New approach to nonleptonic weak interactions. III. Application to hyperon nonleptonic decays

A new approach to hyperon nonleptonic weak interactions is discussed. It is based on (i) the derived asymptotic constraints on the two-body ground-state-baryon matrix elements of the weak nonleptonic Hamiltonian which satisfy the $\left|\Delta \overrightarrow{\mathrm{I}}\right|=\frac{1}{2}$ rule and its SU(3) counterpart and (ii) the new soft-pion approximation in the infinite-momentum frame of parent particle. In the new extrapolation, a part of the so-called surface term servives in addition to the usual equal-time-commutator term. The result based on the first approximation which keeps only the ground-state-baryon contribution to the surface term is presented. It is shown that the Lee-Sugawara sum rules are satisfied reasonably well for both the $S$ and $P$ waves. Improvement of the approximation should be possible with less ambiguity than the usual approach, by including the contribution of the $L=1\mathrm{}$ baryon states to the surface term. Nowhere is the concept of exact SU(3) symmetry used.