Since its discovery in 1977, the spin parity of <math><mi>Ξ</mi><mo>(</mo><mn>2030</mn><mo>)</mo></math> has not been fully determined experimentally. The latest Particle Data Group listing suggests it may be a baryon with <math><mi>J</mi><mo>=</mo><mn>5</mn><mo>/</mo><mn>2</mn></math>. Therefore, studying the mass spectrum and decay properties of <math><mi>Ξ</mi><mo>(</mo><mn>2030</mn><mo>)</mo></math> has become a current hot topic to definitively establish its spin parity. As the three-quark model fails to explain <math><mi>Ξ</mi><mo>(</mo><mn>2030</mn><mo>)</mo></math>, we previously proposed it may be a molecule primarily composed of <math><msup><mover><mi>K</mi><mo>¯</mo></mover><mo>*</mo></msup><mi>Σ</mi></math> with <math><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><mn>5</mn><mo>/</mo><msup><mn>2</mn><mo>+</mo></msup></math>, based on its mass spectrum study. To verify its molecular state interpretation, this work proposes studying the strong decays of <math><mi>Ξ</mi><mo>(</mo><mn>2030</mn><mo>)</mo></math> assuming it is a <math><mi>P</mi></math>-wave <math><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><mn>5</mn><mo>/</mo><msup><mn>2</mn><mo>+</mo></msup></math> meson-baryon molecule predominantly composed of <math><msup><mover><mi>K</mi><mo>¯</mo></mover><mo>*</mo></msup><mi>Σ</mi></math>. We calculated all experimentally measured two-body and three-body final state decay widths of <math><mi>Ξ</mi><mo>(</mo><mn>2030</mn><mo>)</mo></math>, including <math><mi>Ξ</mi><mo>(</mo><mn>2030</mn><mo>)</mo><mo>→</mo><mover><mi>K</mi><mo>¯</mo></mover><mi>Λ</mi><mo>,</mo><mover><mi>K</mi><mo>¯</mo></mover><mi>Σ</mi><mo>,</mo><mi>π</mi><mi>Ξ</mi><mo>,</mo><mi>π</mi><msup><mi>Ξ</mi><mo>*</mo></msup></math>, and <math><mi>Ξ</mi><mo>(</mo><mn>2030</mn><mo>)</mo><mo>→</mo><mi>π</mi><mi>π</mi><mi>Ξ</mi><mo>,</mo><mi>π</mi><mover><mi>K</mi><mo>¯</mo></mover><mi>Σ</mi><mo>,</mo><mi>π</mi><mover><mi>K</mi><mo>¯</mo></mover><mi>Λ</mi></math>. The results indicate that both the total decay width and partial decay widths agree well with experimental values within the error margins. This supports that <math><mi>Ξ</mi><mo>(</mo><mn>2030</mn><mo>)</mo></math> is a molecule with spin-parity <math><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><mn>5</mn><mo>/</mo><msup><mn>2</mn><mo>+</mo></msup></math>, predominantly composed of <math><msup><mover><mi>K</mi><mo>¯</mo></mover><mo>*</mo></msup><mi>Σ</mi></math>. Compared to the experimental central values, our results are slightly smaller, which suggests that <math><mi>Ξ</mi><mo>(</mo><mn>2030</mn><mo>)</mo></math> may contain additional components besides meson-baryon molecular components, such as three-quark structures.

China

Jing-wen Feng

Cai Cheng

Yin Huang

Studying the <math><mi>Ξ</mi><mo>(</mo><mn>2030</mn><mo>)</mo></math> as a predominantly <math><msup><mover><mi>K</mi><mo>¯</mo></mover><mo>*</mo></msup><mi>Σ</mi></math> molecular state

