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

• Published in: The journal of high energy physics 2023-04, Vol.2023 (4), Article 67
• Main Authors: Davier, M., Díaz-Calderón, D., Malaescu, B., Pich, A., Rodríguez-Sánchez, A., Zhang, Z.
• Format: Article
• Language: English
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP04(2023)067

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 $$ \Delta {\alpha}_{\textrm{QED}}^{\textrm{had}} $$ Δ α QED 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.