Effects of the Lorentz symmetry violation on relativistic neutral scalar bosons: Scattering and bound states

TL;DR

This paper explores how Lorentz symmetry violation influences the behavior of relativistic neutral scalar bosons, affecting scattering and bound states, with analytical solutions derived using the Klein-Gordon formalism and partial wave analysis.

Contribution

It introduces a novel analysis of Lorentz symmetry violation effects on scalar bosons within the Klein-Gordon framework, highlighting the necessity of specific violation parameters for bound states.

Findings

Bound states exist only within a restricted range of Lorentz violation parameters.

Lorentz violation significantly alters phase shifts and scattering amplitudes.

Contradicts previous studies by showing bound states depend on specific violation parameters.

Abstract

In this letter, we investigate the effects of Lorentz symmetry violation on a relativistic neutral scalar boson within the framework of the Klein-Gordon formalism. We consider a tensor $(K_F)_{\mu \nu \alpha \beta}$ out of the Standard Model Extension, which describes the field configuration consisting of a constant magnetic field $\vec{B}=B\hat{z}$ and a cylindrical electric field $\vec{E}=\frac{\lambda}{r}\hat{r}$. We analyze and discuss the effects of Lorentz symmetry violation on the equation of motion and show that the presence of a specific Lorentz symmetry violation parameter is essential to obtain analytical solutions for scattering and bound states. Employing the partial wave approach in cylindrical coordinates, we calculate the relativistic phase shift, scattering amplitude and $S$-matrix, and discuss the effects of Lorentz symmetry violation on the phase shift. Furthermore, we obtain bound-state solutions by examining the poles of the $S$-matrix and compare our findings with those reported in the literature. Our results reveal that bound-state solutions are only feasible for a restrict range of Lorentz symmetry violation parameters, which contradict previous studies.