A series of vector charmonium(like) states, accompanied by a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>K</mi></math> meson, have been observed in the decays of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>B</mi></mrow></math> meson. These processes are color-suppressed at the quark level, as inferred from topological diagram analysis. In this work, we calculate the branching fractions of the decays <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><mi>ψ</mi><mi>K</mi></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ψ</mi></math> denotes the charmonium(like) states <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ψ</mi><mo stretchy="false">(</mo><mn>1</mn><mi>S</mi><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ψ</mi><mo stretchy="false">(</mo><mn>2</mn><mi>S</mi><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ψ</mi><mo stretchy="false">(</mo><mn>4040</mn><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ψ</mi><mo stretchy="false">(</mo><mn>3770</mn><mo stretchy="false">)</mo></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ψ</mi><mo stretchy="false">(</mo><mn>4160</mn><mo stretchy="false">)</mo></math>. Our analysis incorporates both short-distance (naive factorization approach) and long-distance (final-state interactions) contributions. Within reasonable parameters, our results align with experimental data except for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ψ</mi><mo stretchy="false">(</mo><mn>4160</mn><mo stretchy="false">)</mo></math>, suggesting its possible exotic nature. Furthermore, we find that long-distance contributions dominate these decay processes, highlighting the crucial role of final-state interactions in the productions of charmonium(like) states in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi></math> decays.

China

Qi-Wei Yuan

Qi Wu

Ming-Zhu Liu

<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi></math>-meson decays to vector charmoniumlike states and a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>K</mi></math> meson: The role of final-state interactions

We investigate the radiative decays of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>X</mi><mo stretchy="false">(</mo><mn>3872</mn><mo stretchy="false">)</mo></math> to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>γ</mi><mi>V</mi><mtext> </mtext><mo stretchy="false">(</mo><mi>V</mi><mo>=</mo><msup><mrow><mi>ρ</mi></mrow><mrow><mn>0</mn></mrow></msup><mo>,</mo><mi>ω</mi><mo stretchy="false">)</mo></mrow></math> in the molecule scenario, where the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>X</mi><mo stretchy="false">(</mo><mn>3872</mn><mo stretchy="false">)</mo></math> is regarded as a pure hadronic molecule of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>D</mi><msup><mrow><mover accent="true"><mrow><mi>D</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow><mrow><mo>*</mo></mrow></msup><mo>+</mo><mi mathvariant="normal">c</mi><mn>.</mn><mi mathvariant="normal">c</mi><mn>.</mn></mrow></math> in an <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi></math>-wave with the quantum numbers <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>J</mi><mrow><mi>P</mi><mi>C</mi></mrow></msup><mo>=</mo><msup><mn>1</mn><mrow><mo>+</mo><mo>+</mo></mrow></msup></math>. The radiative processes were assumed to occur via the triangle hadronic loops, and the relevant calculations were conducted using an effective Lagrangian approach. It is found that the absolute decay widths are model-dependent, but the relative width ratio is rather independent of the model parameter. Moreover, the calculated results indicate that the radiative decays of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>X</mi><mo stretchy="false">(</mo><mn>3872</mn><mo stretchy="false">)</mo></math> are strongly influenced by the molecular configuration characterized by the proportion of the charged and neutral constituents. We hope that the present calculations could be tested by the experimental measurements.

Fan Wang

Gang Li

Shi-Dong Liu

Radiative decays of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>X</mi><mo stretchy="false">(</mo><mn>3872</mn><mo stretchy="false">)</mo></math> in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><msup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mo>*</mo></msup></math> molecule scenario

