  This work presents a determination of potential short-distance contributions
to the unphysical $\pi^-\rightarrow\pi^+ e^- e^-$ decay through lattice QCD
calculations. The hadronic contributions to the transition amplitude are
described by the pion matrix elements of five Standard Model Effective Field
Theory operators, which are computed on five ensembles of domain-wall fermions
with $N_f = 2 + 1$ quark flavors with a range of heavier-than-physical values
of the light quark masses. The matrix elements are extrapolated to the
continuum, physical light-quark mass, and infinite volume limit using a
functional form derived in chiral Effective Field Theory ($\chi\mathrm{EFT}$).
This extrapolation also yields the relevant low-energy constants of
$\chi\mathrm{EFT}$, which are necessary input for $\chi\mathrm{EFT}$
calculations of neutrinoless double beta decay of nuclei.
