In this work, we adopt the one-boson exchange model to analyze the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mrow><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo></mrow><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msubsup><msubsup><mi>B</mi><mrow><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo></mrow><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msubsup></math> interactions from a coupled-channel perspective. For the <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>1</mn><mo stretchy="false">(</mo><msup><mn>1</mn><mo>+</mo></msup><mo stretchy="false">)</mo></math> <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><msup><mi>B</mi><mo>*</mo></msup><mo>/</mo><msup><mi>D</mi><mo>*</mo></msup><mi>B</mi><mo>/</mo><msup><mi>D</mi><mo>*</mo></msup><msup><mi>B</mi><mo>*</mo></msup></math> system, employing the complex scaling method, we obtain a loosely bound state and two resonant states located below the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><msup><mi>B</mi><mo>*</mo></msup></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mo>*</mo></msup><mi>B</mi></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mo>*</mo></msup><msup><mi>B</mi><mo>*</mo></msup></math> thresholds, respectively. Assuming that the charmoniumlike states <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>Z</mi><mi>c</mi></msub><mo stretchy="false">(</mo><mn>3900</mn><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>Z</mi><mi>c</mi></msub><mo stretchy="false">(</mo><mn>4020</mn><mo stretchy="false">)</mo></math>, as well as the bottomoniumlike states <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>Z</mi><mi>b</mi></msub><mo stretchy="false">(</mo><mn>10610</mn><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>Z</mi><mi>b</mi></msub><mo stretchy="false">(</mo><mn>10650</mn><mo stretchy="false">)</mo></math>, are molecular states near their respective thresholds, we suggest that the predicted states in the <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>1</mn><mo stretchy="false">(</mo><msup><mn>1</mn><mo>+</mo></msup><mo stretchy="false">)</mo><msup><mi>D</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup><msup><mi>B</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msup></math> system could be their bottom-charmed analogs. In addition, we extend our analysis to other <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mrow><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo></mrow><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msubsup><msubsup><mi>B</mi><mrow><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo></mrow><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msubsup></math> combinations with various quantum numbers. Our results indicate that, besides the <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>1</mn><mo stretchy="false">(</mo><msup><mn>1</mn><mo>+</mo></msup><mo stretchy="false">)</mo></math> channel, more molecular states with 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>0</mn><mo>+</mo></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><mo>,</mo><mn>0</mn><mo stretchy="false">(</mo><msup><mn>2</mn><mo>+</mo></msup><mo stretchy="false">)</mo></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1</mn><mo stretchy="false">(</mo><msup><mn>0</mn><mo>+</mo></msup><mo stretchy="false">)</mo></math> may also exist in the bottom-charmed sector. Compared with our earlier study of hidden-bottom systems [<a href="http://dx.doi.org/10.1103/PhysRevD.110.074038">Phys. Rev. D 110, 074038 (2024)</a>], where two bound states were obtained in the <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>1</mn><mo stretchy="false">(</mo><msup><mn>1</mn><mrow><mo>+</mo><mo>−</mo></mrow></msup><mo stretchy="false">)</mo></math> channel, the present work instead finds resonant states in the <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>1</mn><mo stretchy="false">(</mo><msup><mn>1</mn><mo>+</mo></msup><mo stretchy="false">)</mo></math> sector. Moreover, while no molecular state with strangeness was identified in the previous hidden bottom systems, we now obtain molecular states near the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mi>s</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msubsup><msubsup><mi>B</mi><mi>s</mi><mo>*</mo></msubsup></math> threshold. Finally, we provide possible decay channels for future experimental searches, recommending the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>B</mi><mi>c</mi></msub><mo>/</mo><msubsup><mi>B</mi><mi>c</mi><mo>*</mo></msubsup></math> plus light mesons for bound states, and the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mrow><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo></mrow><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msubsup><msubsup><mi>B</mi><mrow><mo stretchy="false">(</mo><mi>s</mi><mo stretchy="false">)</mo></mrow><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msubsup></math> channels for resonances.

