Hadronic molecular states with the quark contents bcs¯q¯, bc¯sq¯, and bc¯s¯q

Liu, Wen-Ying; Chen, Hua-Xing; Wang, En

doi:10.1103/PhysRevD.107.054041

Hadronic molecular states with the quark contents $b c \bar{s} \bar{q}$ , $b \bar{c} s \bar{q}$ , and $b \bar{c} \bar{s} q$

Wen-Ying Liu (School of Physics, Southeast University, Nanjing 210094, China) ; Hua-Xing Chen (School of Physics, Southeast University, Nanjing 210094, China) ; En Wang (School of Physics, Zhengzhou University, Zhengzhou 450001, China)

We study the hadronic molecular states with the quark content $b c \bar{s} \bar{q}$ by investigating the interactions of the ${\bar{B}}_{s} D$ , $\bar{B} D_{s}$ , ${\bar{B}}_{s}^{*} D$ , ${\bar{B}}^{*} D_{s}$ , ${\bar{B}}_{s} D^{*}$ , $\bar{B} D_{s}^{*}$ , ${\bar{B}}_{s}^{*} D^{*}$ , and ${\bar{B}}^{*} D_{s}^{*}$ systems. By solving the Bethe-Salpeter equation within the extended local hidden gauge formalism, we find altogether six poles qualifying as possible hadronic molecular states: one pole of $J^{P} = 0^{+}$ below the ${\bar{B}}_{s} D − \bar{B} D_{s}$ threshold, one pole of $J^{P} = 1^{+}$ below the ${\bar{B}}_{s}^{*} D − {\bar{B}}^{*} D_{s}$ threshold, one pole of $J^{P} = 1^{+}$ below the ${\bar{B}}_{s} D^{*} − \bar{B} D_{s}^{*}$ threshold, and three poles of $J^{P} = 0^{+} / 1^{+} / 2^{+}$ below the ${\bar{B}}_{s}^{*} D^{*} − {\bar{B}}^{*} D_{s}^{*}$ threshold. Their binding energies are calculated to be about 10–20 MeV with the cutoff momentum $q_{\max} = 600 MeV$ . Similarly, we study the hadronic molecular states with $b s \bar{c} \bar{q}$ by investigating the interactions of the $\bar{B} {\bar{D}}_{s}$ , ${\bar{B}}_{c} \bar{K}$ , ${\bar{B}}^{*} {\bar{D}}_{s}$ , ${\bar{B}}_{c}^{*} \bar{K}$ , $\bar{B} {\bar{D}}_{s}^{*}$ , ${\bar{B}}_{c} {\bar{K}}^{*}$ , ${\bar{B}}^{*} {\bar{D}}_{s}^{*}$ , ${\bar{B}}_{c}^{*} {\bar{K}}^{*}$ systems, and the states with $b q \bar{c} \bar{s}$ by investigating the interactions of the ${\bar{B}}_{s} \bar{D}$ , ${\bar{B}}_{c} K$ , ${\bar{B}}_{s}^{*} \bar{D}$ , ${\bar{B}}_{c}^{*} K$ , ${\bar{B}}_{s} {\bar{D}}^{*}$ , ${\bar{B}}_{c} K^{*}$ , ${\bar{B}}_{s}^{*} {\bar{D}}^{*}$ , ${\bar{B}}_{c}^{*} K^{*}$ systems. However, no deeply bound poles are found in these systems.

