The Mellin-Barnes Approach to Hadronic Vacuum Polarization and $g_{\mu}-2$

Abstract : It is shown that with a precise determination of a few derivatives of the hadronic vacuum polarization (HVP) self-energy function $\Pi(Q^2)$ at $Q^2=0$, from lattice QCD (LQCD) or from a dedicated low-energy experiment, one can obtain an evaluation of the lowest order HVP contribution to the anomalous magnetic moment of the muon $a_{\mu}^{\rm HVP}$ with an accuracy comparable to the one reached using the $e^+ e^-$ annihilation cross section into hadrons. The technique of Mellin-Barnes approximants (MBa) that we propose is illustrated in detail with the example of the two loop vacuum polarization function in QED. We then apply it to the first few moments of the hadronic spectral function obtained from experiment and show that the resulting MBa evaluations of $a_{\mu}^{\rm HVP}$ converge very quickly to the full experimental determination.
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Contributeur : Jérôme Charles <>
Soumis le : lundi 23 avril 2018 - 16:22:33
Dernière modification le : vendredi 11 mai 2018 - 16:05:20
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Jérôme Charles, David Greynat, Eduardo De Rafael. The Mellin-Barnes Approach to Hadronic Vacuum Polarization and $g_{\mu}-2$. Physical Review D, American Physical Society, 2018, 〈10.1103/PhysRevD.97.076014〉. 〈hal-01658449〉

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