Quark Chromo-Electric Dipole Moment Operator on the Lattice

Abstract

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.