Complex angular momenta approach for scattering problems in the presence of both monopoles and short range potentials

TL;DR

This paper extends the complex angular momenta method to analyze quantum scattering involving monopoles and short-range potentials, revealing unique features in the angular momentum plane that could signal topological structures in strong interactions.

Contribution

It introduces a novel application of the complex angular momenta technique to systems with monopoles, accounting for internal rotations and resulting in fixed cuts in the complex plane.

Findings

Fixed cuts in the complex angular momentum plane due to monopoles.

Background integral does not decrease at large cos(Theta).

Potential link to the soft Pomeron in strong interactions.

Abstract

It is analyzed the quantum mechanical scattering off a topological defect (such as a Dirac monopole) as well as a Yukawa-like potential(s) representing the typical effects of strong interactions. This system, due to the presence of a short-range potential, can be analyzed using the powerful technique of the complex angular momenta which, so far, has not been employed in the presence of monopoles (nor of other topological solitons). Due to the fact that spatial spherical symmetry is achieved only up to internal rotations, the partial wave expansion becomes very similar to the Jacob-Wick helicity amplitudes for particles with spin. However, since the angular-momentum operator has an extra "internal" contribution, fixed cuts in the complex angular momentum plane appear. Correspondingly, the background integral in the Regge formula does not decrease for large values of cos(Theta) (namely, large values of the Mandelstam variable s). Hence, the experimental observation of this kind of behavior could be a direct signal of non-trivial topological structures in strong interactions. The possible relations of these results with the soft Pomeron are shortly analyzed.