Two-loop corrections to Lamb shift and hyperfine splitting in hydrogen via multi-loop methods

Abstract

Abstract We revisit the contributions of order α 2(Zα)5 m and α 2(Zα)E F , respectively, to the Lamb shift and to the hyperfine splitting from mixed self-energy-vacuum-polarization diagrams, involving fermionic loop. We use modern multi-loop calculation techniques based on IBP reduction and differential equations. We construct the ϵ-regular basis [1] and explicitly demonstrate that it is compatible with the renormalization. We obtain analytic results in terms of one-fold integral involving elliptic function and dilogarithm. As a by-product, we obtain the analogous contribution for the limiting cases of heavy and light fermionic loop.

Keywords

• Higher Order Electroweak Calculations
• Precision QED