Symmetries and Symmetry Breaking *

In understanding the world of matter the introduction of symmetry principles following experimentation or using the predictive power of symmetry principles to guide experimentation is most profound. The conservation of energy, linear momentum, angular momentum, charge, and CPT involve fundamental symmetries. All other conservation laws are valid within a restricted subspace of the four interactions: the strong, the electromagnetic , the weak, and the gravitational interaction. In what follows comments will be made regarding parity violation in hadronic systems, charge symmetry breaking in two nucleon and few nucleon systems, and time-reversal-invariance in hadronic systems. In hadronic parity violation, theory and experiment meet in the weak meson-nucleon couplings as defined, for instance, in the seminal article by Desplanques, Donoghue, and Holstein (DDH). [1] In analogy with the one boson exchange model for the strong N-N interaction, one defines seven weak meson-nucleon couplings for π, ρ, and ω exchanges and according the change in isospin. These seven weak meson-nucleon couplings or another set of seven parameters in another theoretical framework characterize the hadronic weak interaction. For a more recent calculation of the weak meson-nucleon couplings see Feldman, Crawford, Dubach, and Holstein. [2] The latest experimental contribution to the determination of the weak meson-nucleon couplings is the measurement at TRIUMF of the longitudinal analyzing power, A z = (σ + − σ −)/(σ + + σ −), in polarized proton-proton scattering at 221 MeV, where σ + and σ − are the scattering cross sections for positive and negative helicity, respectively. The measurements were performed in transmission geometry with the beam energy and the detector layout selected to ensure that the contribution of the lowest order parity mixing amplitude (1 S 0 − 3 P 0) integrates to zero, hence leaving essentially only a contribution of the (3 P 2 − 1 D 2) parity mixing amplitude. As a consequence the experiment determined the weak meson-nucleon coupling h pp ρ. In the experiment the beam current was measured before and after passing a 0.40 m thick liquid hydrogen target by transverse electric field ionization chambers (TRICs), and the difference determined as function of the helicity state of the incident proton beam. Since many beam parameters may change upon helicity flips and be the cause of false asymmetries, great care was taken to have the sensitivity of the data taking apparatus to the unwanted beam parameters minimized as much as possible, and further to …