Currently, there is much controversy surrounding the interpretation of the <math><mi>Ξ</mi><mo>(</mo><mn>2030</mn><mo>)</mo></math> and <math><mi>Ξ</mi><mo>(</mo><mn>2012</mn><mo>)</mo></math> as traditional hadrons containing double strange quarks. In particular, the ratios of the partial decay widths into <math><mi>Λ</mi><mover><mi>K</mi><mo>¯</mo></mover></math> and <math><mi>Σ</mi><mover><mi>K</mi><mo>¯</mo></mover></math> for <math><mi>Ξ</mi><mo>(</mo><mn>2030</mn><mo>)</mo></math> cannot obtain a suitable explanation under the <math><mi>q</mi><mi>s</mi><mi>s</mi></math> three-quark structure. Thus, we suggest the <math><mi>Ξ</mi><mo>(</mo><mn>2030</mn><mo>)</mo></math> and <math><mi>Ξ</mi><mo>(</mo><mn>2012</mn><mo>)</mo></math> to be <math><mi>V</mi><mi>B</mi><mo>(</mo><mo>=</mo><msup><mover><mi>K</mi><mo>¯</mo></mover><mo>*</mo></msup><mi>Σ</mi><mo>/</mo><mi>ρ</mi><mi>Ξ</mi><mo>/</mo><msup><mover><mi>K</mi><mo>¯</mo></mover><mo>*</mo></msup><mi>Λ</mi><mo>/</mo><mi>ϕ</mi><mi>Ξ</mi><mo>/</mo><mi>ω</mi><mi>Ξ</mi><mo>)</mo></math> molecular states. In this work, we perform a systematical investigation of possible molecular states from the <math><mi>V</mi><mi>B</mi><mo>(</mo><mo>=</mo><msup><mover><mi>K</mi><mo>¯</mo></mover><mo>*</mo></msup><mi>Σ</mi><mo>/</mo><mi>ρ</mi><mi>Ξ</mi><mo>/</mo><msup><mover><mi>K</mi><mo>¯</mo></mover><mo>*</mo></msup><mi>Λ</mi><mo>/</mo><mi>ϕ</mi><mi>Ξ</mi><mo>/</mo><mi>ω</mi><mi>Ξ</mi><mo>)</mo></math> interaction. The interaction of the system considered is described by the <math><mi>t</mi></math>-channel vector (<math><mi>ρ</mi><mo>,</mo><mi>ω</mi><mo>,</mo><mi>ϕ</mi><mo>,</mo><msup><mover><mi>K</mi><mo>¯</mo></mover><mo>*</mo></msup></math>) and pseudoscalar (<math><mi>π</mi><mo>,</mo><msup><mi>η</mi><mrow><msup><mo>(</mo><mo>′</mo></msup><mo>)</mo></mrow></msup><mo>,</mo><mover><mi>K</mi><mo>¯</mo></mover></math>) meson exchanges. By solving the nonrelativistic Schrödinger equation with the obtained one-boson-exchange potentials, the <math><mi>V</mi><mi>B</mi><mo>(</mo><mo>=</mo><msup><mover><mi>K</mi><mo>¯</mo></mover><mo>*</mo></msup><mi>Σ</mi><mo>/</mo><mi>ρ</mi><mi>Ξ</mi><mo>/</mo><msup><mover><mi>K</mi><mo>¯</mo></mover><mo>*</mo></msup><mi>Λ</mi><mo>/</mo><mi>ϕ</mi><mi>Ξ</mi><mo>/</mo><mi>ω</mi><mi>Ξ</mi><mo>)</mo></math> bound states with different quantum numbers are searched. The calculation suggests that <math><mi>Ξ</mi><mo>(</mo><mn>2030</mn><mo>)</mo></math> can be assigned as a <math><mi>P</mi></math>-wave <math><msup><mover><mi>K</mi><mo>¯</mo></mover><mo>*</mo></msup><mi>Σ</mi><mo>/</mo><mi>ρ</mi><mi>Ξ</mi><mo>/</mo><msup><mover><mi>K</mi><mo>¯</mo></mover><mo>*</mo></msup><mi>Λ</mi><mo>/</mo><mi>ϕ</mi><mi>Ξ</mi><mo>/</mo><mi>ω</mi><mi>Ξ</mi></math> molecular state with spin-parity <math><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><mn>5</mn><mo>/</mo><msup><mn>2</mn><mo>+</mo></msup></math>. The calculation also predicts the existence of four <math><msup><mover><mi>K</mi><mo>¯</mo></mover><mo>*</mo></msup><mi>Σ</mi><mo>/</mo><mi>ρ</mi><mi>Ξ</mi><mo>/</mo><msup><mover><mi>K</mi><mo>¯</mo></mover><mo>*</mo></msup><mi>Λ</mi><mo>/</mo><mi>ϕ</mi><mi>Ξ</mi><mo>/</mo><mi>ω</mi><mi>Ξ</mi></math> bound states with <math><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>±</mo></msup></math> and <math><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><mn>3</mn><mo>/</mo><msup><mn>2</mn><mo>±</mo></msup></math>. The <math><mi>Ξ</mi><mo>(</mo><mn>2012</mn><mo>)</mo></math> may be a candidate for one of these four bound states. If <math><mi>Ξ</mi><mo>(</mo><mn>2012</mn><mo>)</mo></math> is an <math><mi>S</mi></math>-wave molecular state with <math><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></math> or <math><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><mn>3</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></math>, we suggest determining its spin and parity by studying its decay width, owing to the difference in their molecular components.