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      "value": "We study the hadronic molecular states with the quark content <math><mi>b</mi><mi>c</mi><mover><mi>s</mi><mo>\u00af</mo></mover><mover><mi>q</mi><mo>\u00af</mo></mover></math> by investigating the interactions of the <math><msub><mover><mi>B</mi><mo>\u00af</mo></mover><mi>s</mi></msub><mi>D</mi></math>, <math><mover><mi>B</mi><mo>\u00af</mo></mover><msub><mi>D</mi><mi>s</mi></msub></math>, <math><mrow><msubsup><mrow><mover><mrow><mi>B</mi></mrow><mrow><mo>\u00af</mo></mrow></mover></mrow><mrow><mi>s</mi></mrow><mrow><mo>*</mo></mrow></msubsup><mi>D</mi></mrow></math>, <math><msup><mover><mi>B</mi><mo>\u00af</mo></mover><mo>*</mo></msup><msub><mi>D</mi><mi>s</mi></msub></math>, <math><msub><mover><mi>B</mi><mo>\u00af</mo></mover><mi>s</mi></msub><msup><mi>D</mi><mo>*</mo></msup></math>, <math><mover><mi>B</mi><mo>\u00af</mo></mover><msubsup><mi>D</mi><mi>s</mi><mo>*</mo></msubsup></math>, <math><msubsup><mover><mi>B</mi><mo>\u00af</mo></mover><mi>s</mi><mo>*</mo></msubsup><msup><mi>D</mi><mo>*</mo></msup></math>, and <math><msup><mover><mi>B</mi><mo>\u00af</mo></mover><mo>*</mo></msup><msubsup><mi>D</mi><mi>s</mi><mo>*</mo></msubsup></math> systems. By solving the Bethe-Salpeter equation within the extended local hidden gauge formalism, we find altogether six poles qualifying as possible hadronic molecular states: one pole of <math><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><msup><mn>0</mn><mo>+</mo></msup></math> below the <math><mrow><msub><mrow><mover><mrow><mi>B</mi></mrow><mrow><mo>\u00af</mo></mrow></mover></mrow><mrow><mi>s</mi></mrow></msub><mi>D</mi><mtext>\u2212</mtext><mover><mrow><mi>B</mi></mrow><mrow><mo>\u00af</mo></mrow></mover><msub><mrow><mi>D</mi></mrow><mrow><mi>s</mi></mrow></msub></mrow></math> threshold, one pole of <math><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><msup><mn>1</mn><mo>+</mo></msup></math> below the <math><mrow><msubsup><mrow><mover><mrow><mi>B</mi></mrow><mrow><mo>\u00af</mo></mrow></mover></mrow><mrow><mi>s</mi></mrow><mrow><mo>*</mo></mrow></msubsup><mi>D</mi><mtext>\u2212</mtext><msup><mrow><mover><mrow><mi>B</mi></mrow><mrow><mo>\u00af</mo></mrow></mover></mrow><mrow><mo>*</mo></mrow></msup><msub><mrow><mi>D</mi></mrow><mrow><mi>s</mi></mrow></msub></mrow></math> threshold, one pole of <math><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><msup><mn>1</mn><mo>+</mo></msup></math> below the <math><mrow><msub><mrow><mover><mrow><mi>B</mi></mrow><mrow><mo>\u00af</mo></mrow></mover></mrow><mrow><mi>s</mi></mrow></msub><msup><mrow><mi>D</mi></mrow><mrow><mo>*</mo></mrow></msup><mtext>\u2212</mtext><mover><mrow><mi>B</mi></mrow><mrow><mo>\u00af</mo></mrow></mover><msubsup><mrow><mi>D</mi></mrow><mrow><mi>s</mi></mrow><mrow><mo>*</mo></mrow></msubsup></mrow></math> threshold, and three poles of <math><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><msup><mn>0</mn><mo>+</mo></msup><mo>/</mo><msup><mn>1</mn><mo>+</mo></msup><mo>/</mo><msup><mn>2</mn><mo>+</mo></msup></math> below the <math><mrow><msubsup><mrow><mover><mrow><mi>B</mi></mrow><mrow><mo>\u00af</mo></mrow></mover></mrow><mrow><mi>s</mi></mrow><mrow><mo>*</mo></mrow></msubsup><msup><mrow><mi>D</mi></mrow><mrow><mo>*</mo></mrow></msup><mtext>\u2212</mtext><msup><mrow><mover><mrow><mi>B</mi></mrow><mrow><mo>\u00af</mo></mrow></mover></mrow><mrow><mo>*</mo></mrow></msup><msubsup><mrow><mi>D</mi></mrow><mrow><mi>s</mi></mrow><mrow><mo>*</mo></mrow></msubsup></mrow></math> threshold. Their