Some Features of Scattering Problem in a $\kappa$-Deformed Minkowski Spacetime

TL;DR

This paper explores how a $$-deformed Minkowski spacetime, inspired by doubly special relativity, affects two-body scattering processes, revealing that Planck-scale modifications can change elastic collisions into inelastic ones and alter relativistic variables.

Contribution

It introduces a phenomenological analysis of two-body collisions in $$-Minkowski spacetime, highlighting the impact of quantum gravity-inspired modifications on relativistic kinematics.

Findings

Turning on $$-spacetime makes elastic collisions become inelastic.

The rapidity variable is not additive under nonlinear Lorentz transformations.

Planck-scale effects significantly modify relativistic collision properties.

Abstract

The doubly special relativity (DSR) theories are suggested in order to incorporate an observer-independent length scale in special theory of relativity. The Magueijo-Smolin proposal of DSR is realizable through a particular form of the noncommutative (NC) spacetime (known as $\kappa$-Minkowski spacetime) in which the Lorentz symmetry is preserved. In this framework, the NC parameter $\kappa$ provides the origin of natural cutoff energy scale. Using a nonlinear deformed relativistic dispersion relation along with the Lorentz transformations, we investigate some phenomenological facets of two-body collision problem (without creation of new particles) in a $\kappa$-Minkowski spacetime. By treating an elastic scattering problem, we study effects of the Planck scale energy cutoff on some relativistic kinematical properties of this scattering problem. The results are challenging in the sense that as soon as one turns on the $\kappa$-spacetime extension, the nature of the two-body collision alters from elastic to inelastic one. It is shown also that a significant kinematical variable involving in heavy ion collisions, the rapidity, is not essentially an additive quantity under a sequence of the nonlinear representation of the Lorentz transformations.