Speaker
Description
The complete set of six relations, which mutually express the spacelike and
timelike kernel functions for the hadronic vacuum polarization contributions
to the muon anomalous magnetic moment $a^{\text{HVP}}_{\mu}$ 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 $a^{\text{HVP}}_{\mu}$ involving the hadronic
vacuum polarization function, is obtained. The corresponding next-to-leading
order spacelike kernel function, which appears in the representation for
$a^{\text{HVP}}_{\mu}$ involving the Adler function, is calculated
numerically. The obtained results can be employed in the assessments of the
hadronic vacuum polarization contributions to the muon anomalous magnetic
moment in the framework of the spacelike methods, such as lattice studies,
MUonE project, and others.
Additionally, it is shown that the quark flavour thresholds of the hadronic
vacuum polarization function generate additional contributions to
$a^{\text{HVP}}_{\mu}$ expressed in terms of the Adler function and the
$R$-ratio and the explicit expressions for such contributions are obtained.
The contributions due to the heavy quark thresholds to $a^{\text{HVP}}_{\mu}$
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.
[1] A.V.Nesterenko, J.Phys.G49, 055001 (2022); arXiv:2112.05009[hep-ph].
https://doi.org/10.1088/1361-6471/ac5d0a
[2] A.V.Nesterenko, J.Phys.G50, 029401 (2023); arXiv:2209.03217[hep-ph].
https://doi.org/10.1088/1361-6471/aca3c1
[3] A.V.Nesterenko, J.Phys.G51, 015005 (2024); arXiv:2306.16392[hep-ph].
https://doi.org/10.1088/1361-6471/ad0b33
[4] A.V.Nesterenko, J.Phys.G53, 025003 (2026); arXiv:2505.10339[hep-ph].
https://doi.org/10.1088/1361-6471/ae16c4
| Are you an early career researcher? | No |
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