Abstract
We estimate the size of the hadronic matrix elements of CP-violating three-gluon and four-gluon Weinberg operators using sum-rule techniques. In the three-gluon case, we are able to reproduce the expressions given in earlier works, while the four-gluon results obtained in this article are new. Our paper therefore represents the first systematic study of contributions to the electric dipole moment of the neutron due to CP-violating dimension-six and dimension-eight operators. We provide many details on both the derivation of the sum rules as well as the analysis of the uncertainties that plague our final predictions.
Highlights
Uncertainties [30, 31], nucleon, nuclear and diamagnetic EDMs receive contributions from several effective operators that are plagued by theoretical uncertainties of different sizes
The EDM contributions from down and up quarks to the nEDM have been calculated with an accuracy of O(5%) using lattice QCD (LQCD) [32,33,34], while sum-rule calculations [35,36,37] allow to determine the nEDM contributions from the down-quark and up-quark chromomagnetic EDMs (CEDMs) with uncertainties of O(50%)
Inserting (5.28) into (3.19), we find for the Ioffe interpolating current, i.e. β = −1, the following expression for the nEDM contribution of the dimension-eight Weinberg operators dn m O8
Summary
The central object for the derivation of the sum-rule estimates for the hadronic matrix elements of operators of the type (1.1) is the following correlation function. The basic idea is to calculate (2.1) using two different approaches and to match the results to obtain an analytic expression for the nEDM in terms of hadronic quantities. One defines a phenomenological form Πphen of the correlator, which incorporates the wave function of the neutron, its EDM and other parameters. The second approach relies instead on an OPE of the correlator leading to the object ΠOPE that depends on the expectation values of effective operators, such as the three-gluon and four-gluon interactions introduced in (1.1). Matching the expressions for Πphen and ΠOPE yields the contribution of the effective operators of interest to the nEDM.
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