Electric dipole moments of nucleons, nuclei, and atoms: The Standard Model and beyond

We dicuss the utility of precision probes for flavour-diagonal CP-violation, namely, searches for electric dipole moments of nucleons, atoms, and molecules, in looking for new physics thresholds that manifest themselves primarily through higher dimensional operators. After reviewing the status of the electric dipole moment (EDM) constraints, we consider first the sensitivity to a generic class of dimension-five operators generated at a supersymmetric threshold, through their contribution to CP- and flavour-violating observables. Such thresholds can be probed by EDMs up to a scale of order 108 GeV depending on the flavour structure. We then turn to consider the possibility that electroweak baryogenesis is made feasible by the introduction of dimension-six operators at a TeV-scale threshold. The EDM costraints on dimension-six couplings of the Higgs to the fermions currently still allow a reasonable window in parameter space for these models, but the next generation of experiments should provide a conclusive test. PACS Nos.: 11.30.Er, 12.60.Fr, 12.60.Jv

We review the importance of precision probes for flavor‐diagonal CP‐violation, specifically searches for electric dipole moments of nucleons, atoms and molecules, in accessing new CP‐odd physics at high scales. We summarize the effective field theory analysis of observable EDMs in terms of a general set of CP‐odd operators at 1 GeV, and the ensuing model‐independent new physics constraints, incorporating the recently improved limit on the Hg EDM. We also discuss the current status of these limits in the context of 1‐ and 2‐loop contributions in supersymmetric models.

Searches for intrinsic electric dipole moments of nucleons, atoms and molecules are precision flavour-diagonal probes of new -odd physics. We review and summarise the effective field theory analysis of the observable EDMs in terms of a general set of CP-odd operators at 1 GeV, and the ensuing model-independent constraints on new physics. We also discuss the implications for supersymmetric models, in light of the mass limits emerging from the LHC.

This article reviews the calculation of nuclear Schiff moments, which one must know in order to interpret experiments that search for time-reversal-violating electric dipole moments in certain atoms and molecules. After briefly reviewing the connection between dipole moments and CP violation in and beyond the Standard Model of particle physics; Schiff's theorem, which concerns the screening of nuclear electric dipole moments by electrons; Schiff moments; and experiments to measure dipole moments in atoms and molecules, this review examines attempts to compute Schiff moments in nuclei such as 199 Hg and octupole-deformed isotopes such as 225 Ra, which are particularly useful in experiments. It then turns to ab initio nuclear-structure theory, describing ways in which both the in-medium similarity renormalization group and coupled-cluster theory can be used to compute important Schiff moments more accurately than the less controlled methods that have been applied so far.

In some models of physics beyond the Standard Model (SM), one of the leading low energy consequences of the model appears in the form of the chromo-electric dipole moments (CEDMs) of the gluons and light quarks. We examine if these CEDMs can be distinguished from the QCD θ-term through the experimentally measurable nuclear and atomic electric dipole moments (EDMs) in both cases with and without the Peccei-Quinn (PQ) mechanism solving the strong CP problem. We find that the nucleon EDMs show a distinctive pattern when the EDMs are dominantly induced by the light quark CEDMs without the PQ mechanism. In the presence of the PQ mechanism, the QCD θ-parameter corresponds to the vacuum value of the axion field, which might be induced either by CEDMs or by UV-originated PQ breaking other than the QCD anomaly, for instance the PQ breaking by quantum gravity effects. We find that in case with the PQ mechanism the nucleon EDMs have a similar pattern regardless of what is the dominant source of EDMs among the CEDMs and θ-term, unless there is a significant cancellation between the contributions from different sources. In contrast, some nuclei or atomic EDMs can have characteristic patterns significantly depending on the dominant source of EDMs, which may allow identifying the dominant source among the CEDMs and θ-term. Yet, discriminating the gluon CEDM from the QCD θ-parameter necessitates additional knowledge of low energy parameters induced by the gluon CEDM, which is not available at the moment. Our results imply that EDMs can reveal unambiguous sign of CEDMs while identifying the origin of the axion vacuum value, however it requires further knowledge of low energy parameters induced by the gluon CEDM.

The electric dipole moments (EDMs) of electron and nucleons are promising probes of the new physics. In generic high-scale supersymmetric (SUSY) scenarios such as models based on mixture of the anomaly and gauge mediations, gluino has an additional contribution to the nucleon EDMs. In this paper, we studied the effect of the $CP$-violating gluon Weinberg operator induced by the gluino chromoelectric dipole moment in the high-scale SUSY scenarios, and we evaluated the nucleon and electron EDMs in the scenarios. We found that in the generic high-scale SUSY models, the nucleon EDMs may receive the sizable contribution from the Weinberg operator. Thus, it is important to compare the nucleon EDMs with the electron one in order to discriminate among the high-scale SUSY models.

