(Received January 5, 1967)
High energy behaviors of forward elastic scattering amplitudes of particles with spin ≤1 are studied by making use of the Regge pole model. In the model forward elastic scattering amplitudes are expressed in terms of four types of Regge trajectories associated with the four types of S = 0 mesons, (i) P = (-1)J, C = (-1)J, (ii) P = (-1)J, C = -(-1)J, (iii) P = -(-1)J, C = (-1)J, (iv) P = -(-1)J, C = -(-1)J. The relation between two Regge trajectories is found to be one of the following four types.
(A) Mother and Daughter, α(i) j(0) = α(ii) j(0)±1 and α(iii) j(0) = α(iv) j(0)±1. There are relations among pole residues such as [β(iii)j(0)]2 = (2αj + 1)αj-1(αj+1)-1[β(iv)j(0)]2 for α(iv) j(0) = α(iii) j(0) + 1 = αj. A mother and its daughter have opposite signatures.
(B) Twin, α(i) j(0) = α(iii) j(0) and α(ii) j(0) = α(iv) j(0). There are relations among pole residues such as [β(iii)j(0)]2 = αj (αj+1)-1[β(i)j(0)]2 for α(i) j(0) = α(iii) j(0) = αj. A twin has a same signature, and a member of a twin can be a mother or daughter.
(C) Isolation. The relations between α and/or the relations between β are not satisfied.
(D) Father and Son, α(i) j(0) = α(iv) j(0)±1 and α(ii) j(0) = α(iii) j(0) ±1. A father and its son have opposite signatures.
The consequences of the model with and without these assumptions to high energy forward elastic scattering amplitudes are studied.
URL :
http://ptp.ipap.jp/link?PTP/37/941/
DOI : 10.1143/PTP.37.941