Speaker
Description
A model-independent dispersive framework for the evaluation of hadronic light-by-light (HLbL) scattering in the anomalous magnetic moment of the muon $(g-2)_\mu$ was recently developed. It is based on the general principles of analyticity, unitarity, and crossing symmetry to attribute the contributions to on-shell form factors and scattering amplitudes accessible from experiment, complementary to lattice QCD calculations of HLbL scattering. Within this framework, we focus on the recent work on the pion-pole contribution to HLbL scattering in the $(g-2)_\mu$, which is fully determined by the doubly-virtual pion transition form factor. The previous analysis of the singly-virtual transition form factor is generalised to the doubly-virtual kinematics in light of the available data for the $\pi^0\to\gamma \gamma$ decay width, $e^+e^-\to 3\pi$ cross section, and the space-like singly-virtual form factor from $e^+e^-\to e^+e^-\pi^0$. The form factor is reconstructed using a dispersive representation that accounts for all the low-lying singularities and incorporates the asymptotic behavior obtained from perturbative QCD. This detailed study accumulates to the first dispersive determination of the pion-pole contribution to the muon $(g-2)_\mu$, $a_\mu^{\pi^0 \text{-pole}}=62.6^{+3.0}_{-2.5}\times 10^{-11}$ [1,2], where its uncertainty can be reduced further owing to more precise singly-virtual measurements in the future.
[1] M. Hoferichter, B.-L. Hoid, B. Kubis, S. Leupold and S. P. Schneider, Phys. Rev. Lett. 121 (2018) 112002, [arXiv:1805.01471 [hep-ph]]
[2] M. Hoferichter, B.-L. Hoid, B. Kubis, S. Leupold and S. P. Schneider, JHEP 1810 (2018) 141, [arXiv:1808.04823 [hep-ph]]