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arXiv · 2207.07320

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

Zhi Yang·Guang-Juan Wang·Jia-Jun Wu·Makoto Oka·Shi-Lin Zhu
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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.

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Zhi Yang, Guang-Juan Wang, Jia-Jun Wu, Makoto Oka, Shi-Lin Zhu. 2022-07-15. The investigations of the $P$-wave $B_s$ states combining quark model and lattice QCD in the coupled channel framework. https://doi.org/10.1007/jhep01(2023)058

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