P-odd and CP-odd Four-Quark Contributions to Neutron EDM

TL;DR

This paper investigates the hadronic matrix elements of P-odd and CP-odd four-quark operators relevant to the neutron EDM, using chiral perturbation theory, nucleon models, and lattice QCD considerations to reduce uncertainties.

Contribution

It classifies operators in chiral representations, derives symmetry relations, and estimates non-perturbative matching coefficients, advancing the understanding of hadronic uncertainties in neutron EDM calculations.

Findings

Provides symmetry relations among matrix elements.

Estimates non-perturbative matching coefficients in quark models.

Compares results with previous methods like QCD sum rules.

Abstract

In a class of beyond-standard-model theories, CP-odd observables, such as the neutron electric dipole moment, receive significant contributions from flavor-neutral P-odd and CP-odd four-quark operators. However, considerable uncertainties exist in the hadronic matrix elements of these operators strongly affecting the experimental constraints on CP-violating parameters in the theories. Here we study their hadronic matrix elements in combined chiral perturbation theory and nucleon models. We first classify the operators in chiral representations and present the leading-order QCD evolutions. We then match the four-quark operators to the corresponding ones in chiral hadronic theory, finding symmetry relations among the matrix elements. Although this makes lattice QCD calculations feasible, we choose to estimate the non-perturbative matching coefficients in simple quark models. We finally compare the results for the neutron electric dipole moment and P-odd and CP-odd pion-nucleon couplings with the previous studies using naive factorization and QCD sum rules. Our study shall provide valuable insights on the present hadronic physics uncertainties in these observables.