Pion-Pole Contribution to Hadronic Light-By-Light Scattering in the Anomalous Magnetic Moment of the Muon

Abstract

The π^{0} pole constitutes the lowest-lying singularity of the hadronic light-by-light (HLBL) tensor, and thus, it provides the leading contribution in a dispersive approach to HLBL scattering in the anomalous magnetic moment of the muon (g-2)_{μ}. It is unambiguously defined in terms of the doubly virtual pion transition form factor, which in principle, can be accessed in its entirety by experiment. We demonstrate that, in the absence of a direct measurement, the full spacelike doubly virtual form factor can be reconstructed very accurately based on existing data for e^{+}e^{-}→3π, e^{+}e^{-}→e^{+}e^{-}π^{0}, and the π^{0}→γγ decay width. We derive a representation that incorporates all the low-lying singularities of the form factor, matches correctly onto the asymptotic behavior expected from perturbative QCD, and is suitable for the evaluation of the (g-2)_{μ} loop integral. The resulting value, a_{μ}^{π^{0}-pole}=62.6_{-2.5}^{+3.0}×10^{-11}, for the first time, represents a complete data-driven determination of the pion-pole contribution with fully controlled uncertainty estimates. In particular, we show that already improved singly virtual measurements alone would allow one to further reduce the uncertainty in a_{μ}^{π^{0}-pole}.

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].…”

Combined explanations of (g−2)μ,e and implications for a large muon EDM

“…The experimental value of the muon g − 2 [1] a exp µ = 116,592,089(63) × 10 −11 (1) differs from the SM prediction at the level of 3-4σ, for definiteness we take [2] ∆a µ = a exp µ − a SM µ ∼ 270(85) × 10 −11 (2) as an estimate of the current status. Recent advances in corroborating and improving the SM prediction include hadronic vacuum polarization [3][4][5][6][7][8][9][10], hadronic light-by-light scattering [11][12][13][14][15][16][17][18][19], and higher-order hadronic corrections [20,21]. The release of first results from the Fermilab experiment [22] is highly anticipated, while a complementary strategy based on ultracold muons is being pursued at J-PARC [23], see also Ref.…”