Nucleon electric dipole form factor in the QCD instanton vacuum

In the quantum chromodynamics (QCD) vacuum, the nucleon form factors receive contributions from the underlying ensemble of topological pseudoparticles, which are sensitive to a finite vacuum angle <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:mi>θ</a:mi> </a:mrow> </a:math> . We use this observation to derive a novel relationship between the Pauli and electric dipole form factors, for light quark flavors. This relationship allows for an explicit derivation of the proton and neutron electric dipole moments induced by a small <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mi>C</c:mi> <c:mi>P</c:mi> </c:math> violating <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mi>θ</e:mi> </e:math> angle, in terms of the vacuum topological susceptibility times pertinent magnetic moments. The results compare well with some recent lattice estimates.