vestifmИзвестия Национальной академии наук Беларуси. Серия физико-математических наукProceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series1561-24302524-2415The Republican Unitary Enterprise Publishing House "Belaruskaya Navuka"10.29235/1561-2430-2022-58-4-412-423vestifm-690Research ArticleФИЗИКАPHYSICSО вкладах высших порядков в аномальные магнитные моменты лептонов от поляризации вакуума лептонными петлямиOn high order contributions to the anomalous magnetic moments of leptons due to the vacuum polarization by lepton loopsЛашкевичВ. И.LashkevichV. I.

Лашкевич Василий Иванович – кандидат физико-математических наук, доцент кафедры «Высшая математика».

пр. Октября, 48, 246029, Гомель

Vasil I. Lashkevich – Ph. D. (Physics and Mathematics), Associate Professor of the Higher Mathematics Department, Sukhoi State Technical University of Gomel.

48, Octiabrya Ave., 246746, Gomel

lashkevich@gstu.gomel.byСоловцоваО. П.SolovtsovaO. P.

Соловцова Ольга Павловна – доктор физико-математических наук, главный научный сотрудник научно-исследовательской части, ГГТУ им. П.О. Сухого; ведущий научный сотрудник лаборатории теоретической физики, ОИЯИ.

пр. Октября, 48, 246029, Гомель; ул. Жолио-Кюри, 6, 141980, Дубна, Московская обл.

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., 246746, Gomel; 6, Joliot-Curie Str., 141980, Dubna, Moscow Region

solovtsova@gstu.gomel.byТеряевО. В.TeryaevO. V.

Теряев Олег  Валерианович  – доктор физико-математических наук, профессор, начальник отдела Лаборатории теоретической физики имени Н.Н. Боголюбова.

ул. Жолио-Кюри, 6, 141980, Дубна, Московская обл.

Oleg V. Teryaev – Dr. Sc. (Physics and Mathematics), Professor, Head of the Department of Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research.

6, Joliot-Curie Str., 141980, Dubna, Moscow Region

teryav@theor.jinr.ruГомельский государственный технический университет имени П.О. СухогоSukhoi State Technical University of GomelГомельский государственный технический университет имени П.О. Сухого; Объединенный институт ядерных исследованийSukhoi State Technical University of Gomel; Joint Institute for Nuclear ResearchОбъединенный институт ядерных исследованийJoint Institute for Nuclear Research202201012023584412423Copyright © Лашкевич В.И., Соловцова О.П., Теряев О.В., 20232023Лашкевич В.И., Соловцова О.П., Теряев О.В.Lashkevich V.I., Solovtsova O.P., Teryaev O.V.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://vestifm.belnauka.by/jour/article/view/690

Анализируются вклады высших порядков разложений по постоянной тонкой структуры α в аномальные магнитные моменты лептонов от диаграмм поляризации вакуума лептонными петлями в случае, если отношение массы лептона в петле к массе внешнего лептона оказывается меньше единицы. Найдена зависимость коэффициентов разложения an от отношения масс лептонов и проведено сравнение с ранее известными аналитическими оценками. Показано, что для реальных значений масс лептонов новые аналитические выражения оказываются более точными, чем известные. Даны оценки порядка разложения n*, начиная с которого для коэффициентов an гарантируется та или иная точность.

We analyze herein the higher orders contributions of expansions in the fine structure constant α to the anomalous magnetic moment of leptons coming from the diagrams of vacuum polarization by lepton loops in the case when the ratio of the mass of lepton in the loop to the mass of external lepton is less than unity. The dependence of the expansion coefficients an on the ratio of lepton masses is found and a comparison is made with the previously known analytical estimates. It is shown that for real values of lepton masses the new analytical expressions turn out to be more accurate than the known ones. Estimates are given for the order of expansion n*, starting from which one or another accuracy is guaranteed for the coefficients an.

