Strong CP Violation and large-$N_c$ spin-flavor symmetry

Abstract: We revisit the contribution of the QCD $\bar \theta$ term to the CP violating pion-nucleon couplings and the nucleon electric dipole moment in a combined large-$N_c$ and chiral perturbation theory framework. In particular, we approach this issue through the emergent spin-flavor symmetry of the baryon sector at large but finite $N_c$. We obtain good agreement with previous analyses for the pion-nucleon couplings and show that the large-$N_c$ framework indicates that tree-level contributions to the electric dipole moment possibly play a dominant role. The spin-flavor symmetry also enables us to provide novel constraints on CP violating pion-$\Delta$ couplings as well as the $\Delta$ electric dipole moment and $\Delta N$ transition moment.