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"10.29235/1561-2430-2025-61-2-118-127vestifm-837Research ArticleФИЗИКАPHYSICSВклады в аномальный магнитный момент лептонов от поляризации вакуума, описываемого смешанными диаграммами в рамках метода Меллина – БарнсаContributions to the anomalous magnetic moment of leptons from vacuum polarization described by mixed diagrams in the framework of the Mellin – Barnes methodЛашкевичВ. И.LashkevichV. I.

Лашкевич Василий Иванович – кандидат физико-математических наук, доцент кафедры высшей математики

пр. Октября, 48, 246029, Гомель

Vasil I. Lashkevich – Ph. D. (Physics and Mathematics), Associate Professor of the Higher Mathematics Department

Oktyabrya Ave., 48, 246746, Gomel

lashkevich@gstu.byГомельский государственный технический университет имени П. О. СухогоSukhoi State Technical University of Gomel202511072025612118127Copyright © Лашкевич В.И., 20252025Лашкевич В.И.Lashkevich V.I.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/837

Исследуется явный вид электромагнитных поправок третьего порядка по постоянной тонкой структуре α3 к аномальному магнитному моменту лептона aL (L = e,μ,τ) от вклада графа вершины шестого порядка с вставкой поляризации вакуума четвертого порядка. Подход основывается на последовательном применении дисперсионных соотношений для поляризационного оператора и преобразования Меллина – Барнса для пропагаторов массивных частиц. Получены явные аналитические выражения для поправок к aL при r = mℓ/mL > 1. Найдены асимптотические разложения в пределе как малых, так и больших значений отношения масс лептонов (r = mℓ/mL), r ^ 1 и r → ∞. Полученные разложения сравниваются с соответствующими выражениями, приведенными в литературе.

The explicit form of the third-order electromagnetic corrections in the fine structure constant α3 to the anomalous magnetic moment of lepton aL (L = e,μ,τ) from the contribution of the sixth – order vertex graph with insertion of fourth – order vacuum polarization. The approach is based on the consistent application of dispersion relations for the polarization operator and the Mellin – Barnes transform for massive particle propagators. Explicit analytical expressions for the corrections to aL are obtained at r = mℓ/mL > 1. 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 expansions obtained are compared with the corresponding expressions given in the literature.

аномальные магнитные моменты лептоновквантово-электродинамические поправки высших порядковпреобразование Меллина – Барнсаanomalous magnetic moments of the leptonshigher-order quantum electromagnetic correctionsMellin – Barnes transformРабота выполнена при поддержке Международной программы сотрудничества между Республикой Беларусь и ОИЯИ. Автор выражает благодарность О. П. Соловцовой и Л. П. Каптарю за ценные замечания, высказанные в ходе обсуждения работы.This work was supported by the In ternational Program of Cooperation between the Repub lic of Belarus and JINR. The author expresses his gratitude to O. P. Solovtsova and L. P. Kaptari for the discussion and valuable comments.ReferencesDirac, P. A. M. The quantum theory of the electron / P. A. M. Dirac // Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character. – 1928. – Vol. 117, № 778. – P. 610–624. https://doi.org/10.1098/rspa.1928.0023Dirac, P. A. M. 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The authors declare that there are no conflicts of interest present.