Strong <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>C</mml:mi> <mml:mi>P</mml:mi> </mml:math> violation and large- <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mi>N</

We revisit the contribution of the QCD <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mover accent="true"> <a:mi>θ</a:mi> <a:mo stretchy="false">¯</a:mo> </a:mover> </a:math> term to the <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mi>C</e:mi> <e:mi>P</e:mi> </e:math> -violating pion-nucleon couplings and the nucleon electric dipole moment in a combined large- <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:msub> <g:mi>N</g:mi> <g:mi>c</g:mi> </g:msub> </g:math> 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 <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:msub> <i:mi>N</i:mi> <i:mi>c</i:mi> </i:msub> </i:math> . We obtain good agreement with previous analyses for the pion-nucleon couplings and show that the large- <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:msub> <k:mi>N</k:mi> <k:mi>c</k:mi> </k:msub> </k:math> 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 <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:mi>C</m:mi> <m:mi>P</m:mi> </m:math> -violating pion- <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:mi mathvariant="normal">Δ</o:mi> </o:math> couplings, as well as the <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"> <r:mi mathvariant="normal">Δ</r:mi> </r:math> electric dipole moment and <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"> <u:mi mathvariant="normal">Δ</u:mi> <u:mi>N</u:mi> </u:math> transition moment.