Lattice calculation of the pion transition form factor $π^0 \to γ^* γ^*$

We calculate the pion transition form factor ${\cal F}_{π^0γ^*γ^*}(q_1^2,q_2^2)$, which describe the interaction of an on-shell pion with two off-shell photons, using lattice QCD simulations with two degenerate flavors of dynamical quarks. This form factor is the main ingredient in the calculation of the pion-pole contribution to hadronic light-by-light scattering in the muon $g-2$, $a_μ^{\mathrm{HLbL}; π^0}$. We focus our study on the spacelike region with photon virtualities up to $1.5~\mathrm{GeV}^2$, not yet measured experimentally. Several lattice spacings and pion masses are used to extrapolate the results to the physical point and a comparison with different phenomenological models is performed. Finally, we use our extrapolated form factor to provide a lattice determinaiton of $a_μ^{\mathrm{HLbL}; π^0}$.

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