Present and future prospects for lattice QCD calculations of matrix elements for nEDM

Abstract

A status report on the calculations of the contribution of four CP violating operators, the $\Theta$-term, the quark chromo EDM, the chromo EDM and the Weinberg operator to the neutron EDM are presented. At this time, there exit precise physical results only for the quark EDM operator by the PNDME collaboration. First results showing signal in the contributions of the $\Theta$-term and the connected part of the chromo EDM operator have been presented. The challenge of divergent mixing in the chromo EDM and Weinberg operators has motivated calculations in the gradient flow scheme. While there is steady progress, the challenges remaining are large. Results with $O(50\%)$ uncertainty with control over all systematic errors can be expected for the $\Theta$-term over the next five years. Prediction of a timeline of progress for the chromo EDM and the Weinberg operators will depend on when the renormalization and divergent mixing of these operators is brought under control. The most optimistic scenario is that the gradient flow scheme provides a solution for the signal and mixing problems for both the gluonic and quark operators.