SU(6)Wand Tensor Forces

The one-meson exchange potentials in $\mathrm{MB}$, $\mathrm{MM}$, $\mathrm{BB}$, and $B\overline{B}$ states may be represented approximately by sums of central and tensor potentials, where $M$ and $B$ denote the meson and baryon supermultiplets of dimensions 36 and 56. This formulation leads to a clarification and generalization of a model developed recently by the author, in which the relative forces in different channels are assumed equal to the relative magnitudes of the Born-approximation scattering amplitudes at the physical threshold. It is shown that the tensor forces dominate the $\mathrm{SU}{\mathrm{}\left(6\right)\mathrm{}}_W$-symmetric meson bootstrap model, in which the $M$ are $\mathrm{MM}$ bound states. A generalization of a theorem proved previously implies that the tensor forces cancel in the $\mathrm{MM}$, $\mathrm{MB}$, and $B\overline{B}$ states corresponding to the larger $\mathrm{SU}\left(3\right)\mathrm{}$ representations, and in all $\mathrm{BB}$ states. Actual nucleon-nucleon forces are very sensitive to symmetry breaking; the implications of the theorem for these forces are discussed and compared with phenomenological analyses of experiment.