Roger F. Dashen

Approximate symmetry and the algebra of current components

It is our purpose to explain in this note, as well as we can, the theoretical foundations of the approximate symmetries of hadrons that have been extensively discussed lately, including the generalization of U(6) symmetry and its application to moving hadrons. A scheme (1-3] using the non-compact group U(6, 6), but not as an approximate symmetry of quantum mechanical states, has attracted wide attention; although the scheme contradicts [ 4] conservation of probability and certain experimental results, it predicts certain other quantities correctly. These correct predictions, by and large, follow from our method, which are consistent with probability conservation and involve applying symmetry operators to the states.

Flavor symmetry breaking in the 1/{ital N}{sub {ital c}} expansion

The breaking of flavor SU(3) symmetry in the axial vector couplings and magnetic moments of baryons is analyzed in the 1/{ital N}{sub {ital c}} expansion. A simple meson loop graph which is known to be of order {radical}{ital m}{sub {ital s}} and leading order in 1/{ital N}{sub {ital c}} correctly predicts the pattern of symmetry breaking in the magnetic moments. It is, however, not possible to use this graph to predict the magnitude of the breaking. The situation with the axial vector couplings is less clear. In this case the breakings are relatively small and do not appear to follow an obvious pattern. Nevertheless there is a clear indication that, with symmetry breaking taken into account, the {ital F}/{ital D} ratio [defined in the presence of SU(3) breaking] is considerably less than the SU(6) value of 2/3. With sizable uncertainty, we find {ital F}/{ital D}{approx_equal}0.44. The quantity 3{ital F}-{ital D} which is relevant for the analysis of spin-dependent deep inelastic scattering is considerably smaller than the SU(6) value of unity. The new value 3{ital F}-{ital D}=0.28{plus_minus}0.09 is consistent with vanishing strange-quark spin in the nucleon. {copyright} {ital 1995 The American Physical Society.}