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

Abstract

Combining the quark model, the quark-pair-creation mechanism and B(*)$$ \overline{K} $$ K ¯ interaction, we have investigated the near-threshold P-wave Bs states in the framework of the Hamiltonian effective field theory. With the heavy quark flavor symmetry, all the parameters are determined in the Ds sector by fitting the lattice data. The masses of the bottom-strange partners of the $$ {D}_{s0}^{\ast }(2317) $$ D s 0 ∗ 2317 and $$ {D}_{s1}^{\ast }(2460) $$ D s 1 ∗ 2460 are predicted to be $$ {M}_{B_{s0}^{\ast }}={5730.2}_{-1.5}^{+2.4} $$ M B s 0 ∗ = 5730.2 − 1.5 + 2.4 MeV and $$ {M}_{B_{s1}^{\ast }}={5769.6}_{-1.6}^{+2.4} $$ M B s 1 ∗ = 5769.6 − 1.6 + 2.4 MeV, respectively, which are well consistent with the lattice QCD component. The two P-wave Bs states are the mixtures of the bare $$ \overline{b}s $$ b ¯ s core and B(*)$$ \overline{K} $$ 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 $$ B\overline{K} $$ B K ¯ scattering. This CDD zero will help deepen the insights of the near-threshold states and can be examined by future lattice calculation.