Hao Hei

Internal structures of the baryons <math><mi>Ξ</mi><mo>(</mo><mn>2030</mn><mo>)</mo></math> and <math><mi>Ξ</mi><mo>(</mo><mn>2120</mn><mo>)</mo></math>

Understanding the production mechanisms and utilizing them as probes to investigate the structure of exotic states represent some of the most actively studied research areas in particle physics. In this study, we present a theoretical analysis of the charmed meson <math><msubsup><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow><mo>−</mo></msubsup></math> in the <math><mi>γ</mi><mi>p</mi><mo>→</mo><msup><mi>D</mi><mo>+</mo></msup><msubsup><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow><mo>−</mo></msubsup><msubsup><mi>Λ</mi><mi>c</mi><mo>+</mo></msubsup></math> and <math><mi>γ</mi><mi>γ</mi><mo>→</mo><msup><mi>D</mi><mo>+</mo></msup><msubsup><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow><mo>−</mo></msubsup><msup><mi>D</mi><mrow><mo>*</mo><mn>0</mn></mrow></msup></math> reactions, considering <math><msubsup><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow><mo>+</mo></msubsup></math> as a <math><mi>D</mi><msup><mi>D</mi><mo>*</mo></msup></math> molecule. The differential cross section and total cross section for the photoproduction of <math><msubsup><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow><mo>−</mo></msubsup></math> in the <math><mi>γ</mi><mi>p</mi><mo>→</mo><msup><mi>D</mi><mo>+</mo></msup><msubsup><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow><mo>−</mo></msubsup><msubsup><mi>Λ</mi><mi>c</mi><mo>+</mo></msubsup></math> and <math><mi>γ</mi><mi>γ</mi><mo>→</mo><msup><mi>D</mi><mo>+</mo></msup><msubsup><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow><mo>−</mo></msubsup><msup><mi>D</mi><mrow><mo>*</mo><mn>0</mn></mrow></msup></math> reactions are presented for nucleus-nucleus (nucleon-nucleon) ultraperipheral collisions at HL-LHC and RHIC, respectively. Taking into account the integrated luminosity per typical run and the luminosity of photons from the nucleus (nucleon), we observe a significant event count for <math><msubsup><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow><mo>−</mo></msubsup></math> production in <math><mrow><mi>p</mi><mtext>−</mtext><mi>p</mi></mrow></math> ultraperipheral collisions at HL-LHC.

Xiaopeng Wang

Yaping Xie

Xurong Chen

Exclusive production of <math><msubsup><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow><mo>−</mo></msubsup></math> in hadron-hadron ultraperipheral collisions

