We calculate the electric dipole moment (EDM) of the nuclei $^7$Li and $^{11}$B in the cluster model with $α$ ($^4$He) and triton ($^3$H) clusters as degrees of freedom. The $^7$Li and $^{11}$B nuclei are treated in the two- and three-body problem, respectively, using the Gaussian expansion method, assuming the one-meson exchange P, CP-odd nuclear forces. We find that $^7$Li and $^{11}$B have larger sensitivity to the CP violation than the deuteron. It is also suggested that the EDMs of $^7$Li and $^{11}$B, together with those of $^6$Li, $^9$Be and the $1/2^+_1$ excited state of $^{13}$C, obey an approximate counting rule accounting for the EDM of the cluster and the $α-N $ polarization. We show their sensitivity on the hadronic level CP violation in terms of the chiral effective field theory, and discuss their role in probing new physics beyond the standard model.
A simple analytical expression for the electric dipole polarizability of the three-hadron bound system having only one stable bound state has been derived neglecting by the higher orbital components of the off-shell three-body transition matrix at the energy of the bound state. As a case in point, we have estimated the electric dipole polarizability of the triton, using a cluster triton wave function and the Hulthen potential to describe the related p-n and n-d bound states.
Making use of the Effective Field Theory(EFT) expansion recently developed by the authors, we compute the charge form factor of triton up to next-to-next-to-leading order (N$^2$LO). The three-nucleon forces(3NF) is required for renormalization of the three-nucleon system and it effects are predicted for process and is qualitatively supported by available experimental data. We also show that, by including higher order corrections, the calculated charge form factor and charge radius of $^3$H are in satisfactory agreement with the experimental data and the realistic Argonne $v_{18}$ two-nucleon a…
The electric dipole moment is a very sensitive probe of CP violation beyond the standard model. Light nuclei are particularly interesting since the CP violation may be enhanced by nuclear many-body effects. In this proceeding, we present the current status of the theoretical evaluations of the electric dipole moment of light nuclei in the ab initio approach and in the cluster model. We add the preliminary result of the evaluation of the electric dipole moment of $^7$Li which is treated in a cluster model with a triton.
Recent calculations of EDMs of light nuclei in the framework of chiral effective field theory are presented. We argue that they can be written in terms of the leading six low-energy constants encoding CP-violating physics. EDMs of the deuteron, triton, and helion are explicitly given in order to corroborate our claim. An eventual non-zero measurement of these EDMs can be used to disentangle the different sources and strengths of CP-violation.
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 CP-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…
We provide a consistent and complete calculation of the electric dipole moments of the deuteron, helion, and triton in the framework of chiral effective field theory. The CP-conserving and CP-violating interactions are treated on equal footing and we consider CP-violating one-, two-, and three-nucleon operators up to next-to-leading-order in the chiral power counting. In particular, we calculate for the first time EDM contributions induced by the CP-violating three-pion operator. We find that effects of CP-violating nucleon-nucleon contact interactions are larger than those found in previous s…
We set up the framework for the calculation of electric dipole moments (EDMs) of light nuclei using the systematic expansion provided by chiral effective field theory (EFT). We take into account parity (P) and time-reversal (T) violation which, at the quark-gluon level, originates from the QCD vacuum angle and dimension-six operators capturing physics beyond the Standard Model. We argue that EDMs of light nuclei can be expressed in terms of six low-energy constants that appear in the P- and T-violating nuclear potential and electric current. As examples, we calculate the EDMs of the deuteron, …
In this review, we summarize the theoretical development on the electric dipole moment of light nuclei. We first describe the nucleon level CP violation and its parametrization. We then present the results of calculations of the EDM of light nuclei in the ab initio approach and in the cluster model. The analysis of the effect of several models beyond standard model is presented, together with the prospects for its discovery. The advantage of the electric dipole moment of light nuclei is focused in the point of view of the many-body physics. The evaluations of the nuclear electric dipole moment…
In this proceeding, we present the results of the theoretical evaluations of the electric dipole moment (EDM) of light nuclei, including the preliminary value for the 11B nucleus. From the data, we can infer an approximate counting rule, and predict the EDM of other light nuclei.