аномальные магнитные моменты лептоновквантово-электродинамические поправкивклады высших порядковanomalous magnetic moment of the leptonsquantum electromagnetic correctionshigher-order contributionsРабота выполнена при поддержке Международной программы сотрудничества между Республикой Беларусь и ОИЯИ.This work was supported by the International Program of Cooperation between the Republic of Belarus and JINR.ReferencesLautrup, B. E. Recent developments in the comparison between theory and experiments in quantum electrodynamics / B. E. Lautrup, A. Peterman, E. Rafael // Phys. Rep. – 1972. – Vol. 3, № 3. – P. 193–259. https://doi.org/10.1016/0370-1573(72)90011-7Lautrup B. E., Peterman A., Rafael E. Recent developments in the comparison between theory and experiments in quantum electrodynamics. Physics Reports, 1972, vol. 3, no. 3, pp. 193–259. https://doi.org/10.1016/0370-1573(72)90011-7The anomalous magnetic moment of the muon in the Standard Model / T. Aoyama [et al.] // Phys. Rep. – 2020. – Vol. 887. – P. 1–166. https://doi.org/10.1016/j.physrep.2020.07.006Aoyama 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.2020.07.00Schwinger, J. S. Quantum Electrodynamics. III. The Electromagnetic Properties of the Electron – Radiative Corrections to Scattering / J. S. Schwinger // Phys. Rev. – 1949. – Vol. 76, № 6. – P. 790–817. https://doi.org/10.1103/physrev.76.790Schwinger J. S. Quantum Electrodynamics. III. The Electromagnetic Properties of the Electron – Radiative Corrections to Scattering. Physical Review, 1949, vol. 76, no. 6, pp. 790–817. https://doi.org/10.1103/physrev.76.790Consa, O. Something is wrong in the state of QED [Electronic resource] / O. Consa // Arxiv [Preprint]. – 2021. – Mode of access: https://arxiv.org/abs/2110.02078. https://doi.org/10.48550/arXiv.2110.02078Consa O. Something is wrong in the state of QED. Arxiv [Preprint], 2021. Available at: https://arxiv.org/abs/2110.02078. https://doi.org/10.48550/arXiv.2110.02078Measurement of the fine-structure constant as a test of the Standard Model / R. H. Parker [et al.] // Science. – 2018. – Vol. 360, № 6385. – P. 191–195. https://doi.org/10.1126/science.aap7706Parker R. H., Chenghui Yu, 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.aap7706Davoudiasl, H. Tale of two anomalies / H. Davoudiasl, W. J. Marciano // Phys. Rev. D. – 2018. – Vol. 98, № 7. – Art. 075011. https://doi.org/10.1103/physrevd.98.075011Davoudiasl H., Marciano W. J. Tale of two anomalies. Physical Review D, 2018, vol. 98, no. 7, art. 075011. https://doi.org/10.1103/physrevd.98.075011Measurement of the Positive Muon Anomalous Magnetic Moment to 0.46 ppm / B. Abi [et al.] (Muon g – 2 Collaboration) // Phys. Rev. Lett. – 2021. – Vol. 126, № 14. – Art. 141801.Abi B., Albahri T., Al-Kilani S., Allspach D., Alonzi L. P. Anastas 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, no. 14, art. 141801.Lautrup, B. E. On high order estimates in QED / B. E. Lautrup // Phys. Lett. B. – 1977. – Vol. 69, № 1. – P. 109–111. https://doi.org/10.1016/0370-2693(77)90145-9Lautrup B. E. 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)90145-9Laursen, M. L. Borel transform technique and the n-bubble-diagram contribution to the lepton anomaly / M. L. Laursen, M. A. Samuel // Phys. Rev. D. – 1981. – Vol. 23, № 10. – P. 2478–2481. https://doi.org/10.1103/physrevd.23.2478Laursen M. L., Samuel M. A. Borel transform technique and the n-bubble-diagram contribution to the lepton anomaly. Physical Review D, 1981, vol. 23, no. 10, pp. 2478–2481. https://doi.org/10.1103/physrevd.23.2478Kinoshita, T. Eighth-order QED contribution to the anomalous magnetic moment of the muon / T. Kinoshita, B. Nizic, Y. Okamoto // Phys. Rev. D. – 1990. – Vol. 41, № 2. – P. 593–610. https://doi.org/10.1103/physrevd.41.593Kinoshita T., Nizic B., Okamoto Y. Eighth-order QED contribution to the anomalous magnetic moment of the muon. Physical Review D, 1990, vol. 41, no. 2, pp. 593–610. https://doi.org/10.1103/physrevd.41.593Jegerlehner, F. The Anomalous Magnetic Moment of the Muon / F. Jegerlehner. – Springer Int. Publ. AG, 2017. – 693 p. – (Springer Tracts in Modern Physics). https://doi.org/10.1007/978-3-319-63577-4Jegerlehner F. The Anomalous Magnetic Moment of the Muon. Springer Tracts in Modern Physic. Springer International Publishing AG, 2017. 