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

TL;DR

This paper presents a first-principles lattice QCD calculation of the neutral pion transition form factor at the physical point, and uses it to estimate the pion-pole contribution to the muon g-2, reducing theoretical uncertainties.

Contribution

It provides an ab-initio lattice QCD determination of the pion transition form factor and its impact on the muon g-2, improving upon previous model-dependent estimates.

Findings

Transition form factor agrees with experimental data.

Calculated pion-pole contribution to muon g-2: 56.7(3.2) x 10^{-11}.

Model-independent conformal expansion used for parameterization.

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 $\mathcal{F}_{\pi^0\gamma\gamma}(q_1^2,q_2^2)$. 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 $a_\mu^{\pi^0\text{-pole}} = 56.7(3.2) \times 10^{-11}$.