binding energies are calculated to be about 10\u201320 MeV with the cutoff momentum <math><msub><mi>q</mi><mi>max</mi></msub><mo>=</mo><mn>600</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>. Similarly, we study the hadronic molecular states with <math><mi>b</mi><mi>s</mi><mover><mi>c</mi><mo>\u00af</mo></mover><mover><mi>q</mi><mo>\u00af</mo></mover></math> by investigating the interactions of the <math><mover><mi>B</mi><mo>\u00af</mo></mover><msub><mover><mi>D</mi><mo>\u00af</mo></mover><mi>s</mi></msub></math>, <math><msub><mover><mi>B</mi><mo>\u00af</mo></mover><mi>c</mi></msub><mover><mi>K</mi><mo>\u00af</mo></mover></math>, <math><msup><mover><mi>B</mi><mo>\u00af</mo></mover><mo>*</mo></msup><msub><mover><mi>D</mi><mo>\u00af</mo></mover><mi>s</mi></msub></math>, <math><msubsup><mover><mi>B</mi><mo>\u00af</mo></mover><mi>c</mi><mo>*</mo></msubsup><mover><mi>K</mi><mo>\u00af</mo></mover></math>, <math><mover><mi>B</mi><mo>\u00af</mo></mover><msubsup><mover><mi>D</mi><mo>\u00af</mo></mover><mi>s</mi><mo>*</mo></msubsup></math>, <math><msub><mover><mi>B</mi><mo>\u00af</mo></mover><mi>c</mi></msub><msup><mover><mi>K</mi><mo>\u00af</mo></mover><mo>*</mo></msup></math>, <math><msup><mover><mi>B</mi><mo>\u00af</mo></mover><mo>*</mo></msup><msubsup><mover><mi>D</mi><mo>\u00af</mo></mover><mi>s</mi><mo>*</mo></msubsup></math>, <math><msubsup><mover><mi>B</mi><mo>\u00af</mo></mover><mi>c</mi><mo>*</mo></msubsup><msup><mover><mi>K</mi><mo>\u00af</mo></mover><mo>*</mo></msup></math> systems, and the states with <math><mi>b</mi><mi>q</mi><mover><mi>c</mi><mo>\u00af</mo></mover><mover><mi>s</mi><mo>\u00af</mo></mover></math> by investigating the interactions of the <math><msub><mover><mi>B</mi><mo>\u00af</mo></mover><mi>s</mi></msub><mover><mi>D</mi><mo>\u00af</mo></mover></math>, <math><msub><mover><mi>B</mi><mo>\u00af</mo></mover><mi>c</mi></msub><mi>K</mi></math>, <math><msubsup><mover><mi>B</mi><mo>\u00af</mo></mover><mi>s</mi><mo>*</mo></msubsup><mover><mi>D</mi><mo>\u00af</mo></mover></math>, <math><msubsup><mover><mi>B</mi><mo>\u00af</mo></mover><mi>c</mi><mo>*</mo></msubsup><mi>K</mi></math>, <math><msub><mover><mi>B</mi><mo>\u00af</mo></mover><mi>s</mi></msub><msup><mover><mi>D</mi><mo>\u00af</mo></mover><mo>*</mo></msup></math>, <math><msub><mover><mi>B</mi><mo>\u00af</mo></mover><mi>c</mi></msub><msup><mi>K</mi><mo>*</mo></msup></math>, <math><msubsup><mover><mi>B</mi><mo>\u00af</mo></mover><mi>s</mi><mo>*</mo></msubsup><msup><mover><mi>D</mi><mo>\u00af</mo></mover><mo>*</mo></msup></math>, <math><msubsup><mover><mi>B</mi><mo>\u00af</mo></mover><mi>c</mi><mo>*</mo></msubsup><msup><mi>K</mi><mo>*</mo></msup></math> systems. However, no deeply bound poles are found in these systems."
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Published on:: 28 March 2023
Publisher:: APS
Published in:: Physical Review D , Volume 107 (2023)
Issue 5
DOI:: https://doi.org/10.1103/PhysRevD.107.054041
arXiv:: 2301.06785
Copyrights:: Published by the American Physical Society
Licence:: CC-BY-4.0

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