693 p. https://doi.org/10.1007/978-3-319-63577-4Kataev, A. L. Analytical eighth-order light-by-light QED contributions from leptons with heavier masses to the anomalous magnetic moment of electron / A. L. Kataev // Phys. Rev. D. – 2012. – Vol. 86, № 1. – Art. 013010. https://doi.org/10.1103/physrevd.86.013010Kataev A. L. Analytical eighth-order light-by-light QED contributions from leptons with heavier masses to the anomalous magnetic moment of electron. Physical Review D, 2012, vol. 86, no. 1, art. 013010. https://doi.org/10.1103/physrevd.86.013010Laursen, M. L The n-bubble diagram contribution to g − 2 of the electron. Mathematical structure of the analytical expression / M. L. Laursen, M. A. Samuel // Phys. Letts. B. – 1980. – Vol. 91, № 2. – P. 249–252. https://doi.org/10.1016/0370-2693(80)90443-8Laursen M. L., Samuel M. A. The n-bubble diagram contribution to g – 2 of the electron. Mathematical structure of the analytical expression. Physics Letters B, 1980, vol. 91, no. 2, pp. 249–252. https://doi.org/10.1016/0370-2693(80)90443-8Aguilar, J.-P. Muon anomaly from lepton vacuum polarization and the Mellin-Barnes representation / J.-P. Aguilar, E. de Rafael, D. Greynat // Phys. Rev. D. – 2008. – Vol. 77, № 9. – Art. 093010. https://doi.org/10.1103/physrevd.77.093010Aguilar J.-P., Rafael E. de, Greynat D. Muon anomaly from lepton vacuum polarization and the Mellin-Barnes representation. Physical Review D, 2008, vol. 77, no. 9, art. 093010. https://doi.org/10.1103/physrevd.77.093010Solovtsova, O. P. On the contribution of three-bubble diagrams to (g-2)L / O. P. Solovtsova, V. I. Lashkevich, A. V. Sidorov // Nonlinear Dynamics and Applications: Proc. XXVI Annual Seminar NPCS’2019, May 21–24. – Minsk, 2019. – Vol. 25. – P. 103–112.Solovtsova O. P., Lashkevich V. I., Sidorov A. V. On the contribution of three-bubble diagrams to (g-2)L. Nonlinear Dynamics and Applications. Proc. XXVI Annual Seminar NPCS’2019, May 21–24. Minsk, 2019, vol. 25, pp. 103–112.Anomalous magnetic moment with heavy virtual leptons / A. Kurz [et al.] // Nucl. Phys. B. – 2014. – Vol. 879. – P. 1–18. https://doi.org/10.1016/j.nuclphysb.2013.11.018Kurz A., Liu T., Marquard P., Steinhauser M. Anomalous magnetic moment with heavy virtual leptons. Nuclear Physics B, 2014, vol. 879, pp. 1–18. https://doi.org/10.1016/j.nuclphysb.2013.11.018Bateman, H. Higher Transcendental Functions / H. Bateman, A. Erdelyi. – New York, McGraw-Hill, 1953. – Vol. 1. – 302 p.Bateman H., Erdelyi A. Higher Transcendental Functions. Vol. 1. New York, McGraw-Hill, 1953. 302 p.Boos, E. E. A method of evaluating massive Feynman integrals / E. E. Boos, A. I. Davydychev // Theor. Math. Phys. – 1991. – Vol. 89, № 1. – P. 1052–1063. https://doi.org/10.1007/bf01016805Boos E. E., Davydychev A. I. A method of evaluating massive Feynman integrals. Theoretical and Mathematical Physics, 1991, vol. 89, no. 1, pp. 1052–1063. https://doi.org/10.1007/bf01016805Friot, S. Asymptotics of Feynman diagrams and the Mellin–Barnes representation / S. Friot, D. Greynat, E. de Rafael // Phys. Lett. B. – 2005. – Vol. 628, № 1–2. – P. 73–84. https://doi.org/10.1016/j.physletb.2005.08.126Friot S., Greynat D., Rafael E de. 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

The authors declare that there are no conflicts of interest present.