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

## TL;DR

This paper reviews the current status and future prospects of lattice QCD calculations for neutron EDM contributions from various CP-violating operators, highlighting progress, challenges, and expected timelines for improved results.

## Contribution

It provides a comprehensive status report on lattice QCD calculations of neutron EDM contributions from four CP-violating operators, emphasizing recent progress and future challenges.

## Key findings

- Precise results currently only for quark EDM from PNDME
- Initial signals observed for $ heta$-term and chromo EDM contributions
- Progress with ~50% uncertainty expected in five years

## Abstract

A status report on the calculations of the contribution of four CP violating operators, the $\Theta$-term, the quark 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 has been 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 for progress on 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 to the numerical signal and mixing problems for both the gluonic and quark operators.