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 \(D^-K^+\).

中文翻译：

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在 Bethe-Salpeter 方程方法中研究 $${\bar{D}}_1K$$ D¯ 1 K 分子

我们在 Bethe-Salpeter 方程方法中将\(X_1(2900)\) 解释为S波\({\bar{D}}_1K\)分子态，使用阶梯和内核的瞬时近似值。通过使用包含单粒子交换图的核对 Bethe-Salpeter 方程进行数值求解，并在顶点中引入三种不同的形状因子（单极子、偶极子和指数形状因子），我们发现束缚态存在。我们还研究了衰减\(X_1(2900)\)到\(D^-K^+\)的衰减宽度。