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

Abstract Combining the quark model, the quark-pair-creation mechanism and B (*) K ¯ $$ \overline{K} $$ 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 s 0 ∗ 2317 $$ {D}_{s0}^{\ast }(2317) $$ and D s 1 ∗ 2460 $$ {D}_{s1}^{\ast }(2460) $$ are predicted to be M B s 0 ∗ = 5730.2 − 1.5 + 2.4 $$ {M}_{B_{s0}^{\ast }}={5730.2}_{-1.5}^{+2.4} $$ MeV and M B s 1 ∗ = 5769.6 − 1.6 + 2.4 $$ {M}_{B_{s1}^{\ast }}={5769.6}_{-1.6}^{+2.4} $$ MeV, respectively, which are well consistent with the lattice QCD component. The two P-wave B s states are the mixtures of the bare b ¯ s $$ \overline{b}s $$ core and B (*) K ¯ $$ \overline{K} $$ 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 B K ¯ $$ B\overline{K} $$ scattering. This CDD zero will help deepen the insights of the near-threshold states and can be examined by future lattice calculation