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

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Cited by in corpus (7)

• Exotic Tetraquark states with two $\bar{b}$-quarks and $J^P=0^{+}$ and $1^{+}$ $B_s$ states in a nonperturbatively-tuned Lattice NRQCD setup
• New insight into the exotic states strongly coupled with the $D{\bar{D}}^{\ast }$ from the $T_{cc}^{+}$
• Isospin-conserving hadronic decay of the $D_{s1}(2460)$ into $D_s{\pi }^{+}{\pi }^{-}$
• Masses and radiative decay widths of the $D_{s0}^{\ast }(2317)$ and $D_{s1}^{\prime }(2460)$ and their bottom analogs
• Structure of the ${\Omega }^{-}(2012)$ with Hamiltonian Effective Field Theory
• Bottomonia in an unquenched quark model
• Investigation on the bottom analogs of the $T_{cc}^{+}$