  The interpretation of nuclear electric dipole moment (EDM) experiments is
clouded by large theoretical uncertainties associated with nonperturbative
matrix elements. In various beyond-the-Standard Model scenarios nuclear and
diamagnetic atomic EDMs are expected to be dominated by CP-violating
pion-nucleon interactions that arise from quark chromo-electric dipole moments.
The corresponding CP-violating pion-nucleon coupling strengths are, however,
poorly known. In this work we propose a strategy to calculate these couplings
by using spectroscopic lattice QCD techniques. Instead of directly calculating
the pion-nucleon coupling constants, a challenging task, we use chiral symmetry
relations that link the pion-nucleon couplings to nucleon sigma terms and mass
splittings that are significantly easier to calculate. In this work, we show
that these relations are reliable up to next-to-next-to-leading order in the
chiral expansion in both SU(2) and SU(3) chiral perturbation theory. We
conclude with a brief discussion about practical details regarding the required
lattice QCD calculations and the phenomenological impact of an improved
understanding of CP-violating matrix elements.
