Finite-volume corrections to the CP-odd nucleon matrix elements of the electromagnetic current from the QCD vacuum angle

Nucleon electric dipole moments originating from strong CP-violation are being calculated by several groups using lattice QCD. We revisit the finite volume corrections to the CP-odd nucleon matrix elements of the electromagnetic current, which can be related to the electric dipole moments in the continuum, in the framework of chiral perturbation theory up to next-to-leading order taking into account the breaking of Lorentz symmetry. A chiral extrapolation of the recent lattice results of both the neutron and proton electric dipole moments is performed, which results in $d_n=(-2.7\pm 1.2)\times {10}^{-16}e{\theta }_0$cm and $d_p=(2.1\pm 1.2)\times {10}^{-16}e{\theta }_0$cm.