Searches for permanent electric dipole moments (EDMs) of fundamental particles, atoms and molecules are promising experiments to constrain and potentially reveal beyond Standard Model (SM) physics. A non-zero EDM is a direct manifestation of time-reversal (T) violation, and, equivalently, violation of the combined operation of charge-conjugation (C) and parity inversion (P). Identifying new sources of CP violation can help to solve fundamental puzzles of the SM, e.g., the observed baryon-asymmetry in the Universe. Theoretical predictions for magnitudes of EDMs in the SM are many orders of magnitude below current experimental limits. However, many theories beyond the SM require larger EDMs. Experimental results, especially when combined in a global analysis, impose strong constraints on CP violating model parameters. Including an overview of EDM searches, I will focus on the future neutron EDM experiment at TRIUMF (Vancouver). For this effort, the TUCAN (TRIUMF Ultra Cold Advanced Neutron source) collaboration is aiming to build a strong, world leading source of ultra cold neutrons (UCN) based on a unique combination of a spallation target and a superfluid helium UCN converter. Another focus will be the search for an EDM of the diamagnetic atom 129 Xe using a 3 He comagnetometer and SQUID detection. The HeXeEDM collaboration has taken EDM data in 2017 and 2018 in the magnetically shielded room (BMSR-2) at PTB Berlin.

New fundamental particles at the mass scale of a few TeV c–2 could account for observed phenomena that cannot be explained by the standard model (SM) of particle physics, including the microscopic origin of dark matter and the macroscopic imbalance of matter over antimatter in the Universe. However, no beyond-the-SM (BSM) particles at the TeV scale have yet been detected at the Large Hadron Collider (LHC). With recent innovations, searches for time-reversal symmetry (T) violation through low-energy precision measurements of electric dipole moments (EDMs) of atoms and molecules have attained the sensitivity to detect indirect signatures of certain particles with masses of more than 10 TeV c–2. In this Perspective, we discuss recent developments in the measurement and interpretation of EDMs, and assess proposed techniques for future experiments that could push experimental limits on T-violating BSM physics to the PeV scale. Electric dipole moments (EDMs) of atoms and molecules are a sensitive probe for sources of time-reversal symmetry violation beyond the standard model. In this Perspective, we review recent progress in EDM searches with atoms and molecules and survey proposed next-generation experiments.

The electric dipole moments (EDMs) of nucleons are sensitive probes of additional $CP$ violation sources beyond the standard model to account for the baryon number asymmetry of the universe. As a fundamental quantity of the nucleon structure, tensor charge is also a bridge that relates nucleon EDMs to quark EDMs. With a combination of nucleon EDM measurements and tensor charge extractions, we investigate the experimental constraint on quark EDMs, and its sensitivity to $CP$ violation sources from new physics beyond the electroweak scale. We obtain the current limits on quark EDMs as $1.27\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}24}\text{ }\text{ }e\ifmmode\cdot\else\textperiodcentered\fi{}\mathrm{cm}$ for the up quark and $1.17\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}24}\text{ }\text{ }e\ifmmode\cdot\else\textperiodcentered\fi{}\mathrm{cm}$ for the down quark at the scale of $4\text{ }\text{ }{\mathrm{GeV}}^{2}$. We also study the impact of future nucleon EDM and tensor charge measurements, and show that upcoming new experiments will improve the constraint on quark EDMs by about 3 orders of magnitude leading to a much more sensitive probe of new physics models.

The observed baryon asymmetry in the universe cannot be reconciled with the current form of the Standard Model (SM) of particle physics. The Standard Model breaks charge conjugation parity (CP) symmetry, but not in a sufficient amount to explain the observed matter-antimatter asymmetry. Historically one of the first systems to be studied in the search of symmetry breaking within the Standard Model is the electric dipole moment (EDM) of the neutron. The contribution to the neutron EDM coming from the SM is several order of magnitudes smaller than the current experimental bound, thus providing a unique, background-free window for potential discovery of physics Beyond the Standard Model (BSM). The strong CP-violating theta term can also contribute to the neutron EDM, as can all the CP-violating effective operators describing, at energies below the electro-weak scale, the contributions from BSM. To constrain all these contributions to the neutron EDM we need to precisely determine the hadronic matrix elements of the corresponding renormalized operators. After a brief introduction on baryon asymmetry and baryogenesis, I summarize the current stuatus for experiments in search of a neutron EDM. I then describe in more details the different CP-violating sources, and some results in Chiral Perturbation Theory precede a discussion on the current status of Lattice QCD calculations. I will in particular focus on the 2 main challenges for these type of calculations: the signal-to-noise ratio and the renormalization. I will discuss several improvement techniques trying to improve these two aspects of the calculation and I will conclude with an optimistic view into the future.

