Abstract
The dual representation of $K\ensuremath{\rightarrow}3\ensuremath{\pi}$ decay amplitudes is studied. It is found that $K\ensuremath{\rightarrow}3\ensuremath{\pi}$ decay amplitudes in a generalized Veneziano model are incompatible with current-algebra relations. For example, pion poles and kaon poles are not dual to other poles. An example of realistic $K\ensuremath{\rightarrow}3\ensuremath{\pi}$ decay amplitudes which contain pion and kaon poles, which contain both $|\ensuremath{\Delta}\mathbf{I}|=\frac{1}{2} \mathrm{and} \frac{3}{2}$ parts, and which are compatible with current-algebra relations is obtained. Our results seem to suggest that we should prefer the charged-current \ifmmode\times\else\texttimes\fi{} charged-current nonleptonic weak Hamiltonian to Hamiltonians with pure $|\ensuremath{\Delta}\mathbf{I}|=\frac{1}{2}$.
Published Version
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