  In this report we present the status of the Mainz group's lattice QCD
calculation of the pion transition form factor, which describes the interaction
of an on-shell pion with two off-shell photons. This form factor is the main
ingredient in the calculation of the pion-pole contribution to hadronic
light-by-light scattering in the muon $g-2$. We use the $N_f = 2 + 1$ CLS gauge
ensembles, and we update our previous work by including a physical pion mass
ensemble (E250). We compute the transition form factor in a moving frame as
well as in the pion rest frame in order to have access to a wider range of
photon virtualities. In addition to the quark-line connected correlator we also
compute the quark-line disconnected diagrams that contribute to the form
factor. At the final stage of the analysis, the result on E250 will be combined
with the previous work published in 2019 to extrapolate the form factor to the
continuum and to physical quark masses.
