Nucleon electric dipole moment with the gradient flow: Theθ-term contribution

Abstract

We propose a new method to calculate electric dipole moments induced by the strong QCD θ-term. The method is based on the gradient flow for gauge fields and is free from renormalization ambiguities. We test our method by computing the nucleon electric dipole moments in pure Yang-Mills theory at several lattice spacings, enabling a first-of-its-kind continuum extrapolation. The method is rather general and can be applied for any quantity computed in a θ vacuum. This first application of the gradient flow has been successful and demonstrates proof-ofprinciple, thereby providing a novel method to obtain precise results for nucleon and light nuclear electric dipole moments.

Direct and indirect constraints on CP-violating Higgs-quark and Higgs-gluon interactions

“…Currently the effect of θ ind is taken into account within the QCD sum rule approach. Progress in lattice-QCD evaluations of dn(θ) (for recent results see [63][64][65]) will also improve the contribution to the nucleon EDM proportional toθ ind .…”

New Physics Searches from Nucleon Matrix Elements in Lattice QCD

“…Similar methods have been extended for the calculation of other matrix elements [49]. So far we discussed the extraction of the nEDM from the CP-odd form factor [47,[50][51][52], which is based on the small-θ expansion. However, there are alternative methods to compute the nEDM, such as, simulating the action with an imaginary θ [53], or with an application of an external electric field and measuring the associated energy shifts [54].…”

“…The large statistical error is a demonstration of the difficulty to extract this quantity and the need for development of new techniques. π for: a) N f =2+1+1 TMF [47] (blue square) corresponding to a weighted average using different methods for extracting F 3 (0)), b) N f =0 DWF [50] (magenta upward triangles), N f =2+1 DWF [51] (red circles) and N f =0 Clover fermions [52] (green downward triangles) by extracting the CP-odd F 3 (Q 2 ) and fitting its Q 2 -dependence, c) N f =2 Clover fermions [54] (turquoise left triangles) obtained using a background electric field, d) N f =2+1 Clover fermions [53] (orange diamonds) by implementing an imaginary θ.…”

Neutron Electric Dipole Moment on the Lattice

“…Hence it can be treated as a small expansion parameter. Any expectation value in presence of a small QCD Θ-term can then be written as follows [23][24][25][26][27]:…”

“…We illustrate these three approaches for the case of the CP-violating Θ-term whose volume integral is the topological charge Q top . They are the external electric field method [19][20][21][22], expansion in θ [23][24][25][26][27], and simulation with imaginary θ [28][29][30].…”