The Euclidean Adler function and its interplay with Δ α QED had $$ \Delta {\alpha}_{\textrm{QED}}^{\textrm{had}} $$ and α s

• Published in: The journal of high energy physics 2023-04, Vol.2023 (4), p.1-57
• Main Authors: M. Davier, D. Díaz-Calderón, B. Malaescu, A. Pich, A. Rodríguez-Sánchez, Z. Zhang
• Format: Article
• Language: English
• Subjects: Correlation Functions; Effective Field Theories of QCD; The Strong Coupling
• ISSN: 1029-8479
• DOI: 10.1007/JHEP04(2023)067

Abstract Three different approaches to precisely describe the Adler function in the Euclidean regime at around 2 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 Δ α QED had $$ \Delta {\alpha}_{\textrm{QED}}^{\textrm{had}} $$ (Q 2), using both the DHMZ compilation of e + e − data and published lattice results. Taking as input the FLAG value of α 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 α 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.