We investigate the sextet <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>b</mi></math>-baryon decay processes <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ω</mi><mi>b</mi></msub><mo stretchy="false">→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><msup><mi mathvariant="normal">Ω</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi mathvariant="normal">Ω</mi><mo>*</mo></msup></math> represents the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1</mn><mi>P</mi></math>-, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1</mn><mi>D</mi></math>- and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>2</mn><mi>S</mi></math>-wave excited <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Ω</mi></math> hyperons in the spectroscopy. Using the constituent quark model, we obtain <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msub><mi mathvariant="normal">Ω</mi><mi>b</mi></msub><mo stretchy="false">→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mi mathvariant="normal">Ω</mi><mo stretchy="false">)</mo><mo>=</mo><mn>8.8</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>4</mn></mrow></msup></math>, which agrees with the previous studies to the order of magnitude. By identifying <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Ω</mi><mo stretchy="false">(</mo><mn>2012</mn><mo stretchy="false">)</mo></math> as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="normal">Ω</mi><mo stretchy="false">(</mo><msup><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></msup><msub><mrow><mi>P</mi></mrow><mrow><mn>3</mn><mo>/</mo><msup><mrow><mn>2</mn></mrow><mrow><mo>−</mo></mrow></msup></mrow></msub><mo stretchy="false">)</mo></mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msub><mi mathvariant="normal">Ω</mi><mi>b</mi></msub><mo stretchy="false">→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mi mathvariant="normal">Ω</mi><mo stretchy="false">(</mo><mn>2012</mn><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo>=</mo><mn>1.1</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></math> can be similarly significant. Additionally, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Ω</mi><mo stretchy="false">(</mo><msup><mn>1</mn><mn>2</mn></msup><msub><mi>D</mi><mrow><mn>5</mn><mo>/</mo><msup><mn>2</mn><mo>+</mo></msup></mrow></msub><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Ω</mi><mo stretchy="false">(</mo><msup><mn>1</mn><mn>4</mn></msup><msub><mi>D</mi><mrow><mn>3</mn><mo>/</mo><msup><mn>2</mn><mo>+</mo></msup></mrow></msub><mo>,</mo><msup><mn>1</mn><mn>4</mn></msup><msub><mi>D</mi><mrow><mn>5</mn><mo>/</mo><msup><mn>2</mn><mo>+</mo></msup></mrow></msub><mo stretchy="false">)</mo></math> states exhibit production rates of 0.5, and (0.6, 0.8), respectively, relative to their ground-state counterpart. Notably, our findings suggest that <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msub><mi mathvariant="normal">Ω</mi><mi>b</mi></msub><mo stretchy="false">→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mi mathvariant="normal">Ω</mi><mo stretchy="false">(</mo><msup><mn>2</mn><mn>2</mn></msup><msub><mi>S</mi><mrow><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>+</mo></msup></mrow></msub><mo>,</mo><msup><mn>2</mn><mn>4</mn></msup><msub><mi>S</mi><mrow><mn>3</mn><mo>/</mo><msup><mn>2</mn><mo>+</mo></msup></mrow></msub><mo stretchy="false">)</mo><mo stretchy="false">)</mo></math> are as large as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><mn>4.5</mn><mo>,</mo><mn>20</mn><mo stretchy="false">)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>4</mn></mrow></msup></math>, making them accessible to experiments at LHCb.

China

Kai-Lei Wang

Juan Wang

Yu-Kuo Hsiao

Xian-Hui Zhong

Excited <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Ω</mi></math> hyperon in charmful <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ω</mi><mi>b</mi></msub></math> weak decays

