Theoretical physicists from JINR and Gomel State Technical University (Belarus) performed analytical calculations of the tenth order QED radiative corrections to lepton anomalies within the Mellin-Barnes representation. This allows obtaining exact analytical expressions for the radiative corrections of the tenth order w.r.t. the electromagnetic coupling constant e for the first time.

The authors detail the radiative quantum-electrodynamic corrections to the lepton (L = e, μ and τ) anomalous magnetic moment due to the contributions of diagrams with insertions of the photon vacuum polarisation operator consisting solely of four closed lepton (l = e, μ and τ) loops.

In addition, the researchers focus on specific operators with two loops formed by leptons L of the same type as the external one, the other two formed by leptons ℓ different from L. The approach is essentially based on using the Mellin–Barnes representation of the x-parametrisation of the corresponding Feynman diagrams.

Analytically, the radiative corrections are expressed in terms of the ratio r = m _ℓ/m_L of the internal to external lepton masses. The dependence on r is studied numerically in the whole interval of r, 0 < r < ∞. To make comparisons with earlier published results possible, the exact analytical expressions are expanded as r → 0 and r → ∞ and compared with the corresponding asymptotic expansions known in the literature.

The Journal of Physics G: Nuclear and Particle Physics published this study by scientists Olga Solovtsova, Vasily Lashkevich, and Leonid Kaptari in March 2024.