Effects of the quark flavour thresholds in the hadronic vacuum polarization contributions to the muon anomalous magnetic moment

• Published in: Journal of physics. G, Nuclear and particle physics Nuclear and particle physics, 2024-01, Vol.51 (1), p.15005
• Main Author: Nesterenko, A V
• Format: Article
• Language: English
• Subjects: hadronic vacuum polarization contributions; muon anomalous magnetic moment; quark flavour thresholds; spacelike and timelike domains
• ISSN: 0954-3899; 1361-6471
• DOI: 10.1088/1361-6471/ad0b33

The equivalent representations for the hadronic vacuum polarization contributions to the muon anomalous magnetic moment a μ HVP in the presence of the quark flavour thresholds are studied. Specifically, the explicit relations between the contributions given by the integration over a finite kinematic interval to a μ HVP expressed in terms of the hadronic vacuum polarization function, Adler function, and the R -ratio of electron–positron annihilation into hadrons are derived. It is shown that the quark flavour thresholds of the hadronic vacuum polarization function generate additional contributions to a μ HVP expressed in terms of the Adler function and the R -ratio and the explicit expressions for such contributions are obtained. The commonly employed dispersion relations, which bind together hadronic vacuum polarization function, Adler function, and R -ratio, are extended to account for the effects due to the quark flavour thresholds. The examined additional contributions due to the heavy quark thresholds to a μ HVP expressed in terms of the R -ratio appear to be quite sizable, that can be of a particular relevance for the data-driven method of assessment of the hadronic part of the muon anomalous magnetic moment.