The bottomonium spectrum is systematically studied within an unquenched quark model. Based on a good description of both the masses and widths for the well-established states, we further give predictions for the higher <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi></math>-, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>P</mi></math>-, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi></math>-wave bottomonium states up to a mass region of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo>∼</mo><mn>11.3</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></mrow></math>. For the vector states, the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>S</mi><mtext>−</mtext><mi>D</mi></mrow></math> mixing and dielectron decays are studied. Additionally, to understand the role of the higher vector resonances in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup></math> annihilation reaction, we evaluate the cross section by combining our quark model predictions for the mass, dielectron, and strong decay properties. It is found that (i) The mass shifts of the high-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>b</mi><mover accent="true"><mi>b</mi><mo stretchy="false">¯</mo></mover></math> states due to the coupled-channel effects are on the order of a few tens of MeV; most of the high-lying resonances contain significant non-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>b</mi><mover accent="true"><mi>b</mi><mo stretchy="false">¯</mo></mover></math> components. (ii) The <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">ϒ</mi><mn>1</mn></msub><mo stretchy="false">(</mo><mn>3</mn><mi>D</mi><mo>,</mo><mn>5</mn><mi>D</mi><mo>,</mo><mn>6</mn><mi>D</mi><mo stretchy="false">)</mo></math> states significantly mix with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>4</mn><mi>S</mi><mo>,</mo><mn>6</mn><mi>S</mi><mo>,</mo><mn>7</mn><mi>S</mi><mo stretchy="false">)</mo></math>, respectively, which is mainly induced by the intermediate hadronic loops. (iii) The non-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>b</mi><mover accent="true"><mi>b</mi><mo stretchy="false">¯</mo></mover></math> components will lead a significant suppression for the dielectron decay widths of some vector resonances. (iv) The threshold effects of open-bottom meson pairs can cause rich bump structures in the cross section of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup><mo stretchy="false">→</mo><mi>b</mi><mover accent="true"><mi>b</mi><mo stretchy="false">¯</mo></mover></math>. Our model shows that the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>10753</mn><mo stretchy="false">)</mo></math> may arise from threshold effects due to the strong coupling between <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>4</mn><mi>S</mi><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover><mo>*</mo></msup><msup><mi>B</mi><mo>*</mo></msup></math>.

Ru-Hui Ni

Qian Deng

Jia-Jun Wu

Bottomonia in an unquenched quark model

In a nonrelativistic quark model framework, we carry out a calculation of the mass spectrum for the low-lying <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1</mn><mi>S</mi></math> all-heavy pentaquark states by adopting the explicitly correlated Gaussian method. The obtained states are compact and lie far above the lowest dissociation baryon-meson threshold. Moreover, using the obtained masses and wave functions we evaluate the fall-apart decay properties within a quark-exchange model. The results show that the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1</mn><mi>S</mi></math> all-heavy pentaquark states have a fairly narrow fall-apart width, which scatters in the range of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo>∼</mo><mn>0.1</mn><mi>–</mi><mn>4.0</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></mrow></math>. Their dominant fall-apart decay channels may be ideal for searching for their signals in future experiments.

Zhi-Biao Liang

Feng-Xiao Liu

All-heavy pentaquarks

In this work, we systematically study both the mass spectra and strong decays of the nucleon and <math><mi>Δ</mi></math> resonances up to the <math><mi>N</mi><mo>=</mo><mn>2</mn></math> shell within a unified quark model framework with chiral dynamics. In this framework we achieve a good description of the strong decay properties of the well-established nucleon and <math><mi>Δ</mi></math> resonances. Meanwhile, the mass reversal between <math><mi>N</mi><mo>(</mo><mn>1440</mn><mo>)</mo><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>+</mo></msup></math> as the first radial excitation state and the <math><mn>1</mn><mi>P</mi></math>-wave nucleon resonances can be explained. We show that the three-body spin-orbit potential arising from the one-gluon exchange can cause a large configuration mixing between <math><mi>N</mi><mo>(</mo><mn>1520</mn><mo>)</mo><mn>3</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></math> and <math><mi>N</mi><mo>(</mo><mn>1700</mn><mo>)</mo><mn>3</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></math> and is also responsible for the large splitting between <math><mi>Δ</mi><mo>(</mo><mn>1600</mn><mo>)</mo><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></math> and <math><mi>Δ</mi><mo>(</mo><mn>1700</mn><mo>)</mo><mn>3</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></math>. Some of these baryon resonances tend to weakly couple to the <math><mi>N</mi><mi>π</mi></math>, <math><mi>N</mi><mi>η</mi></math>, <math><mi>K</mi><mi>Λ</mi></math>, and <math><mi>K</mi><mi>Σ</mi></math> channels, which may answer the question of why they have not been established in these channels via the <math><mi>π</mi><mi>N</mi></math> and <math><mi>γ</mi><mi>N</mi></math> scatterings. It shows that these “missing resonances” may have large potentials to be established in the <math><mi>N</mi><mi>π</mi><mi>π</mi></math> final state due to their large decay rates into either the <math><mi>Δ</mi><mo>(</mo><mn>1232</mn><mo>)</mo></math> or <math><mn>1</mn><mi>P</mi></math>-wave nucleon resonances via the pionic decays. Further experimental search for their signals in charmonium decays at BESIII is thus strongly recommended.

