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arXiv · 2302.01359

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

M. Davier·D. Díaz-Calderón·B. Malaescu·A. Pich·A. Rodríguez-Sánchez·Z. Zhang
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Abstract

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.

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M. Davier, D. Díaz-Calderón, B. Malaescu, A. Pich, A. Rodríguez-Sánchez, Z. Zhang. 2023-02-02. The Euclidean Adler Function and its Interplay with $\Delta\alpha^{\mathrm{had}}_{\mathrm{QED}}$ and $\alpha_s$. https://doi.org/10.1007/jhep04(2023)067

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