  The potential importance of short-distance nuclear effects in double-$\beta$
decay is assessed using a lattice QCD calculation of the $nn\rightarrow pp$
transition and effective field theory methods. At the unphysical quark masses
used in the numerical computation, these effects, encoded in the isotensor
axial polarisability, are found to be of similar magnitude to the nuclear
modification of the single axial current, which phenomenologically is the
quenching of the axial charge used in nuclear many-body calculations. This
finding suggests that nuclear models for neutrinoful and neutrinoless
double-$\beta$ decays should incorporate this previously neglected contribution
if they are to provide reliable guidance for next-generation neutrinoless
double-$\beta$ decay searches. The prospects of constraining the isotensor
axial polarisabilities of nuclei using lattice QCD input into nuclear many-body
calculations are discussed.
