  The quest for new sources of the simultaneous violation of $C$ and $CP$
symmetry was popular in the 1960s and has since been mostly neglected for more
than half a century. In this work we revisit fundamental quark-level operators
that break $C$ and $CP$ up to and including mass dimension 8 for
flavor-conserving transitions, relying on the complete operator sets of the
so-called Standard Model effective field theory and the low-energy effective
field theory. With the formalism of chiral perturbation theory, we match these
quark operators to light-meson physics, derive $C$- and $CP$-odd Lagrangians
for several processes in the $\eta$, $\eta'$, and pion sectors, and
furthermore, as a proof of principle, give estimates for the respective
observables in explicit dependence of the underlying high-energy scale for new
physics.
