Factorizing the position-space photon propagator in QED corrections to lattice QCD correlators
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| Format: | Preprint |
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2026
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| _version_ | 1866918386982715392 |
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| author | Erb, Dominik Meyer, Harvey B. Ottnad, Konstantin |
| author_facet | Erb, Dominik Meyer, Harvey B. Ottnad, Konstantin |
| contents | 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 $48^3\times128$ 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 $(g-2)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_13086 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Factorizing the position-space photon propagator in QED corrections to lattice QCD correlators Erb, Dominik Meyer, Harvey B. Ottnad, Konstantin High Energy Physics - Lattice 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 $48^3\times128$ 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 $(g-2)$. |
| title | Factorizing the position-space photon propagator in QED corrections to lattice QCD correlators |
| topic | High Energy Physics - Lattice |
| url | https://arxiv.org/abs/2603.13086 |