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

Autor:	Krachkov, Petr A., Lee, Roman N.
Rok vydání:	2023
Předmět:	High Energy Physics - Phenomenology Physics - Atomic Physics
Druh dokumentu:	Working Paper
DOI:	10.1007/JHEP07(2023)211
Popis:	We revisit the contributions of order $\alpha^2(Z\alpha)^5m$ and $\alpha^2(Z\alpha)E_F$, 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 $\epsilon$-regular basis [LeeOnishchenko2019] 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. Comment: 14 pages, 4 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2306.13369 Zobrazit plný text záznamu View this record from Arxiv