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arXiv · 2505.24344

Isospin-violating vacuum polarization in the muon $(g-2)$ with SU(3) flavour symmetry from lattice QCD

Dominik Erb·Antoine Gérardin·Harvey B. Meyer·Julian Parrino·Volodymyr Biloshytskyi·Vladimir Pascalutsa
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Abstract

We compute the isospin-violating part $a_\mu^{\text{HVP}, 38}$ of the hadronic-vacuum-polarization (HVP) contribution to the muon $(g-2)$ in lattice QCD at the SU$(3)_{\rm f}$-symmetric point where $M_\pi=M_K\simeq 416$ MeV. All diagrams involving internal photons are evaluated in coordinate space, employing a Pauli-Villars-regulated photon propagator with a cutoff scale $\Lambda$ well below the lattice cutoff. The counterterm $(m_u-m_d)$, whose $\Lambda$ dependence is consistent with the expected logarithmic behaviour, is calibrated using the experimental kaon mass splitting as input. The bare electromagnetic contribution at fixed $\Lambda$ is compared to a phenomenological estimate based on the kaon-loop and pseudoscalar-pole contributions to the forward light-by-light amplitude. An extension of these calculations to physical pion and kaon masses appears promising.

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Dominik Erb, Antoine Gérardin, Harvey B. Meyer, Julian Parrino, Volodymyr Biloshytskyi, Vladimir Pascalutsa. 2025-05-30. Isospin-violating vacuum polarization in the muon $(g-2)$ with SU(3) flavour symmetry from lattice QCD. https://arxiv.org/abs/2505.24344

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