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arXiv · 2307.02532

A phenomenological estimate of isospin breaking in hadronic vacuum polarization

Martin Hoferichter·Gilberto Colangelo·Bai-Long Hoid·Bastian Kubis·Jacobo Ruiz de Elvira·Dominic Schuh·Dominik Stamen·Peter Stoffer
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Abstract

Puzzles in the determination of the hadronic-vacuum-polarization contribution currently impede a conclusive interpretation of the precision measurement of the anomalous magnetic moment of the muon at the Fermilab experiment. One such puzzle concerns tensions between evaluations in lattice QCD and using $e^+e^-\to\text{hadrons}$ cross-section data. In lattice QCD, the dominant isospin-symmetric part and isospin-breaking (IB) corrections are calculated separately, with very different systematic effects. Identifying these two pieces in a data-driven approach provides an opportunity to compare them individually and trace back the source of the discrepancy. Here, we estimate the IB component of the lattice-QCD calculations from phenomenology, based on a comprehensive study of exclusive contributions that can be enhanced via infrared singularities, threshold effects, or hadronic resonances, including, for the first time, in the $e^+e^-\to3\pi$ channel. We observe sizable cancellations among different channels, with a sum that even suggests a slightly larger result for the QED correction than obtained in lattice QCD. We conclude that the tensions between lattice QCD and $e^+e^-$ data therefore cannot be explained by the IB contributions in the lattice-QCD calculations.

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Martin Hoferichter, Gilberto Colangelo, Bai-Long Hoid, Bastian Kubis, Jacobo Ruiz de Elvira, Dominic Schuh, Dominik Stamen, Peter Stoffer. 2023-07-05. A phenomenological estimate of isospin breaking in hadronic vacuum polarization. https://doi.org/10.1103/physrevlett.131.161905

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