The investigations of the $P$-wave $B_s$ states combining quark model and lattice QCD in the coupled channel framework

Combining the quark model, the quark-pair-creation mechanism and $B^{(*)}K$ interaction, we have investigated the near-threshold $P$-wave $B_s$ states in the framework of the Hamiltonian effective field theory. With the heavy quark flavor symmetry, all the parameters are determined in the $D_s$ sector by fitting the lattice data. The masses of the bottom-strange partners of the $D^{*}_{s0}(2317)$ and $D^{*}_{s1}(2460)$ are predicted to be $M_{B^{*}_{s0}}=5730.2_{-1.5}^{+2.4}$ MeV and $M_{B^{*}_{s1}}= 5769.6_{-1.6}^{+2.4}$ MeV, respectively, which are well consistent with the lattice QCD simulation. The two P-wave $B_s$ states are the mixtures of the bare $b\bar s$ core and $B^{(*)}K$ component. Moreover, we find a crossing point between the energy levels with and without the interaction Hamiltonian in the finite volume spectrum in the $0^+$ case, which corresponds to a CDD (Castillejo-Dalitz-Dyson) zero in the $T$-matrix of the $BK$ scattering. This CDD zero will help deepen the insights of the near-threshold states and can be examined by the future lattice calculation.Comment: 20 pages, 4 figure