Dispersion relation for hadronic light-by-light scattering: pion pole

Abstract

The pion-pole contribution to hadronic light-by-light scattering in the anomalous magnetic moment of the muon (g − 2) µ is fully determined by the doubly-virtual pion transition form factor. Although this crucial input quantity is, in principle, directly accessible in experiment, a complete measurement covering all kinematic regions relevant for (g − 2) µ is not realistic in the foreseeable future. Here, we report in detail on a reconstruction from available data, both space-and time-like, using a dispersive representation that accounts for all the low-lying singularities, reproduces the correct high-and low-energy limits, and proves convenient for the evaluation of the (g − 2) µ loop integral. We concentrate on the systematics of the fit to e + e − → 3π data, which are key in constraining the isoscalar dependence, as well as the matching to the asymptotic limits. In particular, we provide a detailed account of the pion transition form factor at low energies in the time-and space-like region, including the error estimates underlying our final result for the pion-pole contribution, a π 0 -pole µ = 62.6 +3.0 −2.5 × 10 −11 , and demonstrate how forthcoming singly-virtual measurements will further reduce its uncertainty.

Contribution of neutral pseudoscalar mesons to aμHLbL within a Schwinger-Dyson equations approach to QCD

“…Our SDE prediction of a π 0 ,HLbL µ is compatible with other reported values [42,52,55,56,95,96]. For example, −0.25 ) · 10 −10 (dispersive evaluation).…”

Kaon-box contribution to the anomalous magnetic moment of the muon

“…In contrast to a purely datadriven dispersive framework, the necessary pseudoscalar transition form factors have not been extracted from ex- periment but calculated using DSEs and BSEs. The central values of the pseudoscalar pole contributions to a µ obtained in [29] agree well within error bars with corresponding ones from data-driven dispersion theory [26,27] and a related approach using Canterbury approximants Ref. [30].…”

Pseudoscalar transition form factors and the hadronic light-by-light contribution to the anomalous magnetic moment of the muon from holographic QCD

“…[12]: instead of the value a π 0 µ = 6.54(25) · 10 −10 , quoted therein, we find that the spread of the bottom-up AdS/QCD results is given by 5.9(2) · 10 −10 for fixed f π = 92.4 MeV. This is in between the central results given by a simple VMD model (a VMD µ = 5.7 · 10 −10 ) and the LMD+V model (a VMD µ = 6.3 · 10 −10 ) [5], it is at the lower end of the result [36] (a dispersive µ = 6.3(3) · 10 −10 ) obtained in the dispersion theory framework of Ref. [37], but it happens to agree remarkably well with the recent lattice result [15] of 5.97(36) · 10 −10 for the pion-pole contribution.…”