The Euclidean Adler Function and its Interplay with \(\Delta\alpha^{\mathrm{had}}_{\mathrm{QED}}\) and \(\alpha_s\)

• Published in: arXiv.org 2023-04
• Main Authors: Davier, M, Díaz-Calderón, D, Malaescu, B, Pich, A, Rodríguez-Sánchez, A, Zhang, Z
• Format: Article
• Language: English
• Subjects: Dispersion; Operators (mathematics); Quantum chromodynamics
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2302.01359

Three different approaches to precisely describe the Adler function in the Euclidean regime at around \(2\, \mathrm{GeVs}\) are available: dispersion relations based on the hadronic production data in \(e^+e^-\) annihilation, lattice simulations and perturbative QCD (pQCD). We make a comprehensive study of the perturbative approach, supplemented with the leading power corrections in the operator product expansion. All known contributions are included, with a careful assessment of uncertainties. The pQCD predictions are compared with the Adler functions extracted from \(\Delta\alpha^{\mathrm{had}}_{\mathrm{QED}}(Q^2)\), using both the DHMZ compilation of \(e^+e^-\) data and published lattice results. Taking as input the FLAG value of \(\alpha_s\), the pQCD Adler function turns out to be in good agreement with the lattice data, while the dispersive results lie systematically below them. Finally, we explore the sensitivity to \(\alpha_s\) of the direct comparison between the data-driven, lattice and QCD Euclidean Adler functions. The precision with which the renormalisation group equation can be tested is also evaluated.