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The background magnetic-field formalism of Lattice QCD has been used recentlyto calculate the magnetic polarizability of the charged pion. These $n_f = 2 +1$ numerical simulations are electro-quenched, such that the virtual sea-quarksof the QCD vacuum do not interact with the background field. To understand theimpact of this, we draw on partially quenched chiral perturbation theory. Inthis case, the leading term proportional to $1/M_\pi$ arises at tree level from$\mathcal{L}_4$. To describe the results from lattice QCD, while maintainingthe exact leading terms of chiral perturbation theory, we introduce a Pad\'eapproximant designed to reproduce the slow variation observed in the latticeQCD results. Two-loop contributions are introduced to assess the systematicuncertainty associated with higher-order terms of the expansion. Uponextrapolation, the magnetic polarizability of the charged pion at the physicalpion mass is found to be $\beta_{\pi^\pm}=-1.70\,(14)_{\rm stat}(25)_{\rmsyst}\times 10^{-4}$ fm$^3$, in good agreement with the recent experimentalmeasurement.

Chiral extrapolation of the charged-pion magnetic polarizability with Pad\'e approximant