Vacuum polarization contribution to muon g−2 as an inverse problem

2020/04/30 by Hsiang-nan Li, Hiroyuki Umeeda
Physics and Astronomy · #High-Energy Particle Collisions Research #Muon #Nuclear physics #Particle physics theoretical and experimental studies #Physics #Quantum Chromodynamics and Particle Interactions #hep-ph

paper · pdf · doi:10.1103/physrevd.102.094003

published as Phys. Rev. D 102, 094003 (2020) · 11 pages, 6 figures, version to appear in PRD

openalex created_date 2020/04/24 · arxiv created 2020/10/21 · openalex publication_date 2020/11/09 · arxiv updated 2020/11/18 · openalex updated_date 2026/08/05

Abstract

We analyze the electromagnetic current correlator at an arbitrary photon invariant mass q² by exploiting its associated dispersion relation. The dispersion relation is turned into an inverse problem, by which the involved vacuum polarization function \mathrm\ensuremathΠ(q²) at low q² is solved with the perturbative input of \mathrm\ensuremathΠ(q²) at large q². It is found that the result for \mathrm\ensuremathΠ(q²), including its first derivative \mathrm\ensuremathΠ^\ensuremath'(q²=0), agrees with those from lattice QCD, and its imaginary part accommodates the e⁺e^\ensuremath--annihilation data. The corresponding hadronic vacuum polarization (HVP) contribution a_\ensuremathμ^HVP=(641_\ensuremath-63⁺⁶⁵)\ifmmode×\else\texttimes\fi10^\ensuremath-10 to the muon anomalous magnetic moment g\ensuremath-2, where the uncertainty arises from the variation of the perturbative input, also agrees with those obtained in other phenomenological and theoretical approaches. We point out that our formalism is equivalent to imposing the analyticity constraint to the phenomenological approach solely relying on experimental data and can improve the precision of the a_\ensuremathμ^HVP determination in the Standard Model.

Citations

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