We study the transverse momentum ( $p_T$ ) differential anisotropic flow and flow fluctuation in Pb+Pb collisions at $\sqrt{s_{_{NN}}}$ =5.02 TeV at the LHC. A (3+1)-dimensional CLVisc hydrodynamics framework with fluctuating TRENTO (or AMPT) initial conditions is utilized to simulate the space-time evolution of the quark-gluon plasma (QGP) medium. The effects of shear viscosity and the sub-nucleon structure on anisotropic flow and flow fluctuation are analyzed. Our result shows that shear viscosity tends to suppress both flow coefficients ( ${v_2\{2}\}$ , ${v_2\{4\}}$ , and ${\langle v_2\rangle}$ ) and flow fluctuation ( ${\sigma_{v_2}}$ ) owing to its smearing effect on local density fluctuation. The flow coefficients appear to be insensitive to the sub-nucleon structure, whereas the flow fluctuation ${\sigma_{v_2}}$ tends to be suppressed by the sub-nucleon structure in central collisions but enhanced in peripheral collisions. After taking into account the sub-nucleon structure effect, our numerical result can qualitatively describe the relative flow fluctuations ( ${v_2\{4\}/v_2\{2\}}$ , $F({v_2})$ ) measured by the ALICE Collaboration at the LHC. We further investigate the effects of shear viscosity, sub-nucleon structure, and initial condition model on the flow angle and flow magnitude decorrelations ( ${A_2^f}$ , ${M_2^f}$ ) using the four-particle correlation method. We find that the flow decorrelation effect is typically stronger in central collisions than in peripheral collisions. The flow angle decorrelation is found to be insensitive to the shear viscosity and sub-nucleon structure, whereas the flow magnitude decorrelation shows quite different behaviors when using the TRENTO and AMPT initial condition models. Our study sheds light on the anisotropic flow, transport properties, and initial structure of the QGP created in high-energy nuclear collisions.

Germany

Jie Zhu

Canada

Xiang-Yu Wu

Guang-You Qin

Anisotropic flow, flow fluctuation, and flow decorrelation in relativistic heavy-ion collisions: the roles of sub-nucleon structure and shear viscosity * Supported in part by the Natural Science Foundation of China (12225503, 11890710, 11890711, 11935007). Zhu Jie is supported in part by the China Scholarship Council (202306770009). Wu Xiang-Yu is supported in part by the National Science Foundation within the framework of the JETSCAPE collaboration (OAC-2004571) and in part by the Natural Sciences and Engineering Research Council of Canada. Some of the calculations were performed in the Nuclear Science Computing Center at Central China Normal University (NSC$^{3}$), Wuhan, Hubei, China.

Vector charmonium states can be directly produced in the $$e^+e^{-}$$ annihilation process. Among them, (4230) and (4360) splitting from the previously discovered (4260) are not easily arranged into the conventional charmonium spectrum, while recent studies have indicated that they have strong couplings to $$D\bar{D}_1$$ and $$D^*\bar{D}_1.$$ In this work, we investigate the production of (4230) and (4360) as the heavy-quark spin symmetry doublet hadronic molecules of $$D\bar{D}_1$$ and $$D^*\bar{D}_1$$ in decays via the triangle diagram mechanism. In particular, we propose that the decay constants of (4230) and (4360) extracted in decays are useful for clarifying their nature.

Exploring the nature of

We investigate the Klein-Gordon (KG) oscillators in a global monopole (GM) spacetime in Eddington-inspired Born-Infeld (EiBI) gravity and a Wu-Yang magnetic monopole (WYMM). We discuss the gravitational effects in the presence of Ricci scalar curvature <math altimg='si1.svg'><mi>R</mi><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><msubsup><mrow><mi>R</mi></mrow><mrow><mi>&#965;</mi></mrow><mrow><mi>&#965;</mi></mrow></msubsup></math>. It is observed that the presence of the Ricci scalar curvature, effectively and manifestly, introduces a force field that makes the corresponding quantum mechanical repulsive core more repulsive. Similar effect is also observed for the EiBI-gravitational field. We reiterate and report that the corresponding bosonic KG-oscillator quantum mechanical system admits a solution in the form of confluent Heun functions, the truncation of which into a physically admissible polynomial is shown to be associated with some parametric correlations/conditions. The use of such conditions/correlations is mandatory and yields a set of allowed/restricted quantum mechanical orbital <italic>&#8467;</italic>-excitations, for all radial quantum numbers <math altimg='si2.svg'><msub><mrow><mi>n</mi></mrow><mrow><mi>r</mi></mrow></msub><mo>&#8805;</mo><mn>0</mn></math>. Our procedure is shown to be quite handy, in the sense that it allows one to retrieve results for KG-oscillators in GM-spacetime in different EiBI-gravity and Ricci scalar curvature settings.

