Transition from resonances to surface waves in image elastic scattering Original Research Article

In this article, we study resonances and surface waves in image scattering. We focus on the sequence whose spin-parity values are given by image. A widely-held belief takes for granted that this sequence can be connected by a moving pole in the complex angular momentum (CAM)-plane, which gives rise to a linear trajectory of the form image, which is the standard expression of the Regge pole trajectory. But the phenomenology shows that only the first few resonances lie on a trajectory of this type. For higher image this rule is violated and is substituted by the relation image, where k is the pion-nucleon c.m.s. momentum, and image fm. In this article we prove: (a) Starting from a non-relativistic model of the proton, regarded as composed by three quarks confined by harmonic potentials, we prove that the first three members of this image resonance sequence can be associated with a vibrational spectrum of the proton generated by an algebra image. Accordingly, these first three members of the sequence can be described by Regge poles and lie on a standard linear trajectory. (b) At higher energies the amplitudes are dominated by diffractive scattering, and the creeping waves play a dominant role. They can be described by a second class of poles, which can be called Sommerfeld’s poles, and lie on a line nearly parallel to the imaginary axis of the CAM-plane. (c) The Sommerfeld’s pole which is closest to the real axis of the CAM-plane is dominant at large angles, and describes in a proper way the backward diffractive peak in both the following cases: at fixed k, as a function of the scattering angle, and at fixed scattering angle image, as a function of k. (d) The evolution of this pole, as a function of k, is given in first approximation by image.