Nonleptonic weak decay and the Melosh transformation

Abstract

The PCAC (partially conserved axial-vector current) hypothesis and the Melosh transformation are used with the soft-pion and infinite-momentum techniques to obtain expressions for the nonleptonic weak decay of amplitudes of the $\mathrm{SU}{(6)}_{W}56$, $L=0$ baryons. The following results are obtained: (1) Modified Lee-Sugawara relations are exact for both the parity-violating and parity-conserving amplitudes. (2) Two additional sum rules involving ${\ensuremath{\Omega}}^{\ensuremath{-}}$ decay amplitudes are derived. (3) If the parity-violating part of the weak decay Hamiltonian transforms only as an $\mathrm{SU}{(6)}_{W}35$, then $A({\ensuremath{\Sigma}}_{+}^{+})=0$ automatically. (4) Terms arising from the Melosh transformation are necessary to bring the decay width for ${\ensuremath{\Omega}}^{\ensuremath{-}}\ensuremath{\rightarrow}\ensuremath{\Xi}\ensuremath{\pi}$ into agreement with experiment. (5) All known amplitudes are fitted to within 10%.