Searches for the permanent electric dipole moments (EDMs) of molecules, atoms, nucleons and nuclei provide powerful probes of CP violation both within and beyond the Standard Model (BSM). The interpretation of experimental EDM limits requires careful delineation of physics at a wide range of distance scales, from the long-range atomic and molecular scales to the short-distance dynamics of physics at or beyond the Fermi scale. In this review, we provide a framework for disentangling contributions from physics at these disparate scales, building out from the set of dimension four and six effective operators that embody CP violation at the Fermi scale. We survey existing computations of hadronic and nuclear matrix elements associated with Fermi-scale CP violation in systems of experimental interest, and quantify the present level of theoretical uncertainty in these calculations. Using representative BSM scenarios of current interest, we illustrate how the interplay of physics at various scales generates EDMs at a potentially observable level.

The electric dipole moments (EDMs) of diamagnetic atoms are expected to be sensitive to charge-parity violation particularly in nuclei through the nuclear Schiff moment. I explicitly demonstrate that the well-known form of the Schiff moment operator originating from the nucleon EDM is obtained by considering the screening of the nucleon EDMs in a neutral atom. Consequently, an additional contribution to the Schiff moment arises from the screening of the nuclear EDM induced by the interaction of the nucleon EDMs with the protons. This correction to the Schiff moment of $^{199}$Hg is evaluated in the independent particle model.

The current status of electric dipole moments of diamagnetic atoms which involves the synergy between atomic experiments and three different theoretical areas -- particle, nuclear and atomic is reviewed. Various models of particle physics that predict CP violation, which is necessary for the existence of such electric dipole moments, are presented. These include the standard model of particle physics and various extensions of it. Effective hadron level combined charge conjugation (C) and parity (P) symmetry violating interactions are derived taking into consideration different ways in which a nucleon interacts with other nucleons as well as with electrons. Nuclear structure calculations of the CP-odd nuclear Schiff moment are discussed using the shell model and other theoretical approaches. Results of the calculations of atomic electric dipole moments due to the interaction of the nuclear Schiff moment with the electrons and the P and time-reversal (T) symmetry violating tensor-pseudotensor electron-nucleus are elucidated using different relativistic many-body theories. The principles of the measurement of the electric dipole moments of diamagnetic atoms are outlined. Upper limits for the nuclear Schiff moment and tensor-pseudotensor coupling constant are obtained combining the results of atomic experiments and relativistic many-body theories. The coefficients for the different sources of CP violation have been estimated at the elementary particle level for all the diamagnetic atoms of current experimental interest and their implications for physics beyond the standard model is discussed. Possible improvements of the current results of the measurements as well as quantum chromodynamics, nuclear and atomic calculations are suggested.

Searches for permanent electric dipole moments of particles, nuclei, atoms and molecules offer an extraordinary discovery potential to new mechanisms of CP violation beyond those incorporated in the standard electroweak model. The electric dipole moments induced by speculative scenarios, on different physical systems, require a complementary approach to pave the way to the fundamental CP-violating mechanisms. New avenues presently being explored in order to improve the experimental sensitivities include projects that consider the trapping of neutral particles, the confinement of charged particles in storage rings as well as the use of radioactive nuclei.

Parity-violating and time-reversal conserving (PVTC) and parity-violating and time-reversal-violating (PVTV) forces in nuclei form only a tiny component of the total interaction between nucleons. The study of these tiny forces can nevertheless be of extreme interest because they allow to obtain information on fundamental symmetries using nuclear systems. The PVTC interaction derives from the weak interaction between the quarks inside nucleons and nuclei and the study of PVTC effects opens a window on the quark-quark weak interaction. The PVTV interaction is sensitive to more exotic interactions at the fundamental level, in particular to strong CP violation in the Standard Model Lagrangian, or even to exotic phenomena predicted in various beyond-the-Standard-Model scenarios. The presence of these interactions can be revealed either by studying various asymmetries in polarized scattering of nuclear systems, or by measuring the presence of non-vanishing permanent electric dipole moments of nucleons, nuclei and diamagnetic atoms and molecules. In this contribution, we review the derivation of the nuclear PVTC and PVTV interactions within various frameworks. We focus in particular on the application of chiral effective field theory, which allows for a more strict connection with the fundamental interactions at the quark level. We investigate PVTC and PVTV effects induced by these potential on several few-nucleon observables, such as the longitudinal asymmetry in proton-proton scattering and radiative neutron-proton capture, and the electric dipole momentsof the deuteron and the trinucleon system.