**Facility for Rare Isotope Beams Theory Alliance (FRIB-TA) Topical Program **

The Facility for Rare Isotope Beams (FRIB) will provide an unprecedented opportunity for the search of permanent electric dipole moments (EDM) of rare isotopes. EDMs violate both T-(time-reversal) and P-(parity) symmetries and, by the CPT theorem, CP-(the combination of charge (C) and parity) symmetry. CP-violation has long been thought to be one of the key ingredients needed to explain the matter-antimatter asymmetry of the visible universe. The amount of CP-violation currently encoded in the Standard Model (SM), observed only in the weak interaction, is far too feeble to explain this observed asymmetry. EDMs would be a clean signature of CP-violation complementary to CP-violation searches at the LHC. Since SM EDMs are expected to be very small, any observation of an EDM at present and projected levels of sensitivity would mean the discovery of new physics beyond the SM or a non-zero value for the θQCD angle, a parameter which describes CP-violation within the strong interaction. EDMs of paramagnetic systems, diamagnetic systems, and neutrons have a complementary sensitivity to new sources of CP-violation such as supersymmetry.

Beyond Standard Model (BSM) CP-violating sources at hadronic energy scales are described by effective CP-odd operators such as the quark-chromo and Weinberg operators. Irrespective of the origin, the signal for the EDM will be small and possibly masked by strong-interaction and atomic physics, which presents a formidable challenge to the interpretation of such a signal. To disentangle the origin of a nonzero EDM measurement, a quantitative understanding of the underlying hadronic physics is required. First principle lattice QCD calculations provide the unique opportunity to calculate from the fundamental theory of strong interactions the relevant CP-violating nucleon matrix elements disentangling each and every CP-violating source (e.g. θQCD term or BSM).

For light to intermediate nuclei, effective field theory (EFT) methods are a very powerful tool in understanding low-energy strong interactions. Each interaction appearing in the chiral Lagrangian is associated with a low-energy constant (LEC) whose size is not fixed by symmetry considerations and depends on strong nonperturbative dynamics. The EDMs of light nuclei depend only on a small number of CP-odd LECs. These LECs consist of the nucleon EDMs and CP-odd pion-nucleon interactions which induce CP-odd nucleon-nucleon forces. It has been argued that measurements of the nucleon and a few light-nuclear EDMs would not only convincingly show the existence of BSM physics but also what type of BSM physics. However, the uncertainties are still large. They are dominated by the unknown sizes of the LECs in terms of the θQCD term and CP-odd effective operators. So far, these LECs have only been estimated by model calculations (such as QCD sum rules or dimensional analysis) which only provide order-of-magnitude estimates. Lattice QCD has the potential to determine those LECs from first principles. For heavier octupole deformed nuclei, more phenomenological methods, such as the density functional theory, are the method of choice for a theoretical estimate of the corresponding EDM.

The biggest theoretical challenge of the field is to reduce the uncertainty in the determination of the CP-odd hadronic matrix elements and the LECs (e.g. the status for the Weinberg operator is very unsatisfactory as there exists no systematic calculation of its contribution to the nucleon EDM, while the Hg-199 EDM receives contribution from single nucleon EDMs, LECs and more phenomenological nuclear physics calculations). A topical program including experts on EDM theoretical calculations from nucleons to heavy nuclei provides the possibility to isolate the main sources of uncertainties for each calculational method of choice and better target theoretical efforts for a proper interpretation of future experimental results.

Rare isotopes provide significant discovery potential for EDM searches because, according to theoretical predictions, they amplify the observable EDM by orders of magnitude compared to stable species. Those predictions are based on the existence of parity doublets under simultaneous presence of quadrupole and octupole deformation (or soft quadrupole and octupole collective modes). This implies that less stringent control of the environment factors (such as magnetic fields) and of systematic effects is required in order to have a highly sensitive EDM search. Diamagnetic systems, which have octupole‐deformed nuclei, such as radium, radon, and protactinium, are favorable candidates because the combination of their specific nuclear structure and highly relativistic atomic structure amplify the effects of CP-violating interactions originating within the nucleus by several orders of magnitude compared to nearly spherical nuclei such as mercury or xenon. FRIB is expected to provide quantities of Ra, Rn, and Pa that rivals or are orders of magnitude more than what is currently available. Another possible direction is the search of the magnetic quadrupole moment that also violates fundamental symmetries. A translation of nuclear effects into observables is a serious theoretical problem that requires a better analysis of atomic and molecular physics.

Interpretation of EDMs in the hadronic sector are complex because theory is needed at different energy scales from molecular to atomic to nuclear to hadronic to quarks. BSM physics manifests itself in a wide variety of ways at the low energy scale. Within the domain of nuclear physics, a variety of difference techniques are utilized to understand the connection to BSM physics from Lattice QCD for the nucleon to DFT methods for heavy octupole deformed species. The topical program is timely because several ongoing and new experimental efforts are under way with new results expected coinciding the start of FRIB: neutron EDM, Hg-199, Ra-225, Xe-129, Yb-171, Yb-173 (MQM), and CENTREX (proton EDM).