China

Qing-Fu Song

Wei Liang

Qi-Fang Lü

Xiaonu Xiong

Exploring bottom-charmed molecular tetraquarks with the complex scaling method

In this work, we investigate the resonance structures in the $ \Sigma(1/2^-) $ system from both three-quark and five-quark perspectives within the framework of the chiral quark model. An accurate few-body computational approach, the Gaussian expansion method, is employed to construct the orbital wave functions of multiquark states. To reduce the model dependence on parameters, we fit two sets of parameters to check the stability of the results. The calculations show that our results remain stable despite changes in the parameters. In the three-quark calculations, two $ \Sigma(1/2^-) $ states are obtained with energies around 1.8 GeV, which are good candidates for the experimentally observed $ \Sigma(1750) $ and $ \Sigma(1900) $ . In the five-quark configuration, several stable resonance states are identified, including $ \Sigma \pi $ , $ N \bar{K} $ , and $ N \bar{K}^{*} $ . These resonance states survive the channel-coupling calculations under the complex-scaling framework and manifest as stable structures. Our results support the existence of a two-pole structure for the $ \Sigma(1/2^-) $ system, predominantly composed of $ \Sigma \pi $ and $ N \bar{K} $ configurations, analogous to the well-known $ \Lambda(1380) $ - $ \Lambda(1405) $ ( $ \Sigma \pi $ - $ N \bar{K} $ ) system. On the other hand, although the energy of the $ N \bar{K}^{*} $ configuration is close to that of $ \Sigma(1750) $ and $ \Sigma(1900) $ , the obtained width is not consistent with the experimental values. This suggests that the $ N \bar{K}^{*} $ state needs to mix with three-quark components to better explain the experimental $ \Sigma(1750) $ and $ \Sigma(1900) $ states. According to our decay width calculations, the predicted two resonance states are primarily composed of $ \Sigma \pi $ and $ N \bar{K} $ , with their main decay channel being $ \Lambda \pi $ . Therefore, we encourage experimental groups to search for the predicted two-pole structure of the $ \Sigma(1/2^-) $ system in the invariant mass spectrum of $ \Lambda \pi $ .

Yu Yao

Xuejie Liu

Xiaoyun Chen

Yuheng Wu

Jialun Ping

Yue Tan

Qi Huang

Investigation of resonances in the Σ(1/2$^{–}$) system based on the chiral quark model * Supported partly by the National Science Foundation of China (12205249, 12305087). Yue Tan is supported by the Funding for School-Level Research Projects of Yancheng Institute of Technology (xjr2022039) and the Qinglan Project Fund of Jiangsu Province. Qi Huang is supported by the Start-up Funds of Nanjing Normal University (184080H201B20)

We introduce FANG (Focused Angular $\textit{N}$ -body event Generator), a new Monte Carlo tool for efficient event generation in restricted Lorentz-Invariant Phase Space (LIPS). Unlike conventional approaches that sample the full 4$\textit{π}$ solid angle, FANG directly generates events in which selected final-state particles are constrained to fixed directions or finite angular regions in the laboratory frame. Because of the way the generator is constructed, angular constraints can be imposed directly in the laboratory frame while maintaining the correct LIPS structure, enabling differential and total cross sections or decay rates to be computed with high efficiency. The method is validated against analytic results and existing event generators, showing excellent agreement. By reducing the computational cost of full phase-space event generation by several orders of magnitude, FANG provides a robust and versatile framework applicable to particle, nuclear, and detector physics.

Israel

Itay Horin

Arik Kreisel

Or Alon

Focused angular $\textit{N}$ -body event generator (FANG)

In this work, we investigate the doubly bottom $$H_{(s)}\bar{T}_{(s)}$$ and $$H_{(s)}T_{(s)}$$ systems by adopting the one-boson-exchange model, where $$H_{(s)}$$ and $$T_{(s)}$$ represent $\textit{S}$-wave $$B^{(*)}_{(s)}$$ and $\textit{P}$-wave $$B^{(*)}_{(s)1,2}$$ doublets, respectively. For the $$H\bar{T}$$ systems, we predict some loosely bound states in the $$I(J^{PC})=0(1^{-\pm })$$ $$B\bar{B}_{1},$$ $$I(J^{PC})=0(2^{-\pm })$$ $$B\bar{B}_{2}^{*},$$ $$I(J^{PC})=0(1^{-\pm })$$ $$B^*\bar{B}_{1}$$ and $$I(J^{PC})=0(2^{-\pm })$$ $$B^*\bar{B}_{2}^{*}$$ channels, which are the most promising hidden bottom molecular tetraquarks. For the $\textit{HT}$ systems, the $$B^*B_1$$ channels with quantum numbers $$I(J^P) = 0(1^{-}), 0(2^{-})$$ and the $$B^*B_2^*$$ channels with $$I(J^P) = 0(2^{-})$$ are also likely candidates for forming molecular tetraquarks. In contrast, no molecular candidates have been identified in the bottom-strange sectors. One can hope that our predictions will provide valuable insights to the LHCb and Belle II Collaborations as they continue to explore this fascinating field through experimental research.

