The understanding of the physics of the Universe is derived primarily from conservation laws and fundamental forces which are related to symmetries (global or local). It is very critical to test these symmetries to the best of our ability and more specifically test the domain (energy scale) of their applicability. Three of the four fundamental forces which govern the universe are embodied into the socalled Standard Model (SM) which has been constructed over the last forty years. It is based on the very general assumption of Lorentz invariance (independence of physics from space rotation and boost transformations) and assumes that the product of C(charge), P(parity) and T(time) symmetries (CPT) is invariant. The experimental observation that the P symmetry is maximally violated in weak interactions at energy scales below the weak symmetry breaking scale (100GeV) is accounted for by restricting the possible interactions to a specific combination of Vector  Axial vector couplings. The small observed CP violation in the B and K mesons is accounted for via a rotation of the weak and mass quark eigenstates through phases in their mixing matrix (and possibly similarly for the neutrinos)  hence T also is violated if CPT is to be a good symmetry.
Tests of theses assumptions have been and are still the focus of a large part of the research program in particle physics and in nuclear physics. Moreover, since the observed violations have been incorporated in an adhoc fashion, and since the model includes many arbitrary parameters, it is believed that the SM is only an effective approximation which has been extremely successful at the energy scale that one has been able to probe. It is also conjectured that a more encompassing theory should be developed which would be valid up to the Planck scale and would also incorporate quantum gravity (a force which is not yet included in the SM).
Many extensions to the standard model have been proposed which predict small but measurable deviations from SM predictions in terms of symmetry violations. While particle physics experiments at the energy frontier search for deviations that would be made more apparent with increased energy scales, nuclear physics has a complementary role to play in providing a special quantum laboratory where selection rules can be used to extract specific components of the interactions or enhance the violation effect in nuclei. The searches involve very high precision measurements of SM observables, or of phenomena forbidden or suppressed in the standard model. These “indirect” signatures of new physics can probe very large energy scales. For example a 4% measurement of the proton weak charge tests new physics at the 3 TeV scale and beyond, while rare decays of the muon can probe multiTeV scales not accessible in accelerators. Similarly a high precision measurement of the weak charge of the electron with an upgraded CEBAF has great potential.
The main questions that are the focus of the field are:
1. What is the Lorentz structure of the fundamental interaction?
In a modelindependent way one can write the basic fundamental interactions in terms of Lorentz invariant terms that transform like scalars, pseudoscalars, vectors, axial vectors, and tensors. In its minimal form, the SM includes only the specific combination of vector and axial vector (VA) terms and hence exhibits maximal parity violation and CP and T invariance. The present set of experimental data cannot exclude the presence of a substantial amount of non VA terms at the level of 10%. One goal of the nuclear physics symmetry program is to tighten these constraints in order to provide a set of discriminatory tests of possible extensions of the SM. As an example, high precision experiments are testing the Lorentz structure of the weak interaction in semileptonic decay (betadecay correlations), purely leptonic decays (muons, tau) and hadronic systems.
2. Where does the present MatterAntimatter asymmetry in our Universe come from?
Many extensions to the SM include time reversal violations (CP violation). To explain the small CP violation observed in K decays 40 years ago, one introduced the concept that the fermion weak eigenstates were mixtures of the mass eigenstates (expressed in terms of the CKM matrix for the three generations of quarks and the PMNS matrix for the neutral leptons). The presence of the CP violation term introduced by an extra phase in the mixing matrix of the quarks has been confirmed by experiments in both the Kmeson system and the Bmeson system. However, the level of CP violation produced by the socalled SM phase is too small to explain the present matterantimatter asymmetry in our universe. The CP violating phase in the neutrino mixing matrix is associated with the θ_{13} mixing angle which is very small and for which we have only upper limits (its measurement is the main goal of the worldwide neutrino physics program). In any event, many extensions to the SM induce larger CP violations, and the second focus of the lowenergy symmetry tests is to search for evidence of such CP violation effects using the quantum numbers of nuclei to isolate specific contributions. This is addressed for example in the search for electric dipole moments (EDMs) of leptons, nucleons, atoms or molecules.
3. Is the fundamental assumption of CPT invariance valid?
One of the most sensitive test comes from the mass difference of neutral kaon and antikaon mesons but such comparisons must be extended to all other possible systems ( e+/e, m+/m, H/ , i.e., leptons, mesons, and hadrons and their antiparticles).
4. Can one resolve the remaining pieces of the neutrino puzzle?
There is a sense of neutrino mass splittings and mixings from the results of SNO for solar neutrinos, Kamiokande for atmospheric neutrinos, and the longbaseline neutrino oscillation experiments Kamland and K2K. However, one does not yet have a determination of the absolute scale for the mass of neutrinos. Zero neutrino double beta decay could shed some light on the majorana nature of the neutrino and on their mass scale provided that the transition nuclear matrix elements can be determined (this is a challenge for both experiments and theory).
Experimentally, recent advances in both beam and target polarization and in polarization control have benefited from powerful and precise atomic techniques. The opportunities offered by ion and atom traps to study betadecay in vacuum, advances in ultra cold neutron sources intensities, availability of high duty cycle polarized electron beams, and major developments in the production of exotic radioactive beams have led to a renaissance of this field which complement nicely the search for physics beyond the SM at the energy frontier.
