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1. Major US and European initiatives to test the electric dipole moment (EDM) of the neutron at a sensitivity two orders of magnitude beyond current limits (10^-28 e cm). The US program will be based at the SNS. Theory issues include techniques, such as lattice QCD, that might be used to relate the observable to the underlying parameters governing the CP violation.
   
   
2. Initiatives to probe EDMs in complex nuclei. One of the most stringent current limits on CP violation comes from the ¹⁹⁹Hg vapor cell measurements. New techniques, including both traps and atomic fountains, may allow one to use a greater variety of nuclei in experiments (the vapor cell technique is limited to systems with atomic spin F=0). This implies new opportunities to utilize nuclei with enhanced sensitivity to hadronic CP violation due to accidental level degeneracies, collective effects such as octupole deformation, and the contributions of the unscreened M2 nuclear moment (which does not contribute in F=0 systems). Theory issues include calculations of the Schiff moment, corrections to the Schiff moment due to nuclear polarizability, and nuclear structure issues connected with both the standard C1 and M2 contributions to the atomic EDM. This work is important to prospects for a fundamental symmetries program at FRIB.
   
   
3. The SNS initiative to measure the isovector component of the parity-violation weak hadronic interaction in n + p -> d + γ. This will isolate that neutral current contribution to the hadronic weak interaction, the one weak current that has so far eluded experiment. Theory issues include the isospin character of the weak hadronic current (for 20 years there have been hints of an isospin anomaly similar to the ΔI=1/2 rule in strangeness-changing decays), the determination of the full set of five Danilov S-P amplitudes, the relationship between the effective nuclear couplings that can be extracted from experiment and the underlying couplings at the quark level, and the use of quasi-exact few-body techniques to evaluate candidate experiments, such as neutron spin rotation in He. Another interesting aspect of this problem is nuclear-spin-dependent atomic parity violation: the nuclear anapole moment has been isolated in Cs and, in principle, is a test of the hadronic weak interaction, if the associated nuclear polarizations can be calculated reliably.
   
   
4. Neutrino physics has demonstrated that nature allows mixing among the families. New experiments with neutrinos will test the unknown mixing angle between the first and third mass eigenstates, the mass hierarchy (normal or inverted), and the Dirac CP phase. Such neutrino properties have implications that range from dark matter (where both the absolute neutrino mass and hierarchy may be determined through their characteristic effects on the evolution of large scale structure as a function of Z and scale), to supernova dynamics (where oscillations can alter energy deposition, and where entirely new effects of the MSW mechanism can be probed due to the high density of neutrinos), to Big Bang nucleosynthesis (which probes both the effective number of relativistic degrees of freedom and the neutrino number asymmetry, with WMAP-7 data currently indicating a possible deviation in these parameters). Theory issues include both the astrophysical modeling and the nuclear structure questions that will arise in next-generation long-baseline neutrino detection schemes.
   
   
5. Important new tests of family number are being planned, including plans at FermiLab and JPARC to greatly increase the reach of μ -> e conversion experiments and to test the muon's g-2 to high precision. Theory issues include the effects of nuclear finite size on the coherent process and the possible role of nuclear transitions in the μ -> e experiment, and the hadronic light-by-light contribution to g-2.
   
   
6. Fermi beta decay in nuclei remains our most precise test of CKM unitarity. An important nuclear theory issue is the reliability of the radiative corrections and nuclear wave function isospin corrections that allow one to extract consistent values for V_ud from experiment.
   
   
7. Double beta decay is a fundamental test of the conservation of total lepton number, and specifically remains our only practical test of Majorana neutrino masses, which are essential to the most plausible scheme (the see-saw mechanism) for explaining the anomalously small masses of neutrinos. The Majorana mass term is the leading "effective theory" correction to the Standard Model, and current neutrino mass² differences hint of heavy right-handed Majorana neutrinos with masses near the GUT scale. A key nuclear physics issue is evaluating the highly exclusive nuclear matrix elements that govern the neutrinoless double beta decay mechanism.