Masses of the singly heavy baryons (SHBs), composed of a heavy quark and a light diquark, are studied from the viewpoints of heavy-quark spin symmetry (HQSS) and chiral-symmetry restoration at finite temperature. We consider the light diquarks with spin-parity <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><msup><mn>0</mn><mo>±</mo></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>1</mn><mo>±</mo></msup></math>. Medium corrections to the SHBs are provided through the diquarks whereas the heavy quark is simply regarded as a spectator. The chiral dynamics of the diquark are described by the Nambu-Jona-Lasinio (NJL) model having (pseudo)scalar-type and (axial)vector-type four-point interactions and the six-point ones responsible for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo></math> axial anomaly. The divergences are handled by means of the three-dimensional proper-time regularization with both ultraviolet and infrared cutoffs included, in order to eliminate unphysical imaginary parts. As a result, the mass degeneracies between the parity partners of all the SHBs are predicted in accordance with the chiral restoration. In particular, the HQS-doublet SHBs exhibit clear mass degeneracies due to the absence of the direct anomaly effects. We also predict a mass degeneracy of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Σ</mi><mi>c</mi></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ω</mi><mi>c</mi></msub></math> above the pseudocritical temperature <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mi>pc</mi></msub></math> of chiral restoration, which results in a peculiar mass hierarchy for positive-parity HQS-doublet SHBs where <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mi>c</mi><mo>′</mo></msubsup></math> becomes heavier than <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ω</mi><mi>c</mi></msub></math> Besides, it is found that the decay width of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Σ</mi><mi>c</mi></msub><mo stretchy="false">→</mo><msub><mi mathvariant="normal">Λ</mi><mi>c</mi></msub><mi>π</mi></math> vanishes above <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mi>pc</mi></msub></math> reflecting a closing of the threshold. The predicted modifications of masses and decay widths of the SHBs are expected to provide future heavy-ion collision experiments and lattice simulations with useful information on chiral dynamics of the diquarks.

Japan

Daiki Suenaga

Makoto Oka

Fate of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi mathvariant="normal">Σ</mi></mrow><mrow><mi>c</mi></mrow></msub></mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi mathvariant="normal">Ξ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>′</mo></mrow></msubsup></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ω</mi><mi>c</mi></msub></math> baryons at high temperature with chiral-symmetry restoration

Chiral effective theory of light diquarks is revisited. We construct an effective Lagrangian based on the linear representation of three-flavor chiral symmetry. Here, we focus on the effect of a chiral and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><msub><mo stretchy="false">)</mo><mi>A</mi></msub></math> symmetric term originated from an eight-point quark interaction. From this model, we obtain the mass formulas of scalar, pseudoscalar, vector, and axial-vector diquarks, which also describe the dependence of diquark masses on the spontaneous chiral symmetry breaking and the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><msub><mo stretchy="false">)</mo><mi>A</mi></msub></math> anomaly. We regard singly heavy baryons as two-body systems composed of one heavy quark and one diquark and then predict the fate of the mass spectrum and the strong decay widths under chiral symmetry restoration.

