Quark chromoelectric dipole moment operator on the lattice

We present a lattice QCD study of the contribution of the isovector quark chromoelectric dipole moment (qcEDM) operator to the nucleon electric dipole moments (nEDM). The calculation was carried out on four 2+1+1 flavor highly improved staggered quark (HISQ) ensembles generated by the MILC Collaboration. Wilson-clover quarks were used 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 nonsinglet axial Ward identity (AWI) 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 AWI. 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.