ar X iv : n uc l - th / 9 50 80 30 v 2 2 O ct 1 99 5 Symmetry Problems in Low Energy

Some recent experimental and theoretical work on 1) charge symmetry-breaking, 2) parity non-conservation, and 3) searches for breaking of time reversal invariance are reviewed. The examples illustrate the uses of symmetry to learn about underlying dynamics and/or structure. INTRODUCTION Nuclei are known to be a superb laboratory for studies of symmetries and symmetrybreaking as well as tests of our basic understanding of the physical world. It is easy to change mass, spin, isospin, charge, and other properties of the nuclear target to allow us to probe various aspects of basic theory. Symmetries are particularly useful because they serve to restrict the underlying dynamics, or, if the latter is known, allow a determination of (unknown) structure. In the time allotted to this talk, it clearly is not possible to discuss all the symmetries useful in low energy physics. I intend to concentrate on charge symmetry, parity, and time reversal symmetries. As we have heard at this conference, there are many more symmetries one can discuss, such as chiral symmetry and those that occur in the standard model. Even within the above restriction, I find it necessary to pick out a * Supported in part by the U.S. Department of Energy sample of the many interesting features. 1. Charge Symmetry It is well known that hadronic (QCD) forces respect charge independence and charge symmetry at low energies. These symmetries are of particular interest because their violation is small and can be studied both experimentally and theoretically. The violation occurs due to electromagnetic effects and the mass difference of the up and down (d) quarks in the underlying QCD theory. The violation of charge independence is of the order of a few percent. It is readily measurable in low energy nucleon-nucleon scattering, in the energy spacings of isobaric analog states, and many other phenomena. Recently, there has been more interest in the breaking of the looser charge symmetry. This symmetry does not require full rotational invariance in isospin (charge) space, but only invariance under reflection in a plane perpendicular to the charge (third component of isospin) axis. The symmetry violation is smaller than that of charge independence, but chiral perturbation theory indicates that the violation is considerably enhanced in processes that involve two neutral pions. The nuclear forces which break charge symmetry are of the form (classes III and IV), VIII (1, 2) = UIII [τ3(1) + τ3(2)] (1a)