We analyze the CP-violating electric dipole form factor of the nucleon in the framework of covariant baryon chiral perturbation theory. We give a new upper bound on the vacuum angle, |θ_0| \lesssim 2.5 \cdot 10^{-10}. The quark mass dependence of the electric dipole moment is discussed and compared to lattice QCD data. We also perform the matching between its representations in the three- and two-flavor theories.
The expression for polarized electric dipole moment of well-deformed reflection asymmetric nuclei is obtained in the framework of liquid-drop model in the case of geometrically similar proton and neutron surfaces. The expression for polarized electric dipole moment consists of the first and second orders terms. It is shown that the second-order correction terms of the polarized electric dipole moment are important for well-deformed nuclei.
The neutron, in addition to possibly having a permanent electric dipole moment as a consequence of violation of time-reversal invariance, develops an induced electric dipole moment in the presence of an external electric field. We present here a unified non-relativistic description of these two phenomena, in which the dipole moment operator, $\vec{\cal D}$, is not constrained to lie along the spin operator. Although the expectation value of $\vec{\cal D}$ in the neutron is less than $10^{-13}$ of the neutron radius, $r_n$, the expectation value of $\vec {\cal D}\,^2$ is of order $r_n^2$. We de…
We introduce the strong CP-violation in the framework of AdS/QCD model and calculate the electric dipole moments of nucleons as well as the CP-violating pion-nucleon coupling. Our holographic estimate of the electric dipole moments gives for the neutron d_n=1.08 X 10^{-16} theta (e cm), which is comparable with previous estimates. We also predict that the electric dipole moment of the proton should be precisely the minus of the neutron electric dipole moment, thus leading to a new sum rule on the electric dipole moments of baryons.
We calculate the electric dipole form factor of the nucleon that arises as a low-energy manifestation of time-reversal violation in quark-gluon interactions of effective dimension 6: the quark electric and chromoelectric dipole moments, and the gluon chromoelectric dipole moment. We use the framework of two-flavor chiral perturbation theory to one loop.
I present an exact relationship between the electric dipole moment and anomalous magnetic moment of the nucleon in the light-front formalism of QCD and consider its consequences.
We review the Lorentz integral transform coupled-cluster method for the calculation of the electric dipole polarizability. We benchmark our results with exact hyperspherical harmonics calculations for 4He and then we move to a heavier nucleus studying 16O. We observe that the implemented chiral nucleon-nucleon interaction at next-to-next-to-next-to-leading order underestimates the electric dipole polarizability.
A partial screening of nucleon electric dipole moments (EDMs) in nuclear systems, which is related to the Schiff mechanism known for neutral atomic systems, is discussed. It is shown that the direct contribution from the neutron EDM to the deuteron EDM is partially screened by about 1% in a zero-range approximation calculation.
For a bound state internal wave function respecting parity symmetry, it can be rigorously argued that the mean electric dipole moment must be strictly zero. Thus, both the neutron, viewed as a bound state of three quarks, and the water molecule, viewed as a bound state of ten electrons two protons and an oxygen nucleus, both have zero mean electric dipole moments. Yet, the water molecule is said to have a nonzero dipole moment strength $d=eΛ$ with $Λ_{H_2O} \approx 0.385\ \dot{A}$. The neutron may also be said to have an electric dipole moment strength with $Λ_{neutron} \approx 0.612\ fm$. The…
We calculate the electric dipole moments of the neutron and the Lambda within the framework of heavy baryon chiral perturbation theory. They are induced by strong CP-violating terms of the effective Lagrangian in the presence of the vacuum angle theta_0. The construction of such a Lagrangian is outlined and we are able to give an estimate for theta_0.
Using QCD sum rules, we calculate the electric dipole moment of the neutron d_n induced by all CP violating operators up to dimension five. We find that the chromoelectric dipole moments of quarks \tilde d_i, including that of the strange quark, provide significant contributions comparable in magnitude to those induced by the quark electric dipole moments d_i. When the theta term is removed via the Peccei-Quinn symmetry, the strange quark contribution is also suppressed and d_n =(1\pm 0.5)[1.1e(\tilde d_d + 0.5\tilde d_u)+1.4(d_d-0.25d_u)].
