Forward light-by-light scattering and electromagnetic correction to hadronic vacuum polarization

Abstract

Lattice QCD calculations of the hadronic vacuum polarization (HVP) have reached a precision where the electromagnetic (e.m.) correction can no longer be neglected. This correction is both computationally challenging and hard to validate, as it leads to ultraviolet (UV) divergences and to sizeable infrared (IR) effects associated with the massless photon. While we precisely determine the UV divergence using the operator-product expansion, we propose to introduce a separation scale $\Lambda \sim 400$MeV into the internal photon propagator, whereby the calculation splits into a short-distance part, regulated in the UV by the lattice and in the IR by the scale $\Lambda$, and a UV-finite long-distance part to be treated with coordinate-space methods, thereby avoiding power-law finite-size effects altogether. In order to predict the long-distance part, we express the UV-regulated e.m. correction to the HVP via the forward hadronic light-by-light (HLbL) scattering amplitude and relate the latter via a dispersive sum rule to ${\gamma }^{\ast }{\gamma }^{\ast }$ fusion cross-sections. Having tested the relation by reproducing the two-loop QED vacuum polarization (VP) from the tree-level ${\gamma }^{\ast }{\gamma }^{\ast }\to e^{+}{e}^{-}$ cross-section, we predict the expected lattice-QCD integrand resulting from the ${\gamma }^{\ast }{\gamma }^{\ast }\to {\pi }^0$ process.

29 pages, 6 figures; text matches the published version

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Cited by in corpus (10)

• The anomalous magnetic moment of the muon in the Standard Model: an update
• Improved ${\pi }^0,\eta ,{\eta }^{\prime }$ transition form factors in resonance chiral theory and their $a_{\mu }^{\mathrm{HLbL}}$ contribution
• $\tau$ data-driven evaluation of Euclidean windows for the hadronic vacuum polarization
• Muon $g-2$: Lattice calculations of the hadronic vacuum polarization
• Hadronic light-by-light scattering contribution to the muon $g-2$ from lattice QCD: semi-analytical calculation of the QED kernel
• Tensor Meson Pole contributions to the HLbL piece of $a_{\mu }$ within R$\chi$T
• Running of the Electroweak Gauge Couplings from First Principles
• Precision lattice calculation of the hadronic contribution to the running of the electroweak gauge couplings
• Tau Data-Based Evaluations of the hadronic vacuum polarization contribution to the muon $g-2$
• QED corrections to meson masses