  We compute the electromagnetic corrections to neutron beta decay using a
low-energy hadronic effective field theory. We identify and compute new
radiative corrections arising from virtual pions that were missed in previous
studies. The largest correction is a percent-level shift in the axial charge of
the nucleon proportional to the electromagnetic part of the pion-mass
splitting. Smaller corrections, comparable to anticipated experimental
precision, impact the $\beta$-$\nu$ angular correlations and the
$\beta$-asymmetry. We comment on implications of our results for the comparison
of the experimentally measured axial charge with first-principle computations
using lattice QCD and on the potential of $\beta$-decay experiments to
constrain beyond-the-Standard-Model interactions.
