Impact Parameter Representation of Resonance Correlation

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Abstract
The impact parameter (b) representation of the H-type (s-t dual) amplitude is discussed through a sum of direct channel resonances (Breit-Wigner form) by imposing generalized Ogawa's rule of a constant impact parameter b0 (≃1 ×10-13 cm). This amplitude is shown to have a Breit-Wigner form in the b representation, 1/(b2 - b02 - i ε'). The H-type amplitude fHΔλ (s, t) is found to be proportional to iH(1)Δλ (b0 √-t), where H(1)Δλ is the first kind Hankel function and Δλ denotes the s-channel helicity change. The Hankel function H(1)Δλ has definite real and imaginary parts, just corresponding to “rotation phase”. A physical interpretation of Re fH from s-channel picture is given. The crossed channel amplitude fXΔλ (s, t) of the X-type (t-u dual) is discussed in connection with the form of fHΔλ (s, t).

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