Lepton anomaly from QED diagrams with vacuum polarization insertions within the Mellin-Barnes representation

Understand

The contributions to the anomalous magnetic moment of the lepton $L$ ($L=e\ , \mu $ or $\tau$) generated by a specific class of QED diagrams are evaluated analytically up to the eighth order of the electromagnetic coupling constant.

• The considered class of the Feynman diagrams involves the vacuum polarization insertions into the electromagnetic vertex of the lepton $L$ up to three closed lepton loops.
• The corresponding analytical expressions are obtained as functions of the mass ratios $r=m_l/m_L$ in the whole region $0 < r < \infty$.
• Our consideration is based on a combined use of the dispersion relations for the polarization operators and the Mellin-Barnes integral transform for the Feynman parametric integrals.