Quark Chromo-Electric Dipole Moment Operator on the Lattice

We present a lattice QCD study of the contribution of the isovector quark chromo-electric dipole moment (qcEDM) operator to the nucleon electric dipole moments (nEDM). The calculation was carried out on four 2+1+1-flavor of highly improved staggered quark (HISQ) ensembles using Wilson-clover quarks to construct correlation functions. This clover-on-HISQ formulation is not fully \(O(a)\) improved, and gives rise to additional systematics over and above those due to removing excited state contributions to getting ground-state matrix elements, and the final chiral and continuum extrapolations to get the physical result. We use the non-singlet axial Ward identity including corrections up to \(O(a)\) to show how to control the power-divergent mixing of the isovector qcEDM operator with the lower dimensional pseudoscalar operator. The residual corrections are observed to give rise to \(O(25\%)\) violations in relations arising from the axial Ward identity. We devise three methods attempting to control the resulting uncertainty in the CP violating form factor; each of these, however, can have large \(O(a^2)\) corrections. Preliminary results for the nEDM due to qcEDM are presented choosing the method giving the most uniform behavior.