Tenth-order QED Corrections to the Lepton Anomaly Due to Some Bubble Diagrams

Analytical expressions for the tenth-order mass-dependent radiative corrections to the lepton anomaly of each of the charged leptons are derived explicitly for a certain class of QED Feynman diagrams with insertions of the vacuum polarization operator with four closed lepton loops, where only one loop consists of leptons l different from the external leptons L, l ≠ L. The approach is based on the consecutive application of dispersion relations for the photon polarization operator and of the Mellin–Barnes transform of the propagators of massive particles. The result is expressed in terms of the mass ratio r = ml/mL. We investigate the behaviour of the exact analytical expressions as r ⟶ 0 and r ⟶ ∞ and compare it with the corresponding asymptotic expansions known in the literature. We assert that in the region of physical values of r the asymptotic expansions provide a high precision approximation to the exact results.