Jun-Chao Su

Jingya Zhu

An analysis on doubly bottom molecular tetraquarks composed of $$H_{(s)}$$ and $$T_{(s)}$$ doublets

In this study, we investigate a two-component scalar dark matter framework featuring two singlet scalar fields as dark matter candidates. To ensure vacuum stability, we employ copositive criteria for the scalar potential. We analyze four distinct copositive scenarios characterized by specific negative parameter configurations using direct detection constraints. A comprehensive parameter space scan is performed under joint constraints from the observed dark matter relic density and direct detection experiments. The different signs of couplings not only correspond to different copositive criteria but also contribute to different parameter spaces caused by interference. The allowed values of quartic couplings are different for the four different cases; however, they all require the new Higgs to play a dominant role in determining dark matter relic density within the viable parameter space.

Xin-Xin Qi

Hao Sun

Copositive criteria for a two-component dark matter model * Hao Sun is supported by the National Natural Science Foundation of China (12075043 and 12147205). XinXin Qi is supported by the National Natural Science Foundation of China (12447162)

In the present work, we systematically study various bottom-strange molecular pentaquarks to search for possible bound states and resonances by adopting a one boson exchange model within the complex scaling method. According to our calculations, we predict several bound and resonant states for bottom baryon $$Y_{b}(\Lambda _b,\Sigma _b) \bar{K}^{(*)}$$ and $$Y_{b} K^{(*)}$$ systems. In particular, a bound state in the $$I(J^P)=1/2(1/2^-)\Sigma _b \bar{K}/\Lambda _b \bar{K}^*/\Sigma _b \bar{K}^*$$ system may correspond to the particle $$\Xi _b(6227)$$ . Meanwhile, the predicted bound state with mass in the range of $$6303\sim 6269~\textrm{MeV}$$ in the $$I(J^P)=1/2(1/2^-)\Sigma _bK/\Lambda _bK^*/\Sigma _bK^*$$ system is flavor exotic and does not appear in the spectroscopy of conventional baryons, which may help clarify the nature of $$\Xi _b(6227)$$ . We hope that our study can provide useful guidance for future experimental searches.

A coupled-channel perspective analysis on bottom-strange molecular pentaquarks

We perform a systematic analysis of the low-lying <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ω</mi><mi>c</mi></msub></math> structures in a coupled-channel approach. The couplings between meson-baryon channels, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ξ</mi><mi>c</mi></msub><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mi>c</mi><mo>′</mo></msubsup><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ξ</mi><mi>c</mi><mo>*</mo></msubsup><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ω</mi><mi>c</mi></msub><mi>η</mi></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ω</mi><mi>c</mi><mo>*</mo></msubsup><mi>η</mi></math>, and three-quark bare states <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ω</mi><mi>c</mi></msub><mo stretchy="false">(</mo><mn>1</mn><msub><mi>P</mi><mi>λ</mi></msub><mo stretchy="false">)</mo></math> are considered. We predict a bound state <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ω</mi><mi>c</mi></msub><mo stretchy="false">(</mo><mn>2954</mn><mo stretchy="false">)</mo></math> below the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ξ</mi><mi>c</mi></msub><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover></math> threshold with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><msup><mi>J</mi><mi>P</mi></msup><mo>,</mo><mi>j</mi><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup><mo>,</mo><mn>0</mn><mo stretchy="false">)</mo></math>, which can be studied in the final states of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ω</mi><mi>c</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msubsup><mi>π</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">Ω</mi><mi>c</mi><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo></mrow></msubsup><mi>γ</mi></math>. Also, the resonances <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ω</mi><mi>c</mi></msub><mo stretchy="false">(</mo><mn>3000</mn><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ω</mi><mi>c</mi></msub><mo stretchy="false">(</mo><mn>3050</mn><mo stretchy="false">)</mo></math> can be classified as the lower <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><msup><mi>J</mi><mi>P</mi></msup><mo>,</mo><mi>j</mi><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup><mo>,</mo><mn>1</mn><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><msup><mi>J</mi><mi>P</mi></msup><mo>,</mo><mi>j</mi><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><mn>3</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup><mo>,</mo><mn>1</mn><mo stretchy="false">)</mo></math> states, respectively. Our present assignments based on this coupled-channel perspective are significantly different from those of the traditional three-quark picture and of the molecular scenario. The future BelleII and LHCb experiments can search for the bound state <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ω</mi><mi>c</mi></msub><mo stretchy="false">(</mo><mn>2954</mn><mo stretchy="false">)</mo></math> and measure the spin-parities of particles <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ω</mi><mi>c</mi></msub><mo stretchy="false">(</mo><mn>3000</mn><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ω</mi><mi>c</mi></msub><mo stretchy="false">(</mo><mn>3050</mn><mo stretchy="false">)</mo></math> to test our predictions.

