Two-dimensional birth rate distribution of dBH-MS in the MW shown as a function of LC mass (M_LC), BH mass (M_BH), orbital period (P_orb), and eccentricity (e). The color in each pixel is scaled according to the birth rate of dBH-LC binaries. Left panels: dBH-MS formed through IBE. Right panels: dBH-MS formed through triple evolution. The dark green crosses represent the observational data from Table 1. It is worth noting that our study focuses more on the differences between the dBH-LC populations formed through IBE and triple evolution. Therefore, in Table 1, we classify the observations only by the stellar types of the LCs. We emphasize that explaining these observations still requires attention to additional physical properties (e.g., the metallicity of each observation).