Color flux-tube nature of the states $T_{cs}(2900)$ and $T^a_{c\bar{s}}(2900)$

Inspired by the states $T_{cs0}(2900)^0$, $T_{cs1}(2900)^0$, $T^a_{c\bar{s}0}(2900)^{0}$ and $T^a_{c\bar{s}0}(2900)^{++}$ reported by the LHCb Collaboration, we carry out a systematical investigation on the properties of the ground and $P$-wave states $[cs][\bar{u}\bar{d}]$ and $[cu][\bar{s}\bar{d}]$ with various spin, isospin or $U$-spin, and color combinations in a multiquark color flux-tube model. Matching our results with the spin-parity and mass of the states $T_{cs0}(2900)^0$ and $T_{cs1}(2900)^0$, we can describe them as the compact states $[cs][\bar{u}\bar{d}]$ with $I(J^{P})=1(0^+)$ and $0(1^-)$ in the model, respectively. The ground state $T_{cs0}(2900)^0$ is mainly made of strongly overlapped an axial-vector $[cs]_{\bar{\mathbf{3}}_c}$ and an axial-vector $[\bar{u}\bar{d}]_{\mathbf{3}_c}$. The $P$-wave state $T_{cs1}(2900)^0$ is dominantly consisted of a gradually separated scalar or axial vector $[cs]_{\bar{\mathbf{3}}_c}$ and a scalar $[\bar{u}\bar{d}]_{\mathbf{3}_c}$ in the shape of a dumbbell. Supposing the states $T^a_{c\bar{s}0}(2900)^{0}$ and $T^a_{c\bar{s}0}(2900)^{++}$ belong to the same isospin triplet, the mass of the state $\left [[cu]_{\bar{\mathbf{3}}_c}[\bar{s}\bar{d}]_ {\mathbf{3}_c}\right ]_{\mathbf{1}_c}$ with symmetrical $U$-spin and $J^P=0^+$ is highly consistent with that of the states $T^a_{c\bar{s}0}(2900)^{0}$ and $T^a_{c\bar{s}0}(2900)^{++}$ in the model. After coupling two color configurations, the state $[cu][\bar{s}\bar{d}]$ is slightly lighter than the states $T^a_{c\bar{s}0}(2900)^{0}$ and $T^a_{c\bar{s}0}(2900)^{++}$. In addition, we also discuss the properties of other states in the model.