Recently, a new doubly charged tetraquark <math><mrow><msubsup><mrow><mi>T</mi></mrow><mrow><mi>c</mi><mover><mrow><mi>s</mi></mrow><mrow><mo>¯</mo></mrow></mover><mn>0</mn></mrow><mrow><mi>a</mi></mrow></msubsup><mo>(</mo><mn>2900</mn><msup><mrow><mo>)</mo></mrow><mrow><mo>+</mo><mo>+</mo></mrow></msup></mrow></math> and its neutral partner <math><mrow><msubsup><mrow><mi>T</mi></mrow><mrow><mi>c</mi><mover><mrow><mi>s</mi></mrow><mrow><mo>¯</mo></mrow></mover><mn>0</mn></mrow><mrow><mi>a</mi></mrow></msubsup><mo>(</mo><mn>2900</mn><msup><mrow><mo>)</mo></mrow><mrow><mn>0</mn></mrow></msup></mrow></math> at the invariant mass spectrum of <math><mrow><mi>π</mi><msub><mrow><mi>D</mi></mrow><mrow><mi>s</mi></mrow></msub></mrow></math> were observed by the LHCb Collaboration. According to its properties, such as the mass and decay width, <math><mrow><msubsup><mrow><mi>T</mi></mrow><mrow><mi>c</mi><mover><mrow><mi>s</mi></mrow><mrow><mo>¯</mo></mrow></mover><mn>0</mn></mrow><mrow><mi>a</mi></mrow></msubsup><mo>(</mo><mn>2900</mn><msup><mrow><mo>)</mo></mrow><mrow><mo>+</mo><mo>+</mo><mo>/</mo><mn>0</mn></mrow></msup></mrow></math> has been suggested to be a compact multiquark state or a hadron molecule. In order to distinguish the various interpretations of <math><mrow><msubsup><mrow><mi>T</mi></mrow><mrow><mi>c</mi><mover><mrow><mi>s</mi></mrow><mrow><mo>¯</mo></mrow></mover><mn>0</mn></mrow><mrow><mi>a</mi></mrow></msubsup><mo>(</mo><mn>2900</mn><msup><mrow><mo>)</mo></mrow><mrow><mo>+</mo><mo>+</mo><mo>/</mo><mn>0</mn></mrow></msup></mrow></math>, we investigate the possibility of studying <math><mrow><msubsup><mrow><mover><mrow><mi>T</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mi>c</mi><mover><mrow><mi>s</mi></mrow><mrow><mo>¯</mo></mrow></mover><mn>0</mn></mrow><mrow><mi>a</mi></mrow></msubsup><mo>(</mo><mn>2900</mn><mo>)</mo></mrow></math> [the antiparticle of <math><msubsup><mi>T</mi><mrow><mi>c</mi><mover><mi>s</mi><mo>¯</mo></mover><mn>0</mn></mrow><mi>a</mi></msubsup><mo>(</mo><mn>2900</mn><mo>)</mo></math>] by kaon-induced reactions on a proton target in an effective Lagrangian approach. The production mechanism is characterized by the <math><mi>t</mi></math>-channel <math><mi>D</mi></math>-meson exchange. Our theoretical approach is based on the assumption that <math><msubsup><mover><mi>T</mi><mo>¯</mo></mover><mrow><mi>c</mi><mover><mi>s</mi><mo>¯</mo></mover><mn>0</mn></mrow><mi>a</mi></msubsup><mo>(</mo><mn>2900</mn><mo>)</mo></math> can be either a <math><mrow><msup><mrow><mi>K</mi></mrow><mrow><mo>*</mo></mrow></msup><msup><mrow><mi>D</mi></mrow><mrow><mo>*</mo></mrow></msup><mtext>−</mtext><msubsup><mrow><mi>D</mi></mrow><mrow><mi>s</mi></mrow><mrow><mo>*</mo></mrow></msubsup><mi>ρ</mi></mrow></math> molecule or a compact tetraquark state. Using the coupling constants of <math><msubsup><mover><mi>T</mi><mo>¯</mo></mover><mrow><mi>c</mi><mover><mi>s</mi><mo>¯</mo></mover><mn>0</mn></mrow><mi>a</mi></msubsup><mo>(</mo><mn>2900</mn><mo>)</mo></math> to the <math><mi>K</mi><mi>D</mi></math> channel obtained from the molecule or compact tetraquark picture of <math><msubsup><mover><mi>T</mi><mo>¯</mo></mover><mrow><mi>c</mi><mover><mi>s</mi><mo>¯</mo></mover><mn>0</mn></mrow><mi>a</mi></msubsup><mo>(</mo><mn>2900</mn><mo>)</mo></math>, we compute the cross sections for the process <math><mrow><msup><mrow><mi>K</mi></mrow><mrow><mo>−</mo></mrow></msup><mi>n</mi><mo>→</mo><msubsup><mrow><mover><mrow><mi>T</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mi>c</mi><mover><mrow><mi>s</mi></mrow><mrow><mo>¯</mo></mrow></mover><mn>0</mn></mrow><mrow><mi>a</mi></mrow></msubsup><mo>(</mo><mn>2900</mn><msup><mrow><mo>)</mo></mrow><mrow><mo>−</mo><mo>−</mo></mrow></msup><msubsup><mrow><mi>Λ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup></mrow></math>. The <math><mover><mi>K</mi><mo>¯</mo></mover><mi>N</mi></math> initial-state interaction mediated by Pomeron and Reggeon exchanges is also included, which reduces the production of <math><msubsup><mover><mi>T</mi><mo>¯</mo></mover><mrow><mi>c</mi><mover><mi>s</mi><mo>¯</mo></mover><mn>0</mn></mrow><mi>a</mi></msubsup><mo>(</mo><mn>2900</mn><mo>)</mo></math>. Our calculations show that whether <math><msubsup><mover><mi>T</mi><mo>¯</mo></mover><mrow><mi>c</mi><mover><mi>s</mi><mo>¯</mo></mover><mn>0</mn></mrow><mi>a</mi></msubsup><mo>(</mo><mn>2900</mn><mo>)</mo></math> is a molecule or a compact tetraquark state, the cross sections for the <math><mrow><msup><mrow><mi>K</mi></mrow><mrow><mo>−</mo></mrow></msup><mi>n</mi><mo>→</mo><msubsup><mrow><mover><mrow><mi>T</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mi>c</mi><mover><mrow><mi>s</mi></mrow><mrow><mo>¯</mo></mrow></mover><mn>0</mn></mrow><mrow><mi>a</mi></mrow></msubsup><mo>(</mo><mn>2900</mn><msup><mrow><mo>)</mo></mrow><mrow><mo>−</mo><mo>−</mo></mrow></msup><msubsup><mrow><mi>Λ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup></mrow></math> reaction are of similar magnitude, ranging from approximately 0.150 nb to 0.540 nb. However, a clearer comparison can be made by computing the cross section of the <math><mrow><msup><mrow><mi>K</mi></mrow><mrow><mo>−</mo></mrow></msup><mi>n</mi><mo>→</mo><msubsup><mrow><mover><mrow><mi>T</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mi>c</mi><mover><mrow><mi>s</mi></mrow><mrow><mo>¯</mo></mrow></mover><mn>0</mn></mrow><mrow><mi>a</mi></mrow></msubsup><mo>(</mo><mn>2900</mn><msup><mrow><mo>)</mo></mrow><mrow><mo>−</mo><mo>−</mo></mrow></msup><msubsup><mrow><mi>Λ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup><mo>→</mo><msup><mrow><mi>π</mi></mrow><mrow><mo>−</mo></mrow></msup><msubsup><mrow><mi>D</mi></mrow><mrow><mi>s</mi></mrow><mrow><mo>−</mo></mrow></msubsup><msubsup><mrow><mi>Λ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup></mrow></math> reaction. The results indicate that the cross section for the molecule assignment of <math><mrow><msubsup><mrow><mover><mrow><mi>T</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mi>c</mi><mover><mrow><mi>s</mi></mrow><mrow><mo>¯</mo></mrow></mover><mn>0</mn></mrow><mrow><mi>a</mi></mrow></msubsup><mo>(</mo><mn>2900</mn><mo>)</mo></mrow></math> can reach up to <math><mn>3.66</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup><mtext> </mtext><mtext> </mtext><mi>nb</mi></math>, which is significantly smaller than that of 0.244 nb, by assuming <math><msubsup><mover><mi>T</mi><mo>¯</mo></mover><mrow><mi>c</mi><mover><mi>s</mi><mo>¯</mo></mover><mn>0</mn></mrow><mi>a</mi></msubsup><mo>(</mo><mn>2900</mn><mo>)</mo></math> as a compact tetraquark state. These results can be measured in future experiments, and they can be used to test the nature of <math><msubsup><mover><mi>T</mi><mo>¯</mo></mover><mrow><mi>c</mi><mover><mi>s</mi><mo>¯</mo></mover><mn>0</mn></mrow><mi>a</mi></msubsup><mo>(</mo><mn>2900</mn><mo>)</mo></math>. Lastly, we also propose to search for the unreported charged tetraquark <math><msubsup><mi>T</mi><mrow><mi>c</mi><mover><mi>s</mi><mo>¯</mo></mover><mn>0</mn></mrow><mi>a</mi></msubsup><mo>(</mo><mn>2900</mn><msup><mo>)</mo><mo>+</mo></msup></math> in the <math><mrow><msup><mrow><mi>K</mi></mrow><mrow><mo>−</mo></mrow></msup><mi>p</mi><mo>→</mo><msubsup><mrow><mover><mrow><mi>T</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mi>c</mi><mover><mrow><mi>s</mi></mrow><mrow><mo>¯</mo></mrow></mover><mn>0</mn></mrow><mrow><mi>a</mi></mrow></msubsup><mo>(</mo><mn>2900</mn><msup><mrow><mo>)</mo></mrow><mrow><mo>−</mo></mrow></msup><msubsup><mrow><mi>Λ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup></mrow></math> reaction.

