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The Euclidean Adler Function and its Interplay with \(\Delta\alpha^{\mathrm{had}}_{\mathrm{QED}}\) and \(\alpha_s\)
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 s...
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Published in: | arXiv.org 2023-04 |
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Main Authors: | , , , , , |
Format: | Article |
Language: | English |
Subjects: | |
Online Access: | Get full text |
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Summary: | 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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ISSN: | 2331-8422 |
DOI: | 10.48550/arxiv.2302.01359 |