Yonghee Kim

Kei Suzuki

Chiral effective theory of scalar and vector diquarks revisited

A comprehensive study of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi></math>-wave heavy tetraquark states with identical quarks and antiquarks, specifically <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Q</mi><mi>Q</mi><msup><mover accent="true"><mi>Q</mi><mo stretchy="false">¯</mo></mover><mo>′</mo></msup><msup><mover accent="true"><mi>Q</mi><mo stretchy="false">¯</mo></mover><mo>′</mo></msup></math> (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Q</mi><mo>,</mo><msup><mi>Q</mi><mo>′</mo></msup><mo>=</mo><mi>c</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>b</mi></mrow></math>), <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Q</mi><mi>Q</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover><mo>/</mo><mover accent="true"><mi>Q</mi><mo stretchy="false">¯</mo></mover><mover accent="true"><mi>Q</mi><mo stretchy="false">¯</mo></mover><mi>s</mi><mi>s</mi></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Q</mi><mi>Q</mi><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover><mo>/</mo><mover accent="true"><mi>Q</mi><mo stretchy="false">¯</mo></mover><mover accent="true"><mi>Q</mi><mo stretchy="false">¯</mo></mover><mi>q</mi><mi>q</mi></math> (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>q</mi><mo>=</mo><mi>u</mi></mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>d</mi></mrow></math>), are studied in a unified constituent quark model. This model contains the one-gluon exchange and confinement potentials. The latter is modeled as the sum of all two-body linear potentials. We employ the Gaussian expansion method to solve the full four-body Schrödinger equations, and search bound and resonant states using the complex-scaling method. We then identify 3 bound and 62 resonant states. The bound states are all <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Q</mi><mi>Q</mi><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover></math> states with the isospin and spin-parity quantum numbers <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>I</mi><mo stretchy="false">(</mo><msup><mi>J</mi><mi>P</mi></msup><mo stretchy="false">)</mo><mo>=</mo><mn>0</mn><mo stretchy="false">(</mo><msup><mn>1</mn><mo>+</mo></msup><mo stretchy="false">)</mo></math>: two bound <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>b</mi><mi>b</mi><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover></math> states with the binding energies, 153 MeV and 4 MeV below the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><msup><mi>B</mi><mo>*</mo></msup></math> threshold, and a shallow <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>c</mi><mi>c</mi><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover></math> state at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>−</mo><mn>15</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math> from the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><msup><mi>D</mi><mo>*</mo></msup></math> threshold. The deeper <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>b</mi><mi>b</mi><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover></math> bound state aligns with the lattice QCD predictions, while <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>c</mi><mi>c</mi><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover></math> bound state, still has a much larger binding energy than the recently observed <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow><mo>+</mo></msubsup></math> by LHCb collaboration. No bound states are identified for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Q</mi><mi>Q</mi><msup><mover accent="true"><mi>Q</mi><mo stretchy="false">¯</mo></mover><mo>′</mo></msup><msup><mover accent="true"><mi>Q</mi><mo stretchy="false">¯</mo></mover><mo>′</mo></msup></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Q</mi><mi>Q</mi><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover><mover accent="true"><mi>s</mi><mo stretchy="false">¯</mo></mover></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Q</mi><mi>Q</mi><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover></math> with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>I</mi><mo>=</mo><mn>1</mn></math>. Our analysis shows that the bound <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Q</mi><mi>Q</mi><msup><mover accent="true"><mi>Q</mi><mo stretchy="false">¯</mo></mover><mo>′</mo></msup><msup><mover accent="true"><mi>Q</mi><mo stretchy="false">¯</mo></mover><mo>′</mo></msup></math> states are more probable with a larger mass ratio, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>m</mi><mi>Q</mi></msub><mo>/</mo><msub><mi>m</mi><msup><mi>Q</mi><mo>′</mo></msup></msub></math>. Experimental investigation for these states is desired, which will enrich our understanding of hadron spectroscopy and probe insights into the confinement mechanisms within tetraquarks.

China

Qi Meng

Guang-Juan Wang

Mass spectra of full-heavy and double-heavy tetraquark states in the conventional quark model

We investigate the structure of ground-state heavy mesons within the light-front quark model, utilizing wave functions derived from the single Gaussian ansatz (SGA) and the Gaussian expansion method (GEM). By performing a <math><msup><mi>χ</mi><mn>2</mn></msup></math> fit to static properties such as mass spectra and decay constants, we determine the model parameters for each approach. We then compare the impacts of both methods on the light-front wave functions and structural observables. Our analysis reveals significant differences in the distribution amplitudes <math><msub><mi>ϕ</mi><mrow><mn>2</mn><mo>;</mo><mi>M</mi></mrow></msub><mo>(</mo><mi>x</mi><mo>)</mo></math> near the end points, with GEM showing enhanced amplitudes and correct asymptotic behavior <math><mrow><msub><mrow><mi>ϕ</mi></mrow><mrow><mn>2</mn><mo>;</mo><mi>M</mi></mrow></msub><mo>(</mo><mi>x</mi><mo>→</mo><mn>1</mn><mo>)</mo><mo>∝</mo><mo>(</mo><mn>1</mn><mo>−</mo><mi>x</mi><mo>)</mo></mrow></math>, consistent with perturbative QCD. This end point behavior is linked to the short-range (high-momentum) wave function governed by color Coulomb interaction and relativistic kinematics. GEM accurately reproduces a power-law damping <math><mrow><msub><mrow><mi>ψ</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><mi>k</mi><mo>→</mo><mi>∞</mi><mo>)</mo><mo>∝</mo><mn>1</mn><mo>/</mo><msubsup><mrow><mi>k</mi></mrow><mrow><mo>⊥</mo></mrow><mrow><mn>2</mn></mrow></msubsup></mrow></math>, aligning with perturbative QCD predictions. Furthermore, the electromagnetic form factors of pseudoscalar mesons in the low-<math><msup><mi>Q</mi><mn>2</mn></msup></math> region fall off faster with GEM than with SGA. Overall, while both methods adequately describe static properties, GEM provides a more accurate description of structural properties, being more sensitive to details and asymptotic behaviors.

