Four-loop corrections with two closed fermion loops to fermion self energies and the lepton anomalous magnetic moment

TL;DR

This paper calculates complex four-loop quantum corrections involving fermion loops to the muon's magnetic moment and quark properties, providing explicit integrals and advancing precision in quantum field theory predictions.

Contribution

It presents the first explicit analytical results for four-loop integrals with two fermion loops relevant to muon g-2 and quark renormalization, enhancing theoretical accuracy.

Findings

Analytical results for four-loop master integrals provided

Computed fermionic corrections to muon anomalous magnetic moment

Derived four-loop QCD corrections to quark mass and wave function renormalization

Abstract

We compute the eighth-order fermionic corrections involving two and three closed massless fermion loops to the anomalous magnetic moment of the muon. The required four-loop on-shell integrals are classified and explicit analytical results for the master integrals are presented. As further applications we compute the corresponding four-loop QCD corrections to the mass and wave function renormalization constants for a massive quark in the on-shell scheme.