Hui-Hua Zhong

Ming-Sheng Liu

Mu-Yang Chen

Qiang Zhao

Unified study of nucleon and <math><mi>Δ</mi></math> baryon spectra and their strong decays with chiral dynamics

In this work, we study the charmonium spectrum within an unquenched quark model including coupled-channel effects. In couple-channel calculations, we include all of the opened charmed meson channels with the once-subtracted method, meanwhile we adopt a suppressed factor to soften the hard vertices given by the <math><mrow><mmultiscripts><mrow><msub><mrow><mi>P</mi></mrow><mrow><mn>0</mn></mrow></msub></mrow><mprescripts></mprescripts><none></none><mrow><mn>3</mn></mrow></mmultiscripts></mrow></math> model in the high momentum region. We obtain a good description of both the masses and widths for the well-established states in the charmonium spectrum. Furthermore, we give predictions for the higher <math><mi>S</mi></math>-, <math><mi>P</mi></math>-, and <math><mi>D</mi></math>-wave charmonium states up to mass region of <math><mo>∼</mo><mn>5.0</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>. The magnitude of mass shifts due to the coupled-channel effects is estimated to be about <math><mrow><mn>10</mn><mi>s</mi></mrow></math> MeV. Although many decay channels are opened for the higher charmonium states, they are relatively narrow states. Their widths scatter in the range of <math><mrow><mo>∼</mo><mn>10</mn><mi>s</mi><mi>–</mi><mn>100</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></mrow></math>. Many charmoniumlike states, such as <math><msub><mi>χ</mi><mrow><mi>c</mi><mn>1</mn></mrow></msub><mo>(</mo><mn>4274</mn><mo>)</mo></math>, <math><msub><mi>χ</mi><mrow><mi>c</mi><mn>0</mn></mrow></msub><mo>(</mo><mn>3915</mn><mo>)</mo></math>, <math><msub><mi>χ</mi><mrow><mi>c</mi><mn>0</mn></mrow></msub><mo>(</mo><mn>4500</mn><mo>)</mo></math>, <math><msub><mi>χ</mi><mrow><mi>c</mi><mn>0</mn></mrow></msub><mo>(</mo><mn>4700</mn><mo>)</mo></math>, <math><mi>X</mi><mo>(</mo><mn>4160</mn><mo>)</mo></math>, <math><mi>X</mi><mo>(</mo><mn>4350</mn><mo>)</mo></math>, <math><mi>Y</mi><mo>(</mo><mn>4500</mn><mo>)</mo></math>, and <math><mi>ψ</mi><mo>(</mo><mn>4660</mn><mo>)</mo><mo>/</mo><mi>Y</mi><mo>(</mo><mn>4710</mn><mo>)</mo></math>, can be accommodated by the charmonium spectrum when the unquenched coupled-channel effects are carefully considered.

Qi Li

Charmonia in an unquenched quark model

In this work, an unquenched quark model is proposed for describing the heavy-light mesons by taking into account the coupled-channel effects induced by chiral dynamics. After including a relativistic correction term for the strong transition amplitudes, both the mass spectra and decay widths of the observed heavy-light mesons can be successfully described simultaneously in a unified framework, several long-standing puzzles related to the small masses and broad widths are overcome naturally. We also provide valuable guidance in searching new heavy-light mesons by the detailed predictions of their masses, widths, and branching ratios. The success of the unquenched quark model presented in this work indicates it may be an important step for understanding the hadron spectrum.