Ying Zhang

Japan

Hideko Nagahiro

Atsushi Hosaka

Understanding the low-lying <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ω</mi><mi>c</mi></msub></math> structures from a coupled-channel perspective

Inspired by the newly observed <math><mi>X</mi><mo>(</mo><mn>2085</mn><mo>)</mo></math> by the BESIII Collaboration, we study the strong decay behaviors of excited axial-vector strange mesons within the quark pair creation model. Our results indicate that the <math><msub><mi>K</mi><mn>1</mn></msub><mo>(</mo><mn>1793</mn><mo>)</mo><mo>/</mo><msub><mi>K</mi><mn>1</mn></msub><mo>(</mo><mn>1861</mn><mo>)</mo></math> can be regarded as the same <math><msub><mi>K</mi><mn>1</mn></msub><mo>(</mo><mn>2</mn><mi>P</mi><mo>)</mo></math> state, and the <math><msub><mi>K</mi><mn>1</mn></msub><mo>(</mo><mn>1911</mn><mo>)</mo></math> is assigned as the <math><msub><mi>K</mi><mn>1</mn></msub><mo>(</mo><mn>2</mn><msup><mi>P</mi><mo>′</mo></msup><mo>)</mo></math> state. Considering the mass, spin-parity, and decay behaviors, we interpret the newly observed <math><mi>X</mi><mo>(</mo><mn>2085</mn><mo>)</mo></math> as the radially excited <math><msub><mi>K</mi><mn>1</mn></msub><mo>(</mo><mn>3</mn><mi>P</mi><mo>)</mo></math> state, which mainly decays into the <math><msup><mi>K</mi><mo>*</mo></msup><mo>(</mo><mn>1410</mn><mo>)</mo><mi>π</mi></math>, <math><mi>ρ</mi><msup><mi>K</mi><mo>*</mo></msup></math>, <math><mi>ω</mi><mo>(</mo><mn>1420</mn><mo>)</mo><mi>K</mi></math>, <math><mi>ρ</mi><mo>(</mo><mn>1450</mn><mo>)</mo><mi>K</mi></math>, and <math><mi>ρ</mi><mi>K</mi></math> final states. Also, the width of the <math><msub><mi>K</mi><mn>1</mn></msub><mo>(</mo><mn>3</mn><msup><mi>P</mi><mo>′</mo></msup><mo>)</mo></math> state is predicted to be about 300 MeV, which can be searched for by future experiments. We expect that present calculations can help us to better understand the nature of the <math><mi>X</mi><mo>(</mo><mn>2085</mn><mo>)</mo></math> structure and near-threshold enhancements in the baryon-antibaryon invariant mass distributions.

Tian-Ge Li

Sheng-Chao Zhang

Guan-Ying Wang

Canonical interpretation of the newly observed <math><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><msup><mn>1</mn><mo>+</mo></msup></math> structure <math><mi>X</mi><mo>(</mo><mn>2085</mn><mo>)</mo></math>

