Pion Transition Form Factor from Twisted-Mass Lattice QCD and the Hadronic Light-by-Light $\ddot{I}{€}^0$-pole Contribution to the Muon $g-2$

Abstract

The neutral pion generates the leading pole contribution to the hadronic light-by-light tensor, which is given in terms of the nonperturbative transition form factor ${\mathcal{F}}_{\ddot{I}{€}^0{\hat{I}}^3{\hat{I}}^3}(q_1^2,q_2^2)$. Here we present an ab-initio lattice calculation of this quantity in the continuum and at the physical point using twisted-mass lattice QCD. We report our results for the transition form factor parameterized using a model-independent conformal expansion valid for arbitrary space-like kinematics and compare it with experimental measurements of the single-virtual form factor, the two-photon decay width, and the slope parameter. We then use the transition form factors to compute the pion-pole contribution to the hadronic light-by-light scattering in the muon $g-2$, finding $a_{\hat{I}}{¼}^{\ddot{I}{€}^0\text{-pole}}=56.7(3.2)\times 10^{-11}$.

21 pages, 17 figures, 4 tables, updated to published version