Unified unquenched quark model for heavy-light mesons with chiral dynamics

Stimulated by the exciting progress on the observations of the fully charmed tetraquarks at LHC, we carry out a combined analysis of the mass spectra and fall-apart decays of the <math><mrow><mn>1</mn><mi>S</mi></mrow></math>-, <math><mn>2</mn><mi>S</mi></math>-, and <math><mn>1</mn><mi>P</mi></math>-wave <math><mi>c</mi><mi>c</mi><mover><mi>c</mi><mo>¯</mo></mover><mover><mi>c</mi><mo>¯</mo></mover></math> states in a nonrelativistic quark model. It is found that the <math><mi>X</mi><mo>(</mo><mn>6600</mn><mo>)</mo></math> structure observed in the di-<math><mi>J</mi><mo>/</mo><mi>ψ</mi></math> invariant mass spectrum can be explained by the <math><mn>1</mn><mi>S</mi></math>-wave state <math><msub><mi>T</mi><mrow><mo>(</mo><mn>4</mn><mi>c</mi><mo>)</mo><msup><mn>0</mn><mrow><mo>+</mo><mo>+</mo></mrow></msup></mrow></msub><mo>(</mo><mn>6550</mn><mo>)</mo></math>. This structure may also bear some feed-down effects from the higher <math><mn>2</mn><mi>S</mi></math> and/or <math><mn>1</mn><mi>P</mi></math> tetraquark states. The <math><mi>X</mi><mo>(</mo><mn>6900</mn><mo>)</mo></math> structure observed in both the di-<math><mi>J</mi><mo>/</mo><mi>ψ</mi></math> and <math><mi>J</mi><mo>/</mo><mi>ψ</mi><mi>ψ</mi><mo>(</mo><mn>2</mn><mi>S</mi><mo>)</mo></math> channels can be naturally explained by the <math><mn>2</mn><mi>S</mi></math>-wave state <math><msub><mi>T</mi><mrow><mo>(</mo><mn>4</mn><mi>c</mi><mo>)</mo><msup><mn>0</mn><mrow><mo>+</mo><mo>+</mo></mrow></msup></mrow></msub><mo>(</mo><mn>6957</mn><mo>)</mo></math>. The small shoulder structure around 6.2–6.4 GeV observed at CMS and ATLAS may be due to the feed-down effects from some <math><mn>1</mn><mi>P</mi></math>-wave states with <math><mi>C</mi><mo>=</mo><mo>−</mo><mn>1</mn></math> and/or some <math><mn>2</mn><mi>S</mi></math>-wave states with <math><msup><mi>J</mi><mrow><mi>P</mi><mi>C</mi></mrow></msup><mo>=</mo><msup><mn>0</mn><mrow><mo>+</mo><mo>+</mo></mrow></msup></math>. Other decay channels are implied in such a scenario and they can be investigated by future experimental analyses. Considering the large discovery potential at LHC, we also present predictions for the <math><mi>b</mi><mi>b</mi><mover><mi>b</mi><mo>¯</mo></mover><mover><mi>b</mi><mo>¯</mo></mover></math> states which can be searched for in the future.