Türkiye

Omar Mustafa

KG-oscillators in Eddington-inspired Born-Infeld gravity: Wu-Yang magnetic monopole and Ricci scalar curvature effects

In the present work, we investigate the production of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>X</mi><mo stretchy="false">(</mo><mn>4630</mn><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Y</mi><mo stretchy="false">(</mo><mn>4626</mn><mo stretchy="false">)</mo></math> in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mo>+</mo></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>B</mi><mi>s</mi><mn>0</mn></msubsup></math> decays, where <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>X</mi><mo stretchy="false">(</mo><mn>4630</mn><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Y</mi><mo stretchy="false">(</mo><mn>4626</mn><mo stretchy="false">)</mo></math> are considered as the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>C</mi></mrow></math>- parity pigeon pair in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mi>s</mi><mrow><mo>*</mo><mo>+</mo></mrow></msubsup><msub><mi>D</mi><mrow><mi>s</mi><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><mn>2536</mn><msup><mo stretchy="false">)</mo><mo>−</mo></msup></math> molecular frame. The branching fractions of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mo>+</mo></msup><mo stretchy="false">→</mo><msup><mi>K</mi><mo>+</mo></msup><mi>X</mi><mo stretchy="false">(</mo><mn>4630</mn><mo stretchy="false">)</mo><mo>/</mo><mi>Y</mi><mo stretchy="false">(</mo><mn>4626</mn><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>B</mi><mi>s</mi><mn>0</mn></msubsup><mo stretchy="false">→</mo><mi>η</mi><mi>X</mi><mo stretchy="false">(</mo><mn>4630</mn><mo stretchy="false">)</mo><mo>/</mo><mi>Y</mi><mo stretchy="false">(</mo><mn>4626</mn><mo stretchy="false">)</mo></math> have been evaluated using an effective Lagrangian approach, which are of the order of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>10</mn><mrow><mo>−</mo><mn>5</mn></mrow></msup></math> and the ratios of these branching fractions are almost independent on the model parameter. Based on the present estimations, we propose to search <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Y</mi><mo stretchy="false">(</mo><mn>4626</mn><mo stretchy="false">)</mo></math> in the process <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mo>+</mo></msup><mo stretchy="false">→</mo><msup><mi>K</mi><mo>+</mo></msup><mi>J</mi><mo>/</mo><mi>ψ</mi><msup><mi>η</mi><mrow><mo stretchy="false">(</mo><mo>′</mo><mo stretchy="false">)</mo></mrow></msup></math>, which should be accessible by the LHCb and Belle II Collaborations.

Zhuo Yu

Dian-Yong Chen

<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>X</mi><mo stretchy="false">(</mo><mn>4630</mn><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Y</mi><mo stretchy="false">(</mo><mn>4626</mn><mo stretchy="false">)</mo></math> production in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mo>+</mo></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>B</mi><mi>s</mi><mn>0</mn></msubsup></math> decays

The experimental observations of $$\psi _2(3823)$$ and $$\psi _3(3842)$$ make wave charmonia family abundant. In the present work, we investigate the hidden charm decay processes of spin triplets of the -wave charmonia with the meson loop mechanism. The model parameter $$\alpha _\Lambda $$ is determined by reproducing the branching fraction of $$\psi (3770)\rightarrow J/\psi \eta $$ . With this range of model parameter values, the branching fractions (partial widths) of $$\psi (3770) \rightarrow \eta _c \omega $$ , $$\psi _2(3823)/\psi _3(3842) \rightarrow J/\psi \eta $$ , $$\psi _2(3823)/\psi _3(3842) \rightarrow \eta _c \omega $$ are estimated. Our estimations find that the partial width of $$\psi _2(3823) \rightarrow J/\psi \eta $$ is $$\left( 29.64^{+4.01}_{-4.63}\right) \ \textrm{keV}$$ , and the partial width ratio of $$\psi _2(3823) \rightarrow J/\psi \eta $$ relative to $$\psi _2(3823)\rightarrow \gamma \chi _{c1}$$ is about $$10\%$$ , which could be tested by further precise measurements from the BESIII, Belle II and LHCb Collaborations.

