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The recent lattice QCD calculations of the neutron and proton electric dipole moments and the CP-violating πNN coupling constant due to the θ term are reviewed. Progress toward nucleon electric dipole moment calculations, including the Weinberg three-gluon operator, the quark chromoelectric dipole moment operator, and their renormalization, is also discussed.
An electron can possess an electric dipole moment (edm) only if time reversal symmetry (T) is violated. No edm of any particle has yet been discovered. CP-violation, equivalent to T-violation by the CPT theorem, does occur in Kaon decays and can be accounted for by the standard model. However, this mechanism leads to an electron edm d(sub e) of the order of 10(exp -38) e cm, whereas the current experimental bound on d(sub e) is about 10(exp -27) e cm. However, well-motivated extensions of the standard model such as supersymmetric theories do predict that de could be as large as the current bound. In addition, CP violation in the early universe is required to explain the preponderance of matter over anti-matter, but the exact mechanism of this CP violation is unclear. For these reasons, we are undertaking a new experimental program to determine de to an improved accuracy of 10(exp -29) e cm. Our experiment will use laser-cooled, trapped Cesium atoms to measure the atomic edm d(sub Cs) that occurs if d(sub e) is not zero. In order to do this, we will measure the energy splitting between the atoms spin states in parallel electric and magnetic fields. The signature of an edm would be a linear dependence of the splitting on the electric field E due to the interaction - d(sub Cs) dot E. Our measurement will be much more sensitive than previous measurements because atoms can be stored in the trap for tens of seconds, allowing for much narrower Zeeman resonance linewidths. Also, our method eliminates the most important systematic errors, proportional to atomic velocity, which have limited previous experiments. In this presentation, we will describe the design of our new apparatus, which is presently under construction. An important feature of our experimental apparatus is that magnetic field noise will be suppressed to a very low value of the order of 1 fT/(Hz)1/2. This requires careful attention to the Johnson noise currents in the chamber, which have not been important in previous experiments. In addition we will present estimates of the limits of the various errors that we expect for our experiment.
The permanent electric dipole moments for the X 5Pi and B 5pi states of gas-phase CrO have been experimentally determined using the sub-Doppler optical technique of intermodulated fluorescence spectroscopy in conjunction with the Stark effect. The measured values are 3.88 + or - 0.13 and 4.1 + or - 1.8 D for the X and B states, respectively. The theoretical values determined for the X state using multireference CI iterative-natural-orbital and finite-field calculations are in excellent agreement with the experimental value.
A limit on the permanent electric dipole moment (EDM) of the positive muon is presented based on data from the Fermilab Muon g-2 Experiment taken between 2019 and 2020. The tracking detectors measure the average vertical decay angle of positrons from muon decays, enabling a search for an interaction between a possible muon EDM $d_μ$ and the lab-frame magnetic field. The result, $d_μ= (-0.35 \pm 0.19_{\mathrm{stat}} \pm 0.34_{\mathrm{sys}}) \times10^{-19}~e\cdot$cm, is consistent with zero and sets a new direct limit on the muon EDM of $|d_μ|<1.10\times10^{-19}~e\cdot$cm at the 95 percent confidence level.
Anomalous contributions to the electric and magnetic dipole moments of the τ lepton from new physics scenarios have brought renewed interest in the development of new charge-parity violating signatures in τ -pair production at Belle II energies, and also at higher energies of the Large Hadron Collider and the Future Circular Collider. In this paper, we discuss the effects of spin correlations, including transverse degrees of freedom, in the τ -pair production and decay. These studies include calculating analytical formulas, obtaining numerical results, and building semirealistic observables sensitive to the transverse spin correlations induced by the dipole moments of the τ lepton. The effects of such anomalous contributions to the dipole moments are introduced on top of precision simulations of e − e + → τ − τ + , q q ¯ → τ − τ + and γ γ → τ − τ + processes, involving multibody final states. The τ decays are simulated along with radiative corrections, in particular electroweak box contributions of W W and Z Z exchanges are taken into account. Respective extensions of the Standard Model amplitudes and the reweighting algorithms are implemented into the Monte Carlo, which is used to simulate τ -pair production in e − e + collisions, and the aupinner program, which is used to reweight events with τ pair produced in p p collisions. Published by the American Physical Society 2024
Multipole electric field for selection and focusing of thermal polar diatomic molecular beams in states of positive induced electric dipole moment
The cryogenic approach to the search for the neutron electric dipole moment—performing the experiment in superfluid liquid helium—holds promise for a substantial increase in sensitivity, potentially enabling a sensitivity level of 10 −28 𝑒cm. A crucial component in realizing such an experiment is the high-voltage and electrode system capable of providing an electric field of 75 kV/cm. This, in turn, requires an electric potential of 635 kV to be applied to the high-voltage electrode, while simultaneously satisfying other experimental constraints, such as those on heat load and magnetic noise requirements. In this work, we describe the outcome of a comprehensive development program addressing these challenges. It outlines the system requirements, discusses new insights into relevant physical phenomena, and details selected technical solutions with their corresponding experimental demonstrations and expected performance. The results collectively demonstrate the successful development of the necessary technology for the high-voltage and electrode system for this approach.