Ahmad Jafar Arifi

Lucas Happ

Shuhei Ohno

Structure of heavy mesons in the light-front quark model

Spectrum of the doubly heavy tetraquarks is studied in a constituent quark model including one-pion exchange (OPE) potential. Central and tensor forces induced by OPE between two light quarks are considered. Our results show that <math><mi>I</mi><mo>(</mo><msup><mrow><mi>J</mi></mrow><mrow><mi>P</mi></mrow></msup><mo>)</mo><mo>=</mo><mn>0</mn><mo>(</mo><msup><mrow><mn>1</mn></mrow><mrow><mo>+</mo></mrow></msup><mo>)</mo></math> compact bound states are shifted up because of the repulsive central force between <math><mover><mrow><mi>q</mi></mrow><mrow><mo>¯</mo></mrow></mover><mover><mrow><mi>q</mi></mrow><mrow><mo>¯</mo></mrow></mover></math>. This effect possibly leads to the small binding energy in <math><msub><mrow><mi>T</mi></mrow><mrow><mi>c</mi><mi>c</mi></mrow></msub></math>. In addition, a <math><mi>I</mi><mo>(</mo><msup><mrow><mi>J</mi></mrow><mrow><mi>P</mi></mrow></msup><mo>)</mo><mo>=</mo><mn>1</mn><mo>(</mo><msup><mrow><mn>1</mn></mrow><mrow><mo>+</mo></mrow></msup><mo>)</mo></math> resonant state is reported with <math><mi>E</mi><mo>=</mo><mn>10641</mn><mspace width="0.25em"></mspace><mtext>MeV</mtext><mo>,</mo><mi>Γ</mi><mo>=</mo><mn>15</mn><mspace width="0.25em"></mspace><mtext>MeV</mtext></math> and <math><mi>E</mi><mo>=</mo><mn>10640</mn><mtext> MeV</mtext><mo>,</mo><mi>Γ</mi><mo>=</mo><mn>15</mn><mtext> MeV</mtext></math>, without and with including OPE potential, respectively. The repulsive central force and attractive tensor force almost cancel with each other and leave a small energy difference when OPE potential is included.

Emiko Hiyama

Atsushi Hosaka

Chang Xu

Doubly heavy tetraquarks including one-pion exchange potential

A new color basis system and confinement mechanism for multiquark systems are proposed according to the string-type picture of QCD. The color string configurations in the strong coupling QCD are implemented in the set of color basis states. The extended color Hilbert space for <math><mrow><mi>Q</mi><mi>Q</mi><mover><mrow><mi>Q</mi></mrow><mrow><mo>¯</mo></mrow></mover><mover><mrow><mi>Q</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow></math> systems includes a “hidden color” state, which mixes with two-meson states <math><mi>Q</mi><mover><mi>Q</mi><mo>¯</mo></mover><mo>+</mo><mi>Q</mi><mover><mi>Q</mi><mo>¯</mo></mover></math>, This mixing effect leads to an attractive potential sufficient to form a bound state. We apply a realistic Hamiltonian model with the new scheme to fully charmed tetraquark states, <math><mrow><mi>c</mi><mi>c</mi><mover><mrow><mi>c</mi></mrow><mrow><mo>¯</mo></mrow></mover><mover><mrow><mi>c</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow></math>, and find a bound and two resonant states, which could potentially correspond to the <math><mrow><mi>c</mi><mi>c</mi><mover><mrow><mi>c</mi></mrow><mrow><mo>¯</mo></mrow></mover><mover><mrow><mi>c</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow></math> tetraquark candidates recently observed in experiments.

