Radiative QED corrections to the lepton anomaly from four-loop vacuum polarization insertions with three identical leptons
O. P. Solovtsova, V. I. Lashkevich, L. P. Kaptari
备注：
18 pages, 4 eps figure. Talk presented at the Scientific session of Nuclear Physics section of Physics Division of RAS, April 1-5, Physics of Fundamental Interactions
Analytical expressions for the tenth order electromagnetic corrections to the lepton ($L=e, ~μ$ and $τ$) anomaly $a_L$ are derived explicitly for a class of Feynman diagrams with insertions of the vacuum polarization operator consisting of four closed lepton loops. We consider a particular case when one loop is formed by the lepton $L$ of the same kind as the one under consideration, the other three loops being formed by leptons $\ell\neq L$. The method is based on the consecutive application of dispersion relations for the polarization operator and the Mellin--Barnes transform for the propagators of massive particles. The result is expressed in terms of the mass ratio $r=m_\ell/m_L$. We investigate the behaviour of the exact analytical expressions as $r\to 0$ and $r\to \infty$ and compare them with the corresponding asymptotic expansions known in the literature.
The sixth order QED radiative corrections to lepton anomalies due to the fourth order vacuum polarization insertions within the Mellin-Barnes representation
PSI Center for Neutron and Muon Sciences（保罗谢勒研究所中子与μ子科学中心）；Physik-Institut, Universität Zürich（苏黎世大学物理学院）；Università degli Studi di Torino & INFN（都灵大学及意大利国家核物理研究所）；University of Liverpool（利物浦大学）
Addendum: Timelike and spacelike kernel functions for the hadronic vacuum polarization contribution to the muon anomalous magnetic moment (2022 J. Phys. G: Nucl. Part. Phys. 49 055001)