Electric dipole moments are sensitive probes of new phases in the Higgs Yukawa couplings. We calculate the complete two-loop QCD anomalous dimension matrix for the mixing of CP-odd scalar and tensor operators and apply our results for a phenomenological study of CP violation in the bottom and charm Yukawa couplings. We find large shifts of the induced Wilson coefficients at next-to-leading-logarithmic order. Using the experimental bound on the electric dipole moments of the neutron and mercury, we update the constraints on CP-violating phases in the bottom and charm quark Yukawas.
We revisit the electric dipole moments (EDMs) of quarks and leptons in the Minimal Supersymmetric Standard Model (MSSM) with trilinear R-parity violation (RPV). In this framework, EDMs are induced at the two-loop level via RPV interactions. We perform a comprehensive recalculation of several classes of Barr-Zee type diagrams in a general Rξ gauge. While we find general agreement with previous analytic results in the literature, our work provides a valuable independent cross-check of the complicated calculations. We also point out some subtleties in the intermediate steps and in the choice of the flavor basis for the numerical evaluation of the expressions. By confronting the theoretical predictions with the latest experimental limits on EDMs, we derive updated constraints on combinations of RPV couplings. We highlight an approximate, testable correlation between the proton and neutron EDM that emerges within the considered class of RPV models, offering a distinctive signature for future EDM experiments.
A fully generic treatment of electric dipole moments (EDMs) is presented in the CP-violating and flavor-conserving weak effective field theory (WET) with five flavors of quarks and three flavors of leptons. We systematically analyze leading contributions to EDMs originating from QCD and QED renormalization group running between the electroweak scale and low energy scales of about 2 GeV. We include the full one-loop anomalous dimension and a subset of two-loop corrections, as well as threshold corrections at the bottom, charm and τ masses. This allows us to derive master formulae in the space of generic WET for the neutron and proton EDMs, for EDMs of diamagnetic atoms, and for the precession frequencies constrained in molecular EDM experiments, from which bounds on the electron EDM are extracted. In particular, our master formulae capture the contributions of WET CP-violating operators with heavy quark and lepton flavors. As an application, we study EDM constraints on the Yukawa couplings of the Higgs boson, in both the linear and non-linear realizations of electroweak symmetry breaking.
It is shown that if Higgs-boson exchange mediates CP violation a significant electric dipole moment for the electron can result. Analogous effects can contribute to the neutron's electric dipole moment at a level competitive with Weinberg's three-gluon operator.
The potential energy function and electric dipole moment function (EDMF) are computed for ClO X 2Pi using several different techniques to include electron correlation. The EDMF is used to compute Einstein coefficients, vibrational lifetimes, and dipole moments in higher vibrational levels. The band strength of the 1-0 fundamental transition is computed to be 12 + or - 2 per sq cm atm determined from infrared heterodyne spectroscopy. The theoretical methods used include SCF, CASSCF, multireference singles plus doubles configuration interaction (MRCI) and contracted CI, coupled pair functional (CPF), and a modified version of the CPF method. The results obtained using the different methods are critically compared.