Rong Wang

Production of the newly observed <math><mrow><msub><mrow><mover><mrow><mi>T</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mi>c</mi><mover><mrow><mi>s</mi></mrow><mrow><mo>¯</mo></mrow></mover><mn>0</mn></mrow></msub></mrow></math> by kaon-induced reactions on a proton or neutron target

Stimulated by the measurement of the <math><mi>J</mi><mi>ψ</mi><mi>ϕ</mi></math> decay model of <math><mi>Y</mi><mo>(</mo><mn>4274</mn><mo>)</mo></math> by the LHCb Collaboration, we consider a possible interpretation of this state as a hadron molecular-a bound state of <math><msub><mi>D</mi><mi>s</mi></msub></math> and <math><msub><mover><mi>D</mi><mo>¯</mo></mover><mrow><mi>s</mi><mn>0</mn></mrow></msub><mo>(</mo><mn>2317</mn><mo>)</mo></math> mesons. Using effective Lagrangian approach, we calculate the two-body strong decay channels <math><mi>Y</mi><mo>(</mo><mn>4274</mn><mo>)</mo><mo>→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mi>ϕ</mi><mo>,</mo><msub><mi>χ</mi><mrow><mi>c</mi><mn>0</mn></mrow></msub><mi>η</mi><mo>,</mo><msub><mi>χ</mi><mrow><mi>c</mi><mn>0</mn></mrow></msub><mi>η</mi><mo>,</mo><msubsup><mi>D</mi><mi>s</mi><mo>*</mo></msubsup><msub><mover><mi>D</mi><mo>¯</mo></mover><mi>s</mi></msub></math>, <math><mi>D</mi><msup><mover><mi>D</mi><mo>¯</mo></mover><mo>*</mo></msup></math>, <math><mi>K</mi><msup><mover><mi>K</mi><mo>¯</mo></mover><mo>*</mo></msup></math>, and <math><mi>ϕ</mi><mi>ϕ</mi></math> through hadronic loops and three-body decays into <math><msup><mi>π</mi><mn>0</mn></msup><msub><mi>D</mi><mi>s</mi></msub><msub><mover><mi>D</mi><mo>¯</mo></mover><mi>s</mi></msub></math>. In comparison with the LHCb data, our results show that <math><mi>Y</mi><mo>(</mo><mn>4274</mn><mo>)</mo></math> cannot be assigned to be a <math><msub><mi>D</mi><mi>s</mi></msub><msub><mover><mi>D</mi><mo>¯</mo></mover><mrow><mi>s</mi><mn>0</mn></mrow></msub><mo>(</mo><mn>2317</mn><mo>)</mo></math> molecular state. The calculated partial decay widths with the <math><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><msup><mn>1</mn><mo>+</mo></msup></math> <math><msub><mi>D</mi><mi>s</mi></msub><msub><mover><mi>D</mi><mo>¯</mo></mover><mrow><mi>s</mi><mn>0</mn></mrow></msub></math> molecular state picture indicate that allowed decay modes <math><msub><mi>χ</mi><mrow><mi>c</mi><mn>0</mn></mrow></msub><mi>η</mi></math> and <math><msub><mi>χ</mi><mrow><mi>c</mi><mn>1</mn></mrow></msub><mi>η</mi></math> may have the smallest branching ratio and are of the order of 0.0 MeV. Future experimental measurements of such two processes can be quite useful to test the different interpretations of the <math><mi>Y</mi><mo>(</mo><mn>4274</mn><mo>)</mo></math>. If <math><mi>P</mi></math>-wave <math><msub><mi>D</mi><mi>s</mi></msub><msub><mover><mi>D</mi><mo>¯</mo></mover><mrow><mi>s</mi><mn>0</mn></mrow></msub></math> molecular exists [marked as <math><msup><mi>Y</mi><mo>′</mo></msup><mo>(</mo><mn>4274</mn><mo>)</mo></math>], the total decay is at the order of 1.06–1.84 MeV, which seems to be within the reach of the current experiments such as Belle II. In addition, the calculated partial decay widths indicate that allowed decay mode <math><mi>D</mi><msup><mover><mi>D</mi><mo>¯</mo></mover><mo>*</mo></msup></math> may have the biggest branching ratio. The experimental measurements for this strong decay process could be a crucial to observe such a new state <math><msup><mi>Y</mi><mo>′</mo></msup><mo>(</mo><mn>4274</mn><mo>)</mo></math>.

