Transition from resonances to surface waves in pion+-proton elastic scattering

In this article, we study resonances and surface waves in À+–p scattering. We focus on the sequence whose spin-parity values are given by View the MathML source. 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 View the MathML source, 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 Jp this rule is violated and is substituted by the relation Jnot, vert, similarkR, where k is the pion-nucleon c.m.s. momentum, and Rnot, vert, similar1 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 À+–p resonance sequence can be associated with a vibrational spectrum of the proton generated by an algebra View the MathML source. 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 ¸=À, as a function of k. (d) The evolution of this pole, as a function of k, is given in first approximation by Jsimilar, equalskR.