The $η\rightarrow γ^* γ^*$ transition form factor and the hadronic light-by-light $η$-pole contribution to the muon $g-2$ from lattice QCD

$π^0, η, η^\prime$ two-photon transition form factors in the holographic soft-wall model and contributions to $(g-2)_μ$

“…The White Paper [7] reports for the π 0 , η and η HLbL pole contributions: obtained from dispersive analyses (disp), Canterbury approximants (CA) and lattice QCD. New lattice determinations are in [54,65]. The comparison with the results in Table 1 reflects the comparison between the computed and measured TFFs: a higher value is obtained for π 0 , compatible results for η and η .…”

“…The only available measurements from the BaBar Collaboration concern η [52] for which there is agreement in the first two bins of momentum. For π 0 and η the curves are compared to lattice QCD results [53,54], the dispersive results [55] and the parameterization of Ref. [56].…”

Theory of g-2

“…[65][66][67] for the implementation of SDCs. Work is in progress to combine all these developments, together with improvements to the 𝜂, 𝜂 ′ pole contributions [68][69][70][71], into a full data-driven evaluation of 𝑎 HLbL 𝜇 . Since the WP publication, the HLbL contribution has also been evaluated within lattice QCD with competitive uncertainties.…”

Puzzles in the hadronic contributions to the muon anomalous magnetic moment

“…Therefore, since the publication of the WP, efforts were directed towards an improved evaluation of these sub-dominant contributions, addressing scalar resonances beyond the 𝑓 0 (500) [10], axial-vector resonances [11][12][13][14], tensor resonances and 𝐷-waves [15,16], which require a modification of the dispersive framework itself [17], as well as the SDCs on HLbL [12,[18][19][20]. Work is in progress to combine all these developments, together with improvements of the 𝜂, 𝜂 ′ pole contributions [21][22][23][24], into a full data-driven evaluation of 𝑎 HLbL 𝜇 . Since the WP publication, the HLbL contribution has also been evaluated within lattice QCD with competitive uncertainties.…”