Speaker
Description
We investigate the contribution of the 12-th order QED corrections to the anomalous magnetic moment $a_L$ of a lepton $L$ ($L=e,~\mu$ and $\tau$) from diagrams with insertions of the photon vacuum polarisation operator consisting solely of purely lepton loops. The approach is based on consistent applications of dispersion relations for the polarisation operator and the Mellin-Barnes integral representation for propagators of massive particles. Explicit expressions for the radiative corrections to the anomalous magnetic moments from diagrams with five identical lepton loops in the polarisation operator are obtained, for the first time, as functions of the mass ratios $r = m_\ell/m_L$ of the loop lepton $\ell$ to the external lepton $L$ in the whole interval $0 < r < \infty$. The asymptotic expansions in the limits of both, small $r\ll 1$ and large $r\gg 1$, computed from the exact expressions are presented and the limit of their validity is investigated in detail. It is argued that in the intervals where the physical lepton mass ratios are located, the asymptotic expansions hold with an accuracy higher than the experimentally measured anomalies. Thus, these asymptotics, being much simpler in comparison with the exact, but lengthy expressions, are quite appropriate for practical numerical calculations of QED corrections to $a_L$ up to the desired accuracy.