Xiao-Yu Qi

Xing-Dao Guo

Two-body hidden charm decays of

In the present work, we propose to explore the productions of the bottom and bottom-strange mesons in the high-energy pion and kaon-induced reactions on a proton target. The cross sections are evaluated with an effective Lagrangian constructed by the heavy-quark limit and chiral symmetry. Our estimations show that at $$P_\pi =80$$ <math> <mrow> <msub> <mi>P</mi> <mi>π</mi> </msub> <mo>=</mo> <mn>80</mn> </mrow> </math> GeV, the cross sections for B(5279), $$B^*(5325)$$ <math> <mrow> <msup> <mi>B</mi> <mo>∗</mo> </msup> <mrow> <mo>(</mo> <mn>5325</mn> <mo>)</mo> </mrow> </mrow> </math> , $$B_0^*(5722)$$ <math> <mrow> <msubsup> <mi>B</mi> <mn>0</mn> <mo>∗</mo> </msubsup> <mrow> <mo>(</mo> <mn>5722</mn> <mo>)</mo> </mrow> </mrow> </math> , $$B_1^\prime (5716)$$ <math> <mrow> <msubsup> <mi>B</mi> <mn>1</mn> <mo>′</mo> </msubsup> <mrow> <mo>(</mo> <mn>5716</mn> <mo>)</mo> </mrow> </mrow> </math> , $$B_1(5721)$$ <math> <mrow> <msub> <mi>B</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mn>5721</mn> <mo>)</mo> </mrow> </mrow> </math> and $$B_2^*(5747)$$ <math> <mrow> <msubsup> <mi>B</mi> <mn>2</mn> <mo>∗</mo> </msubsup> <mrow> <mo>(</mo> <mn>5747</mn> <mo>)</mo> </mrow> </mrow> </math> production processes are estimated to be 3.19–86.26, 1.86–51.29, 0.88–24.33, 0.86–23.69, 162.35–4477.66, and 57.16–1604.43 nb, respectively, where uncertainties arise from the model parameter. In addition, the cross sections for the corresponding bottom-strange mesons production processes are very similar. From the heavy quark effective theory point of view, the ratios between the cross sections for bottom mesons and bottom-strange mesons should be similar and the present estimations are consistent with the expectation of heavy quark limit. In particular, the cross-section ratios related to the states in the same doublets are of order one. The cross sections related to the states in the T doublets are about two orders larger than those related to the states in the S doublets.

Jing Liu

Quan-Yun Guo

Jun He

Productions of bottom and bottom-strange mesons in pion and kaon induced reactions

