The $T_{c\bar{s}}(2900)$ as a threshold effect from the interaction of the $D^*K^*$, $D^*_s\rho$ channels

We investigate the $D^*K^*$ and $D^*_s\rho$ interaction in coupled channels within the hidden gauge formalism. A structure is developed around their thresholds, short of producing a bound state, which leads to a peak in the $D_s^+ \pi^-$ mass distribution in the $B^0 \to \bar{D}^0 D_s^+ \pi^-$ decay compatible with the experimental data. We conclude that the interaction between the $D^*K^*$ and $D^*_s\rho$ is essential to produce the cusp structure that we associate to the recently seen $T_{c\bar{s}}(2900)$, and that its experimental width is mainly due to the decay width of the $\rho$ meson. The peak obtained together with a smooth background reproduces fairly well the experimental mass distribution observed in the $B_0 \to \bar{D}^0 D_s^+ \pi^-$ decay.