# Constraining CP-violating electron-gluonic operators

## TL;DR

This paper analyzes constraints on CP-violating electron-gluonic operators from EDM experiments, deriving bounds on their effective scales and discussing the theoretical uncertainties involved.

## Contribution

It provides the first comprehensive analysis of constraints on two specific CP-odd electron-gluonic operators using current and future EDM data, including QCD running effects.

## Key findings

- ACME ThO experiment sets an 8 TeV scale bound for one operator.
- The contribution to EDM mainly comes from CP-odd electron-nucleon interactions.
- The current bound on the second operator is weaker with larger uncertainties.

## Abstract

We present an analysis of constraints on two types of CP-odd electron-gluonic operators $(\bar{e}i\gamma^5 e)G_{\mu\nu}^a G^{a\mu\nu}$ and $(\bar{e}e)G_{\mu\nu}^a \tilde{G}^{a\mu\nu}$ from current and future electric dipole moment (EDM) experiments. The recent result from the ACME experiment using ThO molecules is used to derive an impressive lower bound on the effective scale for $(\bar{e}i\gamma^5 e)G_{\mu\nu}^a G^{a\mu\nu}$ at 8 TeV, assuming a QCD one-loop factor and no helicity suppression from new physics. One interesting aspect is that $(\bar{e}i\gamma^5 e)G_{\mu\nu}^a G^{a\mu\nu}$ contributes to the observable EDM in ThO experiment mainly through CP-odd electron-nucleon interaction rather than direct electron EDM which arises from three-loop running and matching. For $(\bar{e}e)G_{\mu\nu}^a \tilde{G}^{a\mu\nu}$ the current bound is much weaker and suffers from large uncertainties. We also discuss the QCD running and matching for the CP-odd electron-gluonic operators and give an estimate of the relevant nucleon matrix elements and uncertainties that are needed in the calculation.