Isotopic Spin of Exchanged Systems

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Abstract
It is demonstrated that any scattering amplitude can formally be expressed as a sum of terms each corresponding to the exchange of a particular isotopic spin without requiring the concept of crossing. Employing only the optical theorem and invariance under isotopic spin rotations the following theorem is proved: The contribution to the imaginary part of the forward scattering amplitude arising from the exchange of zero isotopic spin cannot be arbitrarily small compared to contributions from the exchange of any other isotopic spin or spins. From the same argument follows a second theorem: If the total cross section for two particles is independent of their isotopic spin state, then only the exchange of isotopic spin zero contributes to the imaginary part of the forward scattering amplitude. In combination with the hypothesis that high-energy scattering is dominated by the exchange of a single Regge pole, it follows that the "Pomeranchuk" pole must have isotopic spin zero. The relation to the Pomeranchuk-Okun' rule is discussed.