R-ratio of electron-positron annihilation into hadrons: higher-order pi2-terms

TL;DR

This paper investigates the high-energy behavior of the R-ratio in electron-positron annihilation into hadrons, focusing on the re-expansion in the ultraviolet domain and the role of pi2-terms in perturbation theory.

Contribution

It demonstrates that at any perturbative order, the R-ratio's ultraviolet behavior can be expressed as a power series in the analytically continued strong coupling, clarifying the structure of higher-order pi2-terms.

Findings

Re-expansion of R-ratio reduces to a power series in the continued coupling.

Convergence range of the re-expanded R-ratio is analyzed.

Higher-order pi2-terms are discussed in the context of ultraviolet asymptotics.

Abstract

High-energy behavior of R-ratio of electron-positron annihilation into hadrons is studied. In particular, it is argued that at any given order of perturbation theory the re-expansion of the R-ratio in the ultraviolet asymptotic can be reduced to the form of power series in the naive continuation of the strong running coupling into the timelike domain. The convergence range of the re-expanded R-ratio and the corresponding higher-order pi2-terms are discussed.