Electric dipole moments (EDMs) of nucleons and nuclei are actively considered as direct evidence of the CP violation. Calculations of nucleon EDMs on lattice are required to connect the quark- and hadron- level effective CP violating interactions within QCD or other CP violating sources in new physics beyond the standard model. Among them, the theta-induced nucleon EDM, that is the only such renormalizable interaction, has widely been investigated on a lattice. In the report, we review recent developments of the lattice calculations of nucleon EDM induced QCD theta term.
Electric dipole moments (EDMs) of nucleons and nuclei, which are sought as evidence of CP violation, require lattice calculations to connect constraints from experiments to limits on the strong CP violation within QCD or CP violation introduced by new physics from beyond the standard model. Nucleon EDM calculations on a lattice are notoriously hard due to large statistical noise, chiral symmetry violating effects, and potential mixing of the EDM and the anomalous magnetic moment of the nucleon. In this report, details of ongoing lattice calculations of proton and neutron EDMs induced by the QC…
We present initial results of computing nucleon electric dipole moment induced by quark chromo-EDM, CP-violating quark-gluon coupling. Using chirally-symmetric domain wall and Möbius fermions with pion mass $m_π=172\text{ MeV}$, we calculate the connected part of the electric dipole form factor $F_3(Q^2)$. In addition, we perform an exploratory study of the method to calculate EDM using uniform background electric field on a lattice introduced without breaking the periodicity in the time direction.
Electric dipole moments (EDMs), which are sought as evidence of CP violation, require lattice calculations to connect constraints from experiments to limits on the strong CP violation within QCD or CP violation in new physics beyond the standard model. Nucleon EDM calculations on a lattice are notoriously hard due to large statistical noise, chiral symmetry violating effects, and potential mixing of the EDM and the anomalous magnetic moment of the nucleon. In this report, details of ongoing lattice calculations of proton and neutron EDMs induced by the QCD $θ$-term and the quark chromo-EDM, th…
We calculate the nucleon electric dipole moment (EDM) from the $θ$ term with overlap fermions on three domain wall lattices with different sea pion masses at lattice spacing 0.11 fm. Due to the chiral symmetry conserved by the overlap fermions, we have well defined topological charge and chiral limit for the EDM. Thus, the chiral extrapolation can be carried out reliably at nonzero lattice spacings. We use three to four different partially quenched valence pion masses for each sea pion mass and find that the EDM dependence on the valence and sea pion masses behaves oppositely, which can be des…
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-of-principle, thereby providing a novel meth…
We present a calculation of the contribution of the $Θ$-term to the neutron and proton electric dipole moments using seven 2+1+1-flavor HISQ ensembles. We also estimate the topological susceptibility for the 2+1+1 theory to be $χ_Q = (66(9)(4) \rm MeV)^4$ in the continuum limit at $M_π= 135$ MeV. The calculation of the nucleon three-point function is done using Wilson-clover valence quarks. The CP-violating form factor $F_3$ is calculated by expanding in small $Θ$. We show that lattice artifacts introduce a term proportional to $a$ that does not vanish in the chiral limit, and we include this …
We analyze commonly used expressions for computing the nucleon electric dipole form factors (EDFF) $F_3$ and moments (EDM) on a lattice and find that they lead to spurious contributions from the Pauli form factor $F_2$ due to inadequate definition of these form factors when parity mixing of lattice nucleon fields is involved. Using chirally symmetric domain wall fermions, we calculate the proton and the neutron EDFF induced by the CP-violating quark chromo-EDM interaction using the corrected expression. In addition, we calculate the electric dipole moment of the neutron using background electr…
We briefly discuss the current status of lattice QCD simulations and review selective results on nucleon observables focusing on recent developments in the lattice QCD evaluation of the nucleon form factors and radii, parton distribution functions and their moments, and the neutron electric dipole moment. Nucleon charges and moments of parton distribution functions are presented using simulations generated at physical values of the quark masses, while exploratory studies are performed for the parton distribution functions and the neutron electric dipole moment at heavier than physical value of…
A nonzero electric dipole moment (EDM) of the neutron, proton, deuteron or helion, in fact, of any finite system necessarily involves the breaking of a symmetry, either by the presence of external fields (i.e. electric fields leading to the case of induced EDMs) or explicitly by the breaking of the discrete parity and time-reflection symmetries in the case of permanent EDMs. We discuss two theorems describing these phenomena and report about the cosmological motivation for an existence of CP breaking beyond what is generated by the Kobayashi-Maskawa mechanism in the Standard Model and what thi…
The quark chromo-electric dipole moment operator and the pseudo-scalar fermion bilinear with which it mixes under renormalization can both be included in a calculation of the electromagnetic form factor of the nucleon using the Schwinger source method. A preliminary calculation of these operators using clover quarks on HISQ lattices generated by MILC collaboration will be presented showing the quality of the signal in the correlators necessary for calculating the neutron electric dipole moment.
In this proceedings, we lay the foundation for computing the contribution of quark chromo-electric dipole moment (qCEDM) operator to the nucleon electric dipole moment. By applying the gradient flow technique, we can parameterize the renormalization and operator mixing issues associated with the qCEDM operator on the lattice. As the nucleon mixing angle $α_N$ is a key component for determining the neutron and proton electric dipole moments induced by the qCEDM operator, we present the formalism and preliminary results for $α_N$ with respect to the gradient flow time $t_f$. The results are comp…
A symmetry-preserving Dyson-Schwinger equation treatment of a vector-vector contact interaction is used to compute dressed-quark-core contributions to the nucleon $σ$-term and tensor charges. The latter enable one to directly determine the effect of dressed-quark electric dipole moments (EDMs) on neutron and proton EDMs. The presence of strong scalar and axial-vector diquark correlations within ground-state baryons is a prediction of this approach. These correlations are active participants in all scattering events and thereby modify the contribution of the singly-represented valence-quark rel…
