The dual model of scattering

Abstract

The bootstrap idea in the sense of finite energy sum rules and the saturation with zero-width resonances are developed further in the thesis for the reaction ƿƿ→ƿo and ƿƿ→ƿy which are identical in all the three channels and therefore provide us with a genuine bootstrap of the Regge trajectories, contrary to, say, the reaction πƿ→ πƿ . A set of fourteen FESR,s for all the invariant amplitudes of the reaction ƿƿ→ƿo and also a set of thirteen FESR,s for ƿƿ→ƿy different steps of approximation have been written down which can be studied further in different aspects. Notice that a previously considered by other authors reaction ππ → πw finally led to a special representation, namely the Veneziano model which has many attractive features. With the appearance of this model and the concept of duality we devoted ourselves to the idea of mass extrapolation along the Regge trajectory, a show-case of which is the annihilation pn-3 π at rest. The Dalitz plot and the overall normalization for this process were obtained with a certain degree of success. An analogous attempt was done for the over all normalization of the annihilation process pp → 4π at rest. The new experimental data on the annihilation process for low laboratory momenta of antiproton P(_lab) = 100 - 700 MeV give a further support to this kind of extrapolation along the Regge trajectory. These data indicate the existence of angular momenta up to l = 3 at these near-threshold energies. An impact parameter picture with the reasonable radius of interaction gives l^1 , while the explanation within the above mode(is very natural since the Regge trajectory a is very near to 3. A step has also been done towards the construction of physical dual resonance models (DRM) with unnatural parity couplings and without the tachyon states. One of the motivations has been to see whether these physical requirements give a natural way to get a double or more degenerate (w - A(_2))-trajectory in 3π-channels when one factorizes the states analogous to the de-generay of the daughters levels. One has to admit that the unitarization of DRM still remains a problem. However, from a theoretical point of view the ZSV-program to consider the model as a Bom term of a field- theoretic expansion is the most attractive one. In admitting this program, the best place to look for its predictions is the field of inclusive experiments both in purely hadronic and photonic processes where one measures the discontinuities. For purely hadronic reactions in DRM Feynman scaling is obtained provided the trajectory exchanged is associated with the Pomeron with unit intercept. For photonic processes in DRM the Bjorken scaling is obtained due to the existence of current algebra fixed pole. The latter question is studied in the thesis in a model where the currents are included into DRM through a minimal gauge interaction prescription, in which one has the minimum amount of freedom, and the dual re-normalization has also been used. With the use of Muellerism the generalized Bjorken scaling for some quasi-inclusive reactions has also been obtained. The motivation for the above analysis has-been the experimental indication that the nondiffractive part of the electroproduction structure functions do show scaling. Without the fixed pole responsibility it would be hard to understand the scaling of the resonant part. Also notice that with the exception of λρ(^3)-theory all the other field-theoretic models have failed to produce Bjorken scaling unless one introduces an unjustified cutoff and therefore one would like to argue that in the DRM the renormalization term as if replaces this cutoff in a more natural way. The above and many other points studied in the young but vast literature may indicate that the DRM might be "not that far" from the real world of hadron physics.