Studying the $\bar{D}_1K$ molecule in the Bethe-Salpeter equation approach

TL;DR

This paper investigates the $X_1(2900)$ as a molecular state of $ar{D}_1K$ using the Bethe-Salpeter equation, demonstrating the existence of a bound state and analyzing its decay properties.

Contribution

It introduces a Bethe-Salpeter equation approach with various form factors to confirm the molecular nature of $X_1(2900)$ and studies its decay width.

Findings

Bound state of $ar{D}_1K$ exists in the model.

Decay width of $X_1(2900)$ to $D^-K^+$ is calculated.

Different form factors influence the bound state properties.

Abstract

We interpret the $X_1(2900)$ as an $S$-wave $\bar{D}_1K$ molecular state in the Bethe-Salpeter equation approach with the ladder and instantaneous approximations for the kernel. By solving the Bethe-Salpeter equation numerically with the kernel containing one-particle-exchange diagrams and introducing three different form factors (monopole, dipole, and exponential form factors) in the verties, we find the bound state exists. We also study the decay width of the decay $X_1(2900)$ to $D^-K^+$.