  The magnetic polarizability of the neutral pion has been calculated in the
background magnetic-field formalism of Lattice QCD. In this investigation, the
chiral extrapolation of these lattice results is considered in a formalism
preserving the exact leading nonanalytic terms of chiral perturbation theory.
The $n_f = 2 + 1$ numerical simulations are electro-quenched, such that the
virtual sea-quarks of the QCD vacuum do not interact with the background field.
To understand the impact of this, we draw on partially quenched chiral
perturbation theory and identify the leading contributions of quark-flow
connected and disconnected diagrams. While electro-quenching does not impact
the leading-loop contribution to the magnetic polarizability, the loops which
generate the leading term have yet to be considered in lattice QCD simulations.
Lattice QCD results are used to constrain the analytic terms in the chiral
expansion and supplementing those with the two-loop result from chiral
perturbation theory enables an evaluation of the polarizability at the physical
quark mass. The resulting magnetic polarizability of the neutral pion is
$\beta_{\pi^0}=3.44(19)^{\rm stat}(37)^{\rm syst}\times 10^{-4}$ fm$^3$, which
lies just above the $1 \sigma$ error bound of the experimental measurement.