Fully heavy tetraquark states and their evidences in LHC observations

For further decoding the inner structure of the two excited <math><msub><mi>Ξ</mi><mi>b</mi></msub></math> states observed by LHCb, we perform a systematical study of the strong decays of the low-lying <math><mn>1</mn><mi>D</mi></math>-wave <math><msub><mi>Ξ</mi><mi>b</mi></msub></math> and <math><msubsup><mi>Ξ</mi><mi>b</mi><mo>′</mo></msubsup></math> excitations using the quark pair creation model within the <math><mi>j</mi><mo>−</mo><mi>j</mi></math> coupling scheme. Combined with the measured masses and decay properties of <math><msub><mi>Ξ</mi><mi>b</mi></msub><mo>(</mo><mn>6327</mn><msup><mo>)</mo><mn>0</mn></msup></math> and <math><msub><mi>Ξ</mi><mi>b</mi></msub><mo>(</mo><mn>6327</mn><msup><mo>)</mo><mn>0</mn></msup></math>, the two excited states can be explained as <math><mn>1</mn><mi>D</mi></math> <math><mi>λ</mi></math>-mode <math><msub><mi>Ξ</mi><mi>b</mi></msub></math> states <math><msub><mi>Ξ</mi><mi>b</mi></msub><mo>|</mo><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><msup><mfrac><mn>3</mn><mn>2</mn></mfrac><mo>+</mo></msup><mo>,</mo><mn>2</mn><msub><mo>⟩</mo><mrow><mi>λ</mi><mi>λ</mi></mrow></msub></math> and <math><msub><mi>Ξ</mi><mi>b</mi></msub><mo>|</mo><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><msup><mfrac><mn>5</mn><mn>2</mn></mfrac><mo>+</mo></msup><mo>,</mo><mn>2</mn><msub><mo>⟩</mo><mrow><mi>λ</mi><mi>λ</mi></mrow></msub></math>, respectively. If such a view is correct, <math><msubsup><mi>Ξ</mi><mi>b</mi><mo>′</mo></msubsup><mi>π</mi></math> and <math><msubsup><mi>Ξ</mi><mi>b</mi><mrow><mo>′</mo><mo>*</mo></mrow></msubsup><mi>π</mi></math> could be other interesting channels for experimental exploration of the <math><msub><mi>Ξ</mi><mi>b</mi></msub><mo>(</mo><mn>6327</mn><msup><mo>)</mo><mn>0</mn></msup></math> and <math><msub><mi>Ξ</mi><mi>b</mi></msub><mo>(</mo><mn>6327</mn><msup><mo>)</mo><mn>0</mn></msup></math>, respectively. The calculations are good and consistent with the results within the chiral quark model. In addition, for the other missing <math><mn>1</mn><mi>D</mi></math>-wave <math><msub><mi>Ξ</mi><mi>b</mi></msub></math> and <math><msubsup><mi>Ξ</mi><mi>b</mi><mo>′</mo></msubsup></math> excitations, our predictions indicate that: (i) the two <math><mi>ρ</mi></math>-mode <math><mn>1</mn><mi>D</mi><mtext> </mtext><mtext> </mtext><msub><mi>Ξ</mi><mi>b</mi></msub></math> states are likely to be moderate states with a width of <math><mi>Γ</mi><mo>∼</mo><mn>50</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>. The <math><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><mn>3</mn><mo>/</mo><msup><mn>2</mn><mo>+</mo></msup></math> state dominantly decays into <math><msub><mi>Σ</mi><mi>b</mi></msub><mi>K</mi></math> and <math><msubsup><mi>Ξ</mi><mi>b</mi><mo>′</mo></msubsup><mi>π</mi></math>, while the <math><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><mn>5</mn><mo>/</mo><msup><mn>2</mn><mo>+</mo></msup></math> state decays primarily through <math><msubsup><mi>Σ</mi><mi>b</mi><mo>*</mo></msubsup><mi>K</mi></math> and <math><msubsup><mi>Ξ</mi><mi>b</mi><mrow><mo>′</mo><mo>*</mo></mrow></msubsup><mi>π</mi></math>; (ii) The <math><mi>λ</mi></math>-mode <math><mn>1</mn><mi>D</mi></math> <math><msubsup><mi>Ξ</mi><mi>b</mi><mo>′</mo></msubsup></math> states may be moderate states with widths of about several MeV to dozens of MeV. Most of the <math><mi>λ</mi></math>-mode <math><mn>1</mn><mi>D</mi></math> <math><msubsup><mi>Ξ</mi><mi>b</mi><mo>′</mo></msubsup></math> states mainly decay into the <math><mn>1</mn><mi>P</mi></math>-wave bottomed baryon via the pionic decay processes. Meanwhile, several <math><mi>λ</mi></math>-mode <math><mn>1</mn><mi>D</mi></math> <math><msubsup><mi>Ξ</mi><mi>b</mi><mo>′</mo></msubsup></math> states have significant decay rates into <math><mi>Λ</mi><mi>B</mi></math>; (iii) While, the <math><mi>ρ</mi></math>-mode <math><mn>1</mn><mi>D</mi></math> <math><msubsup><mi>Ξ</mi><mi>b</mi><mo>′</mo></msubsup></math> states are predicted to be very broad states with a width of about several hundreds of MeV, it is a great challenge to explore the <math><mi>ρ</mi></math>-mode <math><mn>1</mn><mi>D</mi></math> <math><msubsup><mi>Ξ</mi><mi>b</mi><mo>′</mo></msubsup></math> states in experiments because of their broad widths.

