Compatibility of quark and Regge-pole models

The special Regge pole model suggested by Freund to explain high-energy cross-sections is generalized by I) giving up the SU ₃ symmetry of the residue functions and II) assuming that the exchanged mesons could be mixtures of the unitary singlet and octet. These generalizations are shown to be necessary and sufficient for compatibility of this model with the general quark model, without symmetry assumptions. The assumption I) allows us, for example, to account for the experimental values of the differences σ _t (π^-P)-=σ _t (K-P) } σ _t (π⁺P) - σ _t (K^-N) and at the same time satisfy σ _t (K⁺N)=σ _t (K⁺P). The generalization II) leads to the following results: I) It is possible to obtain Freund's relations (see eq. (1)) without assuming M ₁₂ symmetry, only if the exchanged isosinglet vector mesons are certain mixtures of unitary singlet and octet as to correspond to the physical ω and φ mesons. 2) This mixing angle leads naturally to the equality of the quark-quark amplitudes T _pλ and {Mathematical expression} at all energies. 3) The symmetry-breaking term in the total cross-sections must vanish at very high energies, if no singlet-octet mixing for the tensor mesons is allowed. The symmetry-breaking term need not vanish in the quark model. Further, zero mixing cannot explain the energy behaviour of the averages S _π≡1/2[σ _t (π⁺P) + σ _t (π^-P] and S _K≡1/4[σ _t (K⁺P) + σ _t (K^-P) + σ _t (K⁺N)+σ _t (K^-N]. 4) A mixing angle for the I=0 tensor mesons, which is equal to that needed for the vector mesons to obtain ω and φ, leads to a clear contradiction of the experimental data. However, a mixing angle which is close to it can explain the energy behaviour of the S _π and S _K and also leads to the prediction that both S _π and S _K tend to nonvanishing values at infinite energies with S _K(∞)>S _π(∞), (see Table I). No additional Pomeranchuk pole to the tensor nonet is needed. 5) The energy dependence of {Mathematical expression} can be accounted for by breaking universality. However, we can do that without introducing D-coupling of the baryons. 6) If one tries to identify the two I=0 tensor mesons with the physical f(1250) and f′(1525), then the mixing angle required in (4) indicates that f′ rather than f should have an intercept α(0)=1.