Daisuke Jido

Quark confinement for multiquark systems: Application to fully charmed tetraquarks

Effects of the <math><mi>U</mi><mo>(</mo><mn>1</mn><msub><mo>)</mo><mi>A</mi></msub></math> axial anomaly on the mass spectrum of singly heavy baryons (SHBs) is studied in terms of the chiral effective theory based on the chiral linear representation for light flavors. We consider SHBs made of both three quarks (<math><mi>Q</mi><mi>q</mi><mi>q</mi></math>) and five quarks (<math><mi>Q</mi><mi>q</mi><mi>q</mi><mi>q</mi><mover><mi>q</mi><mo>¯</mo></mover></math>). For the three-quark SHBs, we prove that the inverse mass hierarchy for the negative-parity <math><msub><mi>Λ</mi><mi>c</mi></msub></math> and <math><msub><mi>Ξ</mi><mi>c</mi></msub></math> is realized only when the <math><mi>U</mi><mo>(</mo><mn>1</mn><msub><mo>)</mo><mi>A</mi></msub></math> anomaly is present. For the five-quark SHBs, in contrast, it is found that the <math><mi>U</mi><mo>(</mo><mn>1</mn><msub><mo>)</mo><mi>A</mi></msub></math> anomaly does not change the mass spectrum at the leading order, and accordingly, their decay properties induced by emitting a pseudoscalar meson are not affected by the anomaly. Moreover, taking into account small mixings between the three-quark and five-quark SHBs, we find that the observed <math><msub><mi>Ξ</mi><mi>c</mi></msub></math> excited state, either <math><msub><mi>Ξ</mi><mi>c</mi></msub><mo>(</mo><mn>2923</mn><mo>)</mo></math> or <math><msub><mi>Ξ</mi><mi>c</mi></msub><mo>(</mo><mn>2930</mn><mo>)</mo></math>, can be consistently regarded as a negative-parity SHB that is dominated by the five-quark component. We also predict a new negative-parity five-quark dominant <math><msub><mi>Λ</mi><mi>c</mi></msub></math>, whose mass is around 2700 MeV and the decay width is of order a few MeV, which provides useful information for future experiments to check our description.

Hiroto Takada

Masayasu Harada

Axial anomaly effect on three-quark and five-quark singly heavy baryons

Masses of positive-parity and negative-parity diquarks are investigated at finite temperature with a quark chemical potential. We employ the three-flavor Nambu-Jona-Lasinio model, in order to delineate chiral properties of the diquarks, in particular, the mass degeneracy of chiral partners under extreme conditions. We focus on the effects of <math><mi>U</mi><mo>(</mo><mn>1</mn><msub><mo>)</mo><mi>A</mi></msub></math> axial anomaly on manifestation of the chiral-partner structures. We find that, in the absence of anomaly effects to the diquarks, the mass degeneracies in all <math><mo>[</mo><mi>u</mi><mi>d</mi><mo>]</mo></math>, <math><mo>[</mo><mi>s</mi><mi>u</mi><mo>]</mo></math>, and <math><mo>[</mo><mi>s</mi><mi>d</mi><mo>]</mo></math> diquark sectors take place prominently above the pseudocritical temperature of the chiral restoration. On the other hand, the anomaly effects are found to hinder the <math><mo>[</mo><mi>u</mi><mi>d</mi><mo>]</mo></math> diquark from exhibiting the mass degeneracy, accompanied by a slow reduction of the <math><mover><mi>s</mi><mo>¯</mo></mover><mi>s</mi></math> condensate, while the <math><mo>[</mo><mi>s</mi><mi>u</mi><mo>]</mo></math> and <math><mo>[</mo><mi>s</mi><mi>d</mi><mo>]</mo></math> diquarks are not much affected. Our present investigation will provide useful information on the chiral-partner structure with the anomaly effects of diquarks for heavy-ion collision experiments of singly heavy baryons and doubly heavy tetraquarks, and for future lattice simulations of the diquarks.