Yu-Hui Zhou

Wen-Jia Wang

Li-Ye Xiao

Strong decays of low-lying <math><mi>D</mi></math>-wave <math><msub><mi>Ξ</mi><mi>b</mi></msub></math> and <math><msubsup><mi>Ξ</mi><mi>b</mi><mo>′</mo></msubsup></math> baryons with quark-pair creation model

In this work, we systematically study the Okubo-Zweig-Iizuka-allowed two-body strong decay properties of <math><mn>1</mn><mi>P</mi></math>- and <math><mn>1</mn><mi>D</mi></math>-wave <math><msub><mi>Σ</mi><mi>c</mi></msub></math> baryons within the <math><mrow><mi>j</mi><mtext>−</mtext><mi>j</mi></mrow></math> coupling scheme in the framework of the quark pair creation model. For a comparison, we also give the predictions of the chiral quark model. Some model dependencies can be found in the predictions of two models. The calculations indicate that: (i) The <math><mn>1</mn><mi>P</mi></math>-wave <math><mi>λ</mi></math>-mode <math><msub><mi>Σ</mi><mi>c</mi></msub></math> states most likely to be relatively narrow states with a width of <math><mi>Γ</mi><mo>&lt;</mo><mn>80</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>. Their main decay channels are <math><msub><mi>Λ</mi><mi>c</mi></msub><mi>π</mi></math>, or <math><msub><mi>Σ</mi><mi>c</mi></msub><mi>π</mi></math>, or <math><msubsup><mi>Σ</mi><mi>c</mi><mo>*</mo></msubsup><mi>π</mi></math>. The <math><mn>1</mn><mi>P</mi></math>-wave <math><mi>ρ</mi></math>-mode states most might be broad states with a width of <math><mrow><mi>Γ</mi><mo>∼</mo><mn>100</mn><mi>–</mi><mn>200</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></mrow></math>. They dominantly decay into <math><msub><mi>Σ</mi><mi>c</mi></msub><mi>π</mi></math> and <math><msubsup><mi>Σ</mi><mi>c</mi><mo>*</mo></msubsup><mi>π</mi></math> channels. Some evidences of these <math><mn>1</mn><mi>P</mi></math>-wave states are most likely to be observed in the <math><msub><mi>Λ</mi><mi>c</mi></msub><mi>π</mi></math> and <math><msub><mi>Λ</mi><mi>c</mi></msub><mi>π</mi><mi>π</mi></math> invariant mass spectra around the energy range of 2.75–2.95 GeV. (ii) The <math><mn>1</mn><mi>D</mi></math>-wave <math><mi>λ</mi></math>-mode <math><msub><mi>Σ</mi><mi>c</mi></msub></math> excitations may be moderate states with a width of about dozens of MeV. The <math><mn>1</mn><mi>D</mi></math>-wave <math><mi>λ</mi></math>-mode states mainly decay into the <math><mn>1</mn><mi>P</mi></math>-wave charmed baryon via the pionic decay processes. Meanwhile, several <math><mn>1</mn><mi>D</mi></math>-wave <math><mi>λ</mi></math>-mode states have significant decay rates into <math><mi>D</mi><mi>N</mi></math> or <math><msup><mi>D</mi><mo>*</mo></msup><mi>N</mi></math>. Hence, the <math><mi>D</mi><mi>N</mi></math> and <math><msup><mi>D</mi><mo>*</mo></msup><mi>N</mi></math> are likely to be interesting channels for experimental exploration. (iii) Furthermore, the two <math><mn>1</mn><mi>D</mi></math>-wave <math><mi>ρ</mi></math>-mode excitations <math><mrow><msub><mrow><mi>Σ</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>|</mo><msup><mrow><mi>J</mi></mrow><mrow><mi>P</mi></mrow></msup><mo>=</mo><mn>5</mn><mo>/</mo><msup><mrow><mn>2</mn></mrow><mrow><mo>+</mo></mrow></msup><mo>,</mo><mn>3</mn><msub><mrow><mo>⟩</mo></mrow><mrow><mi>ρ</mi><mi>ρ</mi></mrow></msub></mrow></math> and <math><mo>|</mo><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><mn>7</mn><mo>/</mo><msup><mn>2</mn><mo>+</mo></msup><mo>,</mo><mn>3</mn><msub><mo>⟩</mo><mrow><mi>ρ</mi><mi>ρ</mi></mrow></msub></math> are most likely to be fairly narrow state with a width of dozens of MeV, and they mainly decay into <math><msub><mi>Λ</mi><mi>c</mi></msub><mi>π</mi></math>. Some evidences of them might be observed in the <math><msub><mi>Λ</mi><mi>c</mi></msub><mi>π</mi></math> invariant mass spectra around the energy range of 3.1–3.2 GeV.

