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<p>Electromagnetic corrections to the <i>n</i>-point functions of lattice QCD can be evaluated using a position-space photon propagator defined in infinite volume. Here we address the computational challenge arising from the volume-squared sum over the endpoints of the photon propagator. We consider a class of integral representations of the photon propagator that lead to a factorization of the two volume-sums, the Fourier representation being one instance thereof. An alternative choice is based on expressing the free scalar propagator as the autoconvolution of the corresponding five-dimensional propagator. We compare the performance of three different choices in the context of electromagnetic corrections to the hadronic vacuum polarization, on a gauge ensemble of size 48<sup>3</sup> × 128 with a pion mass of 286 MeV. As an outlook, we discuss more generally the factorization of sums over internal vertices, taking as an example the hadronic light-by-light contribution to the muon (<i>g</i> − 2).</p>

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Factorizing the position-space photon propagator in QED corrections to lattice QCD correlators

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  • 发表日期：

    2026年7月8日

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  • Dominik Erb,
  • Harvey B. Meyer,
  • Konstantin Ottnad

摘要

Electromagnetic corrections to the n-point functions of lattice QCD can be evaluated using a position-space photon propagator defined in infinite volume. Here we address the computational challenge arising from the volume-squared sum over the endpoints of the photon propagator. We consider a class of integral representations of the photon propagator that lead to a factorization of the two volume-sums, the Fourier representation being one instance thereof. An alternative choice is based on expressing the free scalar propagator as the autoconvolution of the corresponding five-dimensional propagator. We compare the performance of three different choices in the context of electromagnetic corrections to the hadronic vacuum polarization, on a gauge ensemble of size 483 × 128 with a pion mass of 286 MeV. As an outlook, we discuss more generally the factorization of sums over internal vertices, taking as an example the hadronic light-by-light contribution to the muon (g − 2).