We have considered a mechanism for inducing a time-reversal violating electric dipole moment (EDM) in atoms through the interaction of a nuclear EDM (d_N) with the hyperfine interaction, the "magnetic moment effect". We have derived the operator for this interaction and presented analytical formulas for the matrix elements between atomic states. Induced EDMs in the diamagnetic atoms 129Xe, 171Yb, 199Hg, 211Rn, and 225Ra have been calculated numerically. From the experimental limits on the atomic EDMs of 129Xe and 199Hg, we have placed the following constraints on the nuclear EDMs, |d_N(129Xe)|…
We demonstrate explicitly that some recent calculations of atomic electric dipole moments (EDM) are incomplete. A contribution overlooked therein is pointed out. When included, it cancels exactly the result of those calculations, and thus restores the standard conclusions for nuclear EDM in atoms.
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…
Electric dipole moments of diamagnetic atoms of experimental interest are calculated using the relativistic Hartree-Fock and random-phase approximation methods, the many-body perturbation theory and configuration interaction technique. We consider P,T-odd interactions which give rise to atomic electric dipole moment in the second order of the perturbation theory. These include nuclear Schiff moment, P,T-odd electron-nucleon interaction and electron electric dipole moment. Interpretation of a new experimental constraint of a permanent electric dipole moment of $^{199}$Hg [W. C. Griffith {\it et…
The sensitivity much better than $10^{-24} e$ cm may be expected in the searches for electric dipole moments (EDM) of $β$-active nuclei at ion storage rings. It would be a serious progress in studies of the CP-violation problem.
We show, at leading-order in the multipole expansion of the electron-nucleus interaction, that nucleon electric-dipole moments are completely shielded by electrons so that they contribute nothing to atomic electric-dipole moments, even when relativity in the nucleus is taken into account. It is well known that relativistic electron motion, by contrast, leads to dipole moments that are not screened; we discuss the reasons for the difference.
Effects caused by the electron electric dipole moment (EDM) in gadolinium garnets are considered. Experimental studies of these effects could improve current upper limit on the electron EDM by several orders of magnitude. We suggest a consistent theoretical model and perform calculations of observable effects in gadolinium gallium garnet and gadolinium iron garnet. Our calculation accounts for both direct and exchange diagrams.
The electric dipole moments (EDMs) of neutron-odd nuclei with even protons are systematically evaluated. We first derive the relation between the EDM and the magnetic moment operators by making use of the core polarization scheme. This relation enables us to calculate the EDM of neutron-odd nuclei without any free parameters. From this calculation, one may find the best atomic system suitable for future EDM experiments.
While bulk properties of stable nuclei are successfully reproduced by mean-field theories employing effective interactions, the dependence of the centroid energy of the electric giant dipole resonance on the nucleon number A is not. This problem is cured by considering many-particle correlations beyond mean-field theory, which we do within the "Quasiparticle Time Blocking Approximation". The electric giant dipole resonances in $^{16}$O, $^{40}$Ca, and $^{208}$Pb are calculated using two new Skyrme interactions.
The electric dipole polarizability quantifies the low-energy behaviour of the dipole strength and is related to critical observables such as the radii of the proton and neutron distributions. Its computation is challenging because most of the dipole strength lies in the scattering continuum. In this paper we combine integral transforms with the coupled-cluster method and compute the dipole polarizability using bound-state techniques. Employing different interactions from chiral effective field theory, we confirm the strong correlation between the dipole polarizability and the charge radius, an…
The multiconfiguration Dirac-Hartree-Fock (MCDHF) method has been employed to calculate atomic electric dipole moments (EDM) of 225^Ra, 199^Hg, and 171^Yb. For the calculations of the matrix elements we extended the relativistic atomic structure package GRASP2K. The extension includes programs to evaluate matrix elements of (P, T)-odd e-N tensor-pseudotensor and pseudoscalar-scalar interactions, the atomic electric dipole interaction, the nuclear Schiff moment, and the interaction of the electron electric dipole moment with nuclear magnetic moments. The interelectronic interactions were accoun…
