$C$ and $CP$ violation in effective field theories

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.