Timelike and spacelike kernel functions for the hadronic vacuum polarization contribution to the muon anomalous magnetic moment

Abstract

The complete set of relations, which mutually express the spacelike and timelike kernel functions for the hadronic vacuum polarization contribution to the muon anomalous magnetic moment $a_{\mu }^{\text{HVP}}$ in terms of each other, is obtained. By making use of the derived relations the explicit expression for the next-to-leading order spacelike kernel function, which enters the representation for $a_{\mu }^{\text{HVP}}$ involving the hadronic vacuum polarization function, is obtained. The corresponding next-to-leading order spacelike kernel function, which appears in the representation for $a_{\mu }^{\text{HVP}}$ involving the Adler function, is calculated numerically. The obtained results can be employed in the assessments of the hadronic vacuum polarization contribution to the muon anomalous magnetic moment in the framework of the spacelike methods, such as lattice studies, MUonE project, and others.

arXiv comment16 pages, 6 figures; v3: minor amendments

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Cited by in corpus (8)

• The anomalous magnetic moment of the muon in the Standard Model: an update
• Hadronic vacuum polarization contributions to the muon $g$-2 in the space-like region
• Borel-Laplace Sum Rules with $\tau$ decay data, using OPE with improved anomalous dimensions
• Renormalization group summation and analytic continuation from spacelike to timeline regions
• Effects of the quark flavour thresholds in the hadronic vacuum polarization contributions to the muon anomalous magnetic moment
• Time-kernel for lattice determinations of NLO hadronic vacuum polarization contributions to the muon $g$-$2$
• Addendum: Timelike and spacelike kernel functions for the hadronic vacuum polarization contribution to the muon anomalous magnetic moment (2022 J. Phys. G: Nucl. Part. Phys. 49 055001)
• Window quantities for the hadronic vacuum polarization contributions to the muon anomalous magnetic moment in spacelike and timelike domains