In the present work, we perform a coupled-channel analysis of <math><msubsup><mi>B</mi><mrow><mo>(</mo><mi>s</mi><mo>)</mo></mrow><mrow><mo>(</mo><mo>*</mo><mo>)</mo></mrow></msubsup><msubsup><mover><mi>B</mi><mo>¯</mo></mover><mrow><mo>(</mo><mi>s</mi><mo>)</mo></mrow><mrow><mo>(</mo><mo>*</mo><mo>)</mo></mrow></msubsup></math> systems with the one-boson-exchange potentials. We first study the <math><mi>I</mi><mo>(</mo><msup><mi>J</mi><mrow><mi>P</mi><mi>C</mi></mrow></msup><mo>)</mo><mo>=</mo><mn>1</mn><mo>(</mo><msup><mn>1</mn><mrow><mo>+</mo><mo>−</mo></mrow></msup><mo>)</mo></math> <math><mi>B</mi><msup><mover><mi>B</mi><mo>¯</mo></mover><mo>*</mo></msup><mo>/</mo><msup><mi>B</mi><mo>*</mo></msup><msup><mover><mi>B</mi><mo>¯</mo></mover><mo>*</mo></msup></math> system to describe the <math><msub><mi>Z</mi><mi>b</mi></msub><mo>(</mo><mn>10610</mn><mo>)</mo></math> and <math><msub><mi>Z</mi><mi>b</mi></msub><mo>(</mo><mn>10650</mn><mo>)</mo></math> particles as molecular states and determine the reasonable range of cutoff parameter <math><mi>Λ</mi></math>. Then, other <math><msubsup><mi>B</mi><mrow><mo>(</mo><mi>s</mi><mo>)</mo></mrow><mrow><mo>(</mo><mo>*</mo><mo>)</mo></mrow></msubsup><msubsup><mover><mi>B</mi><mo>¯</mo></mover><mrow><mo>(</mo><mi>s</mi><mo>)</mo></mrow><mrow><mo>(</mo><mo>*</mo><mo>)</mo></mrow></msubsup></math> combinations with different quantum numbers are systematically investigated. Some bound states and resonances appear in the isoscalar systems, while only several shallow bound states exist for isovector systems. Far away from the excited conventional <math><mi>P</mi></math>-wave bottomium, these predicted states can be easily identified as exotic particles both theoretically and experimentally. Moreover, the <math><msub><mi>η</mi><mi>b</mi></msub><mo>(</mo><mi>n</mi><mi>S</mi><mo>)</mo><mo>/</mo><mi>ϒ</mi><mo>(</mo><mi>n</mi><mi>S</mi><mo>)</mo></math> plus light mesons are the excellent final states to search for the bound states, while the <math><mi>B</mi><msup><mover><mi>B</mi><mo>¯</mo></mover><mo>*</mo></msup><mo>+</mo><mi>H</mi><mo>.</mo><mi>c</mi><mo>.</mo></math> and <math><msup><mi>B</mi><mo>*</mo></msup><msup><mover><mi>B</mi><mo>¯</mo></mover><mo>*</mo></msup></math> channels are suitable for the resonances. We highly recommend that the LHCb and Belle II Collaborations hunt for these bottomoniumlike states in the future.

Dian-Yong Chen

Yu-Bing Dong

Predicting hidden bottom molecular tetraquarks with a complex scaling method

In this work, we study the low-lying mass spectra for bottom-charmed baryons in a nonrelativistic quark model by solving the three-body Schrödinger equation. The lowest $$\Xi _{bc}$$ <math> <msub> <mi>Ξ</mi> <mrow> <mi>bc</mi> </mrow> </msub> </math> , $$\Xi _{bc}^\prime $$ <math> <msubsup> <mi>Ξ</mi> <mrow> <mi>bc</mi> </mrow> <mo>′</mo> </msubsup> </math> , $$\Omega _{bc}$$ <math> <msub> <mi>Ω</mi> <mrow> <mi>bc</mi> </mrow> </msub> </math> , and $$\Omega _{bc}^\prime $$ <math> <msubsup> <mi>Ω</mi> <mrow> <mi>bc</mi> </mrow> <mo>′</mo> </msubsup> </math> states are predicted to be about 6979, 6953, 7109, and 7092 MeV, respectively. Also, the strong decays for the low-lying excited states are investigated. Our results indicate that some of $$\lambda $$ <math> <mi>λ</mi> </math> -mode P-wave bottom-charmed baryons are relatively narrow, which can be searched for in future experiments. For the low-lying $$\rho $$ <math> <mi>ρ</mi> </math> -mode and $$\rho -\lambda $$ <math> <mrow> <mi>ρ</mi> <mo>-</mo> <mi>λ</mi> </mrow> </math> hybrid states, their strong decays are highly suppressed and they can survive as extremely narrow states. Moreover, the mass spectra and strong decays for bottom-charmed baryons preserve the heavy quark symmetry well. We hope our calculations can provide helpful information for further experimental and theoretical researches.