Studying the bound state of the $B\bar{K}$ system in the Bethe-Salpeter formalism

TL;DR

This paper investigates whether the $X(5568)$ can be a $Bar{K}$ molecular state using the Bethe-Salpeter formalism, finding it unlikely to be such a bound state based on their calculations.

Contribution

The study applies the Bethe-Salpeter equation with different form factors to analyze the $Bar{K}$ system, providing new insights into its bound state properties.

Findings

$X(5568)$ is unlikely to be a $Bar{K}$ molecule.

The Bethe-Salpeter approach with various form factors was successfully used.

The isoscalar and isovector $Bar{K}$ systems were analyzed.

Abstract

In this work, we study the $B\bar{K}$ molecule in the Bethe-Salpeter (BS) equation approach. With the kernel containing one-particle-exchange diagrams and introducing two different form factors (monopole form factor and dipole form factor) in the vertex, we solve the BS equation numerically in the covariant instantaneous approximation. We investigate the isoscalar and isovector $B\bar{K}$ systems, and we find $X(5568)$ cannot be a $B\bar{K}$ molecule.