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

TL;DR

This study combines quark models and lattice QCD within an effective field theory framework to predict and analyze near-threshold P-wave B_s states, revealing their mixed nature and identifying a CDD zero in the scattering matrix.

Contribution

It introduces a coupled channel approach with lattice data calibration to predict bottom-strange B_s states and explores the role of CDD zeros in their spectral behavior.

Findings

Predicted masses of B_s states consistent with lattice QCD

Identified mixing of core and meson components in states

Discovered a CDD zero affecting the scattering amplitude

Abstract

Combining the quark model, the quark-pair-creation mechanism and $B^{(*)}\bar K$ 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 $D^{*}_{s0}(2317)$ 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 $\bar b s$ core and $B^{(*)}\bar K$ 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.