Axial anomaly effect on the chiral-partner structure of diquarks at high temperature

A chiral effective theory of scalar and vector diquarks is formulated, which is based on <math><mi>S</mi><mi>U</mi><mo>(</mo><mn>3</mn><msub><mo>)</mo><mi>R</mi></msub><mo>×</mo><mi>S</mi><mi>U</mi><mo>(</mo><mn>3</mn><msub><mo>)</mo><mi>L</mi></msub></math> chiral symmetry and includes interactions between scalar and vector diquarks with one or two mesons. We find that the diquark interaction term with two mesons breaks the <math><mi>U</mi><mo>(</mo><mn>1</mn><msub><mo>)</mo><mi>A</mi></msub></math> and flavor <math><mi>S</mi><mi>U</mi><mo>(</mo><mn>3</mn><mo>)</mo></math> symmetries. To determine the coupling constants of the interaction Lagrangians, we investigate one-pion emission decays of singly heavy baryons <math><mi>Q</mi><mi>q</mi><mi>q</mi></math> (<math><mrow><mi>Q</mi><mo>=</mo><mi>c</mi></mrow></math>, <math><mrow><mi>b</mi></mrow></math> and <math><mi>q</mi><mo>=</mo><mi>u</mi></math>, <math><mrow><mi>d</mi></mrow></math>, <math><mrow><mi>s</mi></mrow></math>), where baryons are regarded as diquark–heavy-quark two-body systems. Using this model, we present predictions of the unobserved decay widths of singly heavy baryons. We also study the change of masses and strong decay widths of singly heavy baryons under partial restoration of chiral symmetry.

Strong decays of singly heavy baryons from a chiral effective theory of diquarks

Combining the quark model, the quark-pair-creation mechanism and B (*) <math> <mover> <mi>K</mi> <mo>¯</mo> </mover> </math> $$ \overline{K} $$ 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 <math> <msubsup> <mi>D</mi> <mrow> <mi>s</mi> <mn>0</mn> </mrow> <mo>∗</mo> </msubsup> <mfenced> <mn>2317</mn> </mfenced> </math> $$ {D}_{s0}^{\ast }(2317) $$ and <math> <msubsup> <mi>D</mi> <mrow> <mi>s</mi> <mn>1</mn> </mrow> <mo>∗</mo> </msubsup> <mfenced> <mn>2460</mn> </mfenced> </math> $$ {D}_{s1}^{\ast }(2460) $$ are predicted to be <math> <msub> <mi>M</mi> <msubsup> <mi>B</mi> <mrow> <mi>s</mi> <mn>0</mn> </mrow> <mo>∗</mo> </msubsup> </msub> <mo>=</mo> <msubsup> <mn>5730.2</mn> <mrow> <mo>−</mo> <mn>1.5</mn> </mrow> <mrow> <mo>+</mo> <mn>2.4</mn> </mrow> </msubsup> </math> $$ {M}_{B_{s0}^{\ast }}={5730.2}_{-1.5}^{+2.4} $$ MeV and <math> <msub> <mi>M</mi> <msubsup> <mi>B</mi> <mrow> <mi>s</mi> <mn>1</mn> </mrow> <mo>∗</mo> </msubsup> </msub> <mo>=</mo> <msubsup> <mn>5769.6</mn> <mrow> <mo>−</mo> <mn>1.6</mn> </mrow> <mrow> <mo>+</mo> <mn>2.4</mn> </mrow> </msubsup> </math> $$ {M}_{B_{s1}^{\ast }}={5769.6}_{-1.6}^{+2.4} $$ MeV, respectively, which are well consistent with the lattice QCD component. The two P-wave B s states are the mixtures of the bare <math> <mover> <mi>b</mi> <mo>¯</mo> </mover> <mi>s</mi> </math> $$ \overline{b}s $$ core and B (*) <math> <mover> <mi>K</mi> <mo>¯</mo> </mover> </math> $$ \overline{K} $$ 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 <math> <mi>B</mi> <mover> <mi>K</mi> <mo>¯</mo> </mover> </math> $$ B\overline{K} $$ scattering. This CDD zero will help deepen the insights of the near-threshold states and can be examined by future lattice calculation.