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- W2003399269 abstract "A set of model amplitudes, characterized by two functions $h(x)$ and $ensuremath{omega}(x)$, is given which satisfies the conditions of duality, crossing symmetry, and Regge behavior. These model amplitudes can be written as $G(ensuremath{alpha}(s), ensuremath{alpha}(t))=ensuremath{int}{0}^{1}mathrm{dx}h(x){x}^{ensuremath{-}ensuremath{alpha}(t)}{[ensuremath{omega}(x)]}^{ensuremath{-}ensuremath{alpha}(s)}$ and are generalizations of the beta function. The model has resonances of zero width, like Veneziano's model. We prove that, under certain conditions, the model amplitude has Regge behavior as $sensuremath{rightarrow}ensuremath{infty}$ with $mathrm{arg}(ensuremath{-}s)<ensuremath{pi}$ and $t$ fixed, and that it dies exponentially as $sensuremath{rightarrow}ensuremath{infty}$ with $0<|mathrm{arg}(s)|<ensuremath{pi}$ and $u$ fixed, as does the amplitude in Veneziano's model. We give specific examples of $ensuremath{omega}(x)$ and $h(x)$ which satisfy all the required conditions, and show that the models may be generalized to models which bear the same relation to the model $frac{ensuremath{Gamma}(1ensuremath{-}ensuremath{alpha}(s))ensuremath{Gamma}(1ensuremath{-}ensuremath{alpha}(t))}{ensuremath{Gamma}(1ensuremath{-}ensuremath{alpha}(s)ensuremath{-}ensuremath{alpha}(t))}$ as the above models bear to the beta function." @default.
- W2003399269 created "2016-06-24" @default.
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- W2003399269 date "1970-05-15" @default.
- W2003399269 modified "2023-09-25" @default.
- W2003399269 title "Infinite Set of Models Satisfying Crossing Symmetry, Duality, and Regge Behavior" @default.
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- W2003399269 doi "https://doi.org/10.1103/physrevd.1.2888" @default.
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