In the present work, we investigate the productions of $$X_0(2900)$$ <math> <mrow> <msub> <mi>X</mi> <mn>0</mn> </msub> <mrow> <mo>(</mo> <mn>2900</mn> <mo>)</mo> </mrow> </mrow> </math> and its spin partners in the $$B^+$$ <math> <msup> <mi>B</mi> <mo>+</mo> </msup> </math> decay processes, where $$X_0(2900)$$ <math> <mrow> <msub> <mi>X</mi> <mn>0</mn> </msub> <mrow> <mo>(</mo> <mn>2900</mn> <mo>)</mo> </mrow> </mrow> </math> is regarded as a $$\bar{D}^*K^*$$ <math> <mrow> <msup> <mrow> <mover> <mrow> <mi>D</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> <mo>∗</mo> </msup> <msup> <mi>K</mi> <mo>∗</mo> </msup> </mrow> </math> molecular state. We infer that the initial $$B^+$$ <math> <msup> <mi>B</mi> <mo>+</mo> </msup> </math> meson and the final $$D^+ X_0(2900)$$ <math> <mrow> <msup> <mi>D</mi> <mo>+</mo> </msup> <msub> <mi>X</mi> <mn>0</mn> </msub> <mrow> <mo>(</mo> <mn>2900</mn> <mo>)</mo> </mrow> </mrow> </math> are connected through the $$D_{s1}^{\prime +}(2460) \bar{D}^{*0} $$ <math> <mrow> <msubsup> <mi>D</mi> <mrow> <mi>s</mi> <mn>1</mn> </mrow> <mrow> <mo>′</mo> <mo>+</mo> </mrow> </msubsup> <mrow> <mo>(</mo> <mn>2460</mn> <mo>)</mo> </mrow> <msup> <mrow> <mover> <mrow> <mi>D</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> <mrow> <mrow></mrow> <mo>∗</mo> <mn>0</mn> </mrow> </msup> </mrow> </math> mesons by exchanging a $$K^{*0}$$ <math> <mmultiscripts> <mi>K</mi> <mrow></mrow> <mrow> <mrow></mrow> <mo>∗</mo> <mn>0</mn> </mrow> </mmultiscripts> </math> meson. The contributions of such a meson loop to the process $$B^+ \rightarrow D^+ X_0(2900)$$ <math> <mrow> <msup> <mi>B</mi> <mo>+</mo> </msup> <mo>→</mo> <msup> <mi>D</mi> <mo>+</mo> </msup> <msub> <mi>X</mi> <mn>0</mn> </msub> <mrow> <mo>(</mo> <mn>2900</mn> <mo>)</mo> </mrow> </mrow> </math> are evaluated and our estimations indicate that the measured branching fraction of $$B^+\rightarrow D^+ X_0(2900)$$ <math> <mrow> <msup> <mi>B</mi> <mo>+</mo> </msup> <mo>→</mo> <msup> <mi>D</mi> <mo>+</mo> </msup> <msub> <mi>X</mi> <mn>0</mn> </msub> <mrow> <mo>(</mo> <mn>2900</mn> <mo>)</mo> </mrow> </mrow> </math> could be well reproduced in a reasonable range of model parameters, indicating that $$X_0(2900)$$ <math> <mrow> <msub> <mi>X</mi> <mn>0</mn> </msub> <mrow> <mo>(</mo> <mn>2900</mn> <mo>)</mo> </mrow> </mrow> </math> could be interpreted as a $$\bar{D}^*K^*$$ <math> <mrow> <msup> <mrow> <mover> <mrow> <mi>D</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> <mo>∗</mo> </msup> <msup> <mi>K</mi> <mo>∗</mo> </msup> </mrow> </math> molecular state. In addition, the production processes $$B^+ \rightarrow D^+ \tilde{X}_{1,2}$$ <math> <mrow> <msup> <mi>B</mi> <mo>+</mo> </msup> <mo>→</mo> <msup> <mi>D</mi> <mo>+</mo> </msup> <msub> <mover> <mi>X</mi> <mo>~</mo> </mover> <mrow> <mn>1</mn> <mo>,</mo> <mn>2</mn> </mrow> </msub> </mrow> </math> , $$B^+ \rightarrow D^{*+} X_0(2900)$$ <math> <mrow> <msup> <mi>B</mi> <mo>+</mo> </msup> <mo>→</mo> <mmultiscripts> <mi>D</mi> <mrow></mrow> <mrow> <mrow></mrow> <mo>∗</mo> <mo>+</mo> </mrow> </mmultiscripts> <msub> <mi>X</mi> <mn>0</mn> </msub> <mrow> <mo>(</mo> <mn>2900</mn> <mo>)</mo> </mrow> </mrow> </math> , and $$B^+ \rightarrow D^{*+}\tilde{X}_{1,2}$$ <math> <mrow> <msup> <mi>B</mi> <mo>+</mo> </msup> <mo>→</mo> <mmultiscripts> <mi>D</mi> <mrow></mrow> <mrow> <mrow></mrow> <mo>∗</mo> <mo>+</mo> </mrow> </mmultiscripts> <msub> <mover> <mi>X</mi> <mo>~</mo> </mover> <mrow> <mn>1</mn> <mo>,</mo> <mn>2</mn> </mrow> </msub> </mrow> </math> are investigated, and we find that the fit fraction of $$\tilde{X}_1$$ <math> <msub> <mover> <mi>X</mi> <mo>~</mo> </mover> <mn>1</mn> </msub> </math> in the process $$B^+ \rightarrow D^{*+} D^{*-} K^+$$ <math> <mrow> <msup> <mi>B</mi> <mo>+</mo> </msup> <mo>→</mo> <mmultiscripts> <mi>D</mi> <mrow></mrow> <mrow> <mrow></mrow> <mo>∗</mo> <mo>+</mo> </mrow> </mmultiscripts> <mmultiscripts> <mi>D</mi> <mrow></mrow> <mrow> <mrow></mrow> <mo>∗</mo> <mo>-</mo> </mrow> </mmultiscripts> <msup> <mi>K</mi> <mo>+</mo> </msup> </mrow> </math> is about 6%, which should be accessible by the LHCb and Belle II Collaborations.

$$X_0(2900)$$ <math> <mrow> <msub> <mi>X</mi> <mn>0</mn> </msub> <mrow> <mo>(</mo> <mn>2900</mn> <mo>)</mo> </mrow> </mrow> </math> and its spin partners productions in the $$B^+$$ <math> <msup> <mi>B</mi> <mo>+</mo> </msup> </math> decay processes

