Analytical five-loop expressions for the renormalization group QED $\beta$-function in different renormalization schemes

TL;DR

This paper presents analytical five-loop calculations of the QED beta-function across various renormalization schemes, enhancing precision in understanding quantum electrodynamics' behavior at high orders.

Contribution

It provides the first five-loop analytical expressions for the QED beta-function in multiple renormalization schemes, advancing theoretical accuracy.

Findings

Five-loop beta-function expressions derived analytically

Comparison of beta-function across different schemes

Discussion of theoretical implications

Abstract

We obtain analytical five-loop results for the renormalization group $\beta$-function of Quantum Electrodynamics with the single lepton in different renormalization schemes. The theoretical consequences of the results obtained are discussed.