The potential energy function and electric dipole moment function (EDMF) are computed for CIO Chi(sup 2)Pi using several different techniques to include electron correlation. The EDMF is used to compute Einstein coefficients, vibrational lifetimes, and dipole moments in higher vibrational levels. Remaining questions concerning the position of the maximum of the EDMF may be resolved through experimental measurement of dipole moments of higher vibrational levels. The band strength of the 1-0 fundamental transition is computed to be 12 +/- 2 /sq cm atm in good agreement with three experimental values, but larger than a recent value of 5 /sq cm atm determined from infrared heterodyne spectroscopy. The theoretical methods used include SCF, CASSCF, multireference singles plus doubles configuration interaction (MRCI) and contracted CI, coupled pair functional (CPF), and a modified version of the CPF method. The results obtained using the different methods are critically compared.
We perform a model-independent analysis of the magnetic and electric dipole moments of the muon and electron. We give expressions for the dipole moments in terms of operator coefficients of the low-energy effective field theory (LEFT) and the Standard Model effective field theory (SMEFT). We use one-loop renormalization group improved perturbation theory, including the one-loop matching from SMEFT onto LEFT, and one-loop lepton matrix elements of the effective-theory operators. Semileptonic four-fermion operators involving light quarks give sizable non-perturbative contributions to the dipole moments, which are included in our analysis. We find that only a very limited set of the SMEFT operators is able to generate the current deviation of the magnetic moment of the muon from its Standard Model expectation.
Semiempirical electric dipole moment and derivative in molecular-molecular and molecular-atomic collisions of hydrogen
We calculate the electric dipole moments (EDMs) of three-nucleon systems at leading order in pionless effective field theory. The one-body contributions that arise from permanent proton and neutron EDMs and the two-body contributions that arise from charge-parity-odd nucleon-nucleon interactions are taken into account. Neglecting the Coulomb interaction, we consider the triton and 3 He, and also investigate them in the Wigner-SU(4) symmetric limit. We also calculate the electric dipole form factor and find numerically that the momentum dependence of the electric dipole form factor in the Wigner limit is, up to an overall constant (and numerical accuracy), the same as the momentum dependence of the charge form factor. Finally, we study the cutoff dependence of these observables and find that they are properly renormalized.
The research grant addressed in this final report began its most recent 3-year segment June 1, 2022 and terminated May 31, 2025. The work funded by the grant supported our group at the Massachusetts Institute of Technology (MIT) in its collaboration on the nEDM@SNS (SNS refers to the Spallation Neutron Source) project at the Oak Ridge National Laboratory (ORNL). This project had as its goal the measurement of a non-zero value of the electric dipole moment of the neutron (nEDM). If indeed the neutron has a non-zero electric dipole moment, it will tell us very important information about the Standard Model of Nuclear and Particle Physics. The Standard Model is remarkably successful in describing much of the world we live in, but we know it is not complete. A non-zero nEDM would indicate the existence of strong CP violation, which would be a major addition to the Standard Model.
Baryon number violation is a key ingredient of baryogenesis. It has been hypothesized that there could also be a parity-conjugated copy of the standard model particles, called mirror particles. The existence of such a mirror universe has specific testable implications, especially in the domain of neutral particle oscillation, viz. the baryon number violating neutron to mirror-neutron (n−n′) oscillation. Consequently, there were many experiments that have searched for n−n′ oscillation, and imposed constraints upon the parameters that describe it. Recently, further analysis on some of these results have identified anomalies which could point to the detection of n−n′ oscillation. All the previous efforts searched for n−n′ oscillation by comparing the relative number of ultracold neutrons that survive after a period of storage for one or both of the two cases: (i) comparison of zero applied magnetic field to a non-zero applied magnetic field, and (ii) comparison where the orientation of the applied magnetic field was reversed. However, n−n′ oscillations also lead to variations in the precession frequency of polarized neutrons upon flipping the direction of the applied magnetic field. Precession frequencies are measured, very precisely, by experiments searching for the electric dipole moment. For the first time, we used the data from the latest search for the neutron electric dipole moment to constrain n−n′ oscillation. After compensating for the systematic effects that affect the ratio of precession frequencies of ultracold neutrons and cohabiting 199Hg-atoms, chief among which was due to their motion in non-uniform magnetic field, we constrained any further perturbations due to n−n′ oscillation. We thereby provide a lower limit on the n−n′ oscillation time constant of τnn′/|cos(β)|>5.7s,0.36T′