Strong decays of the low-lying <math><mn>1</mn><mi>P</mi></math>- and <math><mn>1</mn><mi>D</mi></math>-wave <math><msub><mi>Σ</mi><mi>c</mi></msub></math> baryons

In our previous studies, we analyzed the two-body strong decays of the low-lying Ω baryon states within a chiral quark model. The results showed that the mass, total width, and two body decay   $ \Omega(2012) \to \bar{K}\Xi $   could be well reproduced with the spin-parity   $ \Omega(2012) \to \bar{K}\Xi $   state   $ \Omega(2012) \to \bar{K}\Xi $   classified in the quark model. Stimulated by the new observations of the three-body decay process   $ \Omega(2012) \to \bar{K}\Xi $   at Belle, in the present study, we further investigate the three-body strong decay   $ \Omega(2012) \to \bar{K}\Xi $   within the chiral quark model. It is found that the   $ \Omega(2012) \to \bar{K}\Xi $   has a sizeable decay rate into the three-body final states   $ \Omega(2012) \to \bar{K}\Xi $  . When considering   $ \Omega(2012) \to \bar{K}\Xi $   as the   $ \Omega(2012) \to \bar{K}\Xi $   resonance, the predicted ratio   $ \Omega(2012) \to \bar{K}\Xi $     $ \Omega(2012) \to \bar{K}\Xi $   is close to the upper limit   $ \Omega(2012) \to \bar{K}\Xi $   measured by the Belle Collaboration in 2019; however, it is too small to be comparable to the recent measurement   $ \Omega(2012) \to \bar{K}\Xi $  . In addition, the coupled-channel effects on the bare three-quark state   $ \Omega(2012) \to \bar{K}\Xi $   from nearby channels   $ \Omega(2012) \to \bar{K}\Xi $  ,   $ \Omega(2012) \to \bar{K}\Xi $  , and   $ \Omega(2012) \to \bar{K}\Xi $   are studied. Our theoretical results show that the coupled-channel effects on   $ \Omega(2012) \to \bar{K}\Xi $   are not very large, and the molecular component is no more than   $ \Omega(2012) \to \bar{K}\Xi $  . To clarify the nature of   $ \Omega(2012) \to \bar{K}\Xi $   resonance, precise measurements on the ratio   $ \Omega(2012) \to \bar{K}\Xi $   are needed, and further investigation on the effects of coupled channels is recommended.