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

TL;DR

The paper addresses strong CP violation from the QCD $\bar{\theta}$ term by unifying the $1/N_c$ expansion with chiral perturbation theory and exploiting an emergent ${\rm SU}(4)$ spin–flavor symmetry in the baryon sector to relate nucleon and $\Delta$ properties while explicitly incorporating the ${U}(1)_A$ anomaly. The meson sector includes an anomaly term that fixes a flavor-singlet mass via the topological input, enabling a controlled expansion, while the baryon sector yields CP-violating pion–nucleon couplings and SU(4) relations for pion–$\Delta$ couplings and related observables. The electric dipole moments are computed with a one-loop analysis showing a potential dominance of tree-level contributions in the large-$N_c$ limit, leading to a bound $|\bar{\theta}| \lesssim 10^{-11}$ when confronted with neutron EDM data, and the work provides lattice-testable isospin relations for nucleon and $\Delta$ moments. Overall, the framework clarifies the relative size of short- and long-range CP-violating effects and offers concrete predictions and relations for lattice studies to constrain the QCD $\bar{\theta}$ parameter and CP-violating nucleon potentials.

Abstract

We revisit the contribution of the QCD $\bar θ$ 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-$Δ$ couplings as well as the $Δ$ electric dipole moment and $ΔN$ transition moment.