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 $B^{(\ast )}\bar{K}$ 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 $D_{s0}^{\ast }(2317)$ and $D_{s1}^{\ast }(2460)$ are predicted to be $M_{B_{s0}^{\ast }}=5730.2_{-1.5}^{+2.4}$ MeV and $M_{B_{s1}^{\ast }}=5769.6_{-1.6}^{+2.4}$ MeV, respectively, which are well consistent with the lattice QCD simulation. The two $P$-wave $B_s$ states are the mixtures of the bare $\bar{b}s$ core and $B^{(\ast )}\bar{K}$ 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 $B\bar{K}$ scattering. This CDD zero will help deepen the insights of the near-threshold states and can be examined by future lattice calculation.

20 pages, 4 figures. Version accepted by JHEP