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

We calculate the $��^0\to ��^*��^*$ transition form factor ${\cal F}_{��^0��^*��^*}(q_1^2,q_2^2)$ in lattice QCD with two flavors of quarks. Our main motivation is to provide the input to calculate the $��^0$-pole contribution to hadronic light-by-light scattering in the muon $(g-2)$, $a_��^{\rm HLbL;��^0}$. We therefore focus on the region where both photons are spacelike up to virtualities of about $1.5~$GeV$^2$, which has so far not been experimentally accessible. Results are obtained in the continuum at the physical pion mass by a combined extrapolation. We reproduce the prediction of the chiral anomaly for real photons with an accuracy of about $8-9\%$. We also compare to various recen…