In the present work, we investigate the production of the newly observed <math><msubsup><mi>P</mi><mrow><mi>ψ</mi><mi>s</mi></mrow><mi>Λ</mi></msubsup><mo>(</mo><mn>4338</mn><mo>)</mo></math> state in <math><msubsup><mi>Ξ</mi><mi>b</mi><mo>−</mo></msubsup></math> decay, where the <math><msubsup><mi>P</mi><mrow><mi>ψ</mi><mi>s</mi></mrow><mi>Λ</mi></msubsup><mo>(</mo><mn>4338</mn><mo>)</mo></math> is assigned as a <math><msub><mi>Ξ</mi><mi>c</mi></msub><mover><mi>D</mi><mo>¯</mo></mover></math> molecular state. By using an effective Lagrangian approach, we evaluate the branching fractions of <math><msubsup><mi>Ξ</mi><mi>b</mi><mo>−</mo></msubsup><mo>→</mo><msubsup><mi>P</mi><mrow><mi>ψ</mi><mi>s</mi></mrow><mi>Λ</mi></msubsup><mo>(</mo><mn>4338</mn><mo>)</mo><msup><mi>K</mi><mo>−</mo></msup></math> via the triangle loop mechanism. The branching fractions of <math><msubsup><mi>Ξ</mi><mi>b</mi><mo>−</mo></msubsup><mo>→</mo><msubsup><mi>P</mi><mrow><mi>ψ</mi><mi>s</mi></mrow><mi>Λ</mi></msubsup><mo>(</mo><mn>4338</mn><mo>)</mo><msup><mi>K</mi><mo>−</mo></msup></math> are in the order of <math><msup><mn>10</mn><mrow><mo>−</mo><mn>4</mn></mrow></msup></math>; the result is compared with our previous work of <math><msubsup><mi>Ξ</mi><mi>b</mi><mo>−</mo></msubsup><mo>→</mo><msubsup><mi>P</mi><mrow><mi>ψ</mi><mi>s</mi></mrow><mi>Λ</mi></msubsup><mo>(</mo><mn>4459</mn><mo>)</mo><msup><mi>K</mi><mo>−</mo></msup></math>. We also predict the ratio of <math><msubsup><mi>P</mi><mrow><mi>ψ</mi><mi>s</mi></mrow><mi>Λ</mi></msubsup><mo>(</mo><mn>4459</mn><mo>)</mo></math> and <math><msubsup><mi>P</mi><mrow><mi>ψ</mi><mi>s</mi></mrow><mi>Λ</mi></msubsup><mo>(</mo><mn>4338</mn><mo>)</mo></math> productions in the decay <math><msubsup><mi>Ξ</mi><mi>b</mi><mo>−</mo></msubsup><mo>→</mo><msubsup><mi>P</mi><mrow><mi>ψ</mi><mi>s</mi></mrow><mi>Λ</mi></msubsup><msup><mi>K</mi><mo>−</mo></msup><mo>→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mi>Λ</mi><msup><mi>K</mi><mo>−</mo></msup></math>. The predicted branching fractions and their ratios could be tested experimentally, which may be helpful for understanding the molecular picture of <math><msubsup><mi>P</mi><mrow><mi>ψ</mi><mi>s</mi></mrow><mi>Λ</mi></msubsup><mo>(</mo><mn>4338</mn><mo>)</mo></math> as well as other hidden-charm pentaquark states with strangeness. Moreover, the experimental potential of observing <math><msubsup><mi>P</mi><mrow><mi>ψ</mi><mi>s</mi></mrow><mi>Λ</mi></msubsup><mo>(</mo><mn>4338</mn><mo>)</mo></math> in the <math><msubsup><mi>Ξ</mi><mi>b</mi><mo>−</mo></msubsup><mo>→</mo><msup><mi>K</mi><mo>−</mo></msup><mi>J</mi><mo>/</mo><mi>ψ</mi><mi>Λ</mi></math> is discussed.

Production of <math><mrow><msubsup><mrow><mi>P</mi></mrow><mrow><mi>ψ</mi><mi>s</mi></mrow><mrow><mi>Λ</mi></mrow></msubsup><mo>(</mo><mn>4338</mn><mo>)</mo></mrow></math> from <math><mrow><msub><mrow><mi>Ξ</mi></mrow><mrow><mi>b</mi></mrow></msub></mrow></math> decay