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 Λ ~ 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 Λ, 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 γ∗γ∗ fusion cross-sections. Having tested the relation by reproducing the two-loop QED vacuum polarization (VP) from the tree-level γ∗γ∗→ e+e− cross-section, we predict the expected lattice-QCD integrand resulting from the γ∗γ∗→ π0 process.

Coordinate-space calculation of QED corrections to the hadronic vacuum polarization contribution to $(g-2)_\mu$

“…By expanding the QCD path integral to next-to-leading order in the electromagnetic coupling, one is able to express the HVP at NLO in the CCS representation, as shown in Ref. [9]. In contrast to the Hlbl contribution, the HVP at NLO is UV-divergent.…”

Isospin-breaking corrections to weak decays: the current status and a new infrared improvement

“…Lattice QCD+QED is a new frontier for precise numerical calculations and many collaborations have successfully produced results for IB corrections to different hadronic observables: the hadron spectrum [11,[18][19][20][21], the anomalous muon 𝑔−2 [22][23][24][25][26][27] (see also refs. [28,29]) and weak leptonic decays [30][31][32].…”

Muon $g-2$: Lattice calculations of the hadronic vacuum polarization

“…The benefit of being able to reuse existing gauge fields comes at the cost of having to compute a number of additional correlation functions. The combination of infinite-volume QED with finite-volume QCD has been proposed as alternative [25,106,107], similar to calculations of a hlbl µ [108,109]. When QED L [110] is used to formulate QED inside a finite box with periodic boundary conditions in the spatial directions, as it is the case in many calculations, the finite volume effects scale with 1/L 3 [111], where L is the spatial extent.…”