360-023-03834-4
17. Lautrup B. On high order estimates in QED. Physics Letters B, 1977, vol. 69, no. 1, pp. 109–111. https://doi. org/10.1016/0370-2693(77)90145-9
18. Berestetskii V. B., Krohnin O. N., Khlebnikov A. K. Concerning the radiative corrections to the mu-meson magnetic moment. Journal of Experimental and Theoretical Physics, 1956, vol. 30, no. 5, pp. 761–762.
19. Brodsky S. J., Rafael E. Suggested boson-lepton pair coupling and the anamalous magnetic moment of the muon. Physical Review, 1968, vol. 168, pp. 1620–1622. https://doi.org/10.1103/PhysRev.168.1620
20. Dubovyk I., Gluza J., Somogyi G. Mellin-Barnes Integrals: A Primer on Particle Physics Applications. Lecture Notes in Physics. Springer Cham, 2022. 266 p. https://doi.org/10.1007/978-3-031-14272-7
21. Smirnov V. A. Analytic Tools for Feynman Integrals. Springer Tracts in Modern Physics. Berlin, Heidelberg, Springer, 2012. 298 p. https://doi.org/10.1007/978-3-642-34886-0
22. Boos E. E., Davydychev A. I. A method of evaluation massive Feynman diagrams. Theoretical and Mathematical Physics, 1991, vol. 89, pp. 1052–1064. https://doi.org/10.1007/bf01016805
23. Lautrup B. E., Rafael E. Calculation of the sixth-order contribution from the fourth-order vacuum polarization to the difference of the anomalous magnetic moments of muon and electron. Physical Review, 1968, vol. 174, pp. 1835–1842. https:// doi.org/10.1103/PhysRev.174.1835
24. Laursen M. L., Samuel M. A. The n-bubble diagram contribution to g-2. Journal of Mathematical Physics, 1981, vol. 22, no. 5, pp. 1114–1126. https://doi.org/10.1063/1.524995
25. Lashkevich V. I., Solovtsova O. P., Tetyaev O. V. On high order contributions to the anomalous magnetic moments of leptons due to the vacuum polarization by lepton loops. Vestsі Natsyianal’nai akademіі navuk Belarusі. Seryia fіzіkamatematychnykh navuk = Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics series, 2022, vol. 58, no. 4, pp. 412–423 (in Russian). https://doi.org/10.29235/1561-2430-2022-58-4-412-423
26. Tiesinga E., Mohr P. J., Newell D. B., Taylor B. N. CODATA recommended values of the fundamental physical constants: 2018. Reviews of Modern Physics, 2021, vol. 93, no. 2, art. ID 025010. https://doi.org/10.1103/RevModPhys.93.025010
27. Laporta S. Analytical and numerical contributions of some tenth-order graphs containing vacuum polarization insertions to the muon (g−2) in QED. Physics Letters B, 1994, vol. 328, no. 3–4, pp. 522–527. https://doi.org/10.1016/03702693(94)91513-x
Review
Views: 157
Email this article 