MMeson and a Generalization of the Pomeranchuk Relations

Abstract

Under the hypothesis that a $K-\pi$ resonance is vector, we examine its role in the associated production of $\Lambda$ by $\pi$ and in $\Lambda$ production by $\overline{K}$. We shall demonstrate the existence of a new symmetry between two reaction amplitudes. This symmetry may be regarded as a generalization of Pomeranchuk's relations and should appear at high energies and low momentum transfers when both amplitudes are dominated by the same pole or pseudopole, as is to be expected according to the Regge pole hypothesis. Specifically, we find, in considering the details of the role of a strange vector meson in the processes $\pi +N\to \Lambda +K$ and $\overline{K}+N\to \Lambda +\pi$, that the associated production amplitude in the forward direction (for the $K$) at high energies is asymptotically equal to the negative of the amplitude characterizing $\Lambda$ production by a $\overline{K}$. The contribution of the dominant pole terms in these amplitudes is constructed for the high-energy limit and the energy and momentum transfer dependences are compared for the alternative hypothesis of composite or elementary particle behavior of a pole term. We discuss experiments which are needed to supply data for a test of the Regge pole hypothesis. The results of these experiments, which are feasible with the new large accelerators, will be most important as guides for the construction of theories of the strong interactions.