Scattering cross-section in gravitating cosmic string spacetimes

TL;DR

This paper develops a modified partial wave approach to analyze quantum scattering of particles in gravitating cosmic string spacetimes, accounting for unique geometric features and providing explicit scattering amplitudes and cross-section corrections.

Contribution

It introduces a novel correction to the partial wave expansion for particles in complex cosmic string spacetimes, including a toy model and potential extension to Dirac fields.

Findings

Derived explicit phase shifts and scattering amplitudes.

Calculated corrections to differential cross-sections.

Demonstrated the formalism with a toy model.

Abstract

We propose a modification of the partial wave approach to deal with the relativistic quantum scattering of bosonic and fermionic particles in a class of models concerning gravitating cosmic string spacetimes. These spacetimes are characterized by the Minkowski line element at the center of the vortex, non-vanishing curvature at a finite distance from the center but with a conical structure far from the core. We find the correction in the partial wave expansion and the phase shift. Consequently, we show the explicit form of the scattering amplitude and the correction to the differential cross-section for a massive scalar field. We also implement our formalism in a toy model mimicking this class of gravitating cosmic string spacetime. Moreover, we discuss the procedure to apply this formalism to a massive Dirac field.