Hong Qiang Zhu

Possible <math><mi>P</mi></math>-wave <math><msub><mi>D</mi><mi>s</mi></msub><msub><mover><mi>D</mi><mo>¯</mo></mover><mrow><mi>s</mi><mn>0</mn></mrow></msub><mo>(</mo><mn>2317</mn><mo>)</mo></math> molecular state <math><msup><mi>Y</mi><mo>′</mo></msup><mo>(</mo><mn>4274</mn><mo>)</mo></math>

Stimulated by the recent LHCb observation of a new exotic charged structure <math><msubsup><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow><mo>+</mo></msubsup></math>, we propose to use the central diffractive mechanism existing in the <math><mrow><mi>γ</mi><mi>p</mi><mo>→</mo><msup><mrow><mi>D</mi></mrow><mrow><mo>+</mo></mrow></msup><msubsup><mrow><mover><mrow><mi>T</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mi>c</mi><mi>c</mi></mrow><mrow><mo>−</mo></mrow></msubsup><msubsup><mrow><mi>Λ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup></mrow></math> (<math><msubsup><mover><mi>T</mi><mo>¯</mo></mover><mrow><mi>c</mi><mi>c</mi></mrow><mo>−</mo></msubsup></math> is the antiparticle of <math><msubsup><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow><mo>+</mo></msubsup></math>) reaction to produce <math><msubsup><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow><mo>+</mo></msubsup></math>. Our theoretical approach is based on the chiral unitary theory where the <math><msubsup><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow><mo>+</mo></msubsup></math> resonance is dynamically generated. With the coupling constant of the <math><msubsup><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow><mo>+</mo></msubsup></math> to <math><mi>D</mi><msup><mi>D</mi><mo>*</mo></msup></math> channel obtained from chiral unitary theory, the total cross sections of the <math><mrow><mi>γ</mi><mi>p</mi><mo>→</mo><msup><mrow><mi>D</mi></mrow><mrow><mo>+</mo></mrow></msup><msubsup><mrow><mover><mrow><mi>T</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mi>c</mi><mi>c</mi></mrow><mrow><mo>−</mo></mrow></msubsup><msubsup><mrow><mi>Λ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup></mrow></math> reaction are evaluated. Our study indicates that the cross section for <math><mrow><mi>γ</mi><mi>p</mi><mo>→</mo><msup><mrow><mi>D</mi></mrow><mrow><mo>+</mo></mrow></msup><msubsup><mrow><mover><mrow><mi>T</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mi>c</mi><mi>c</mi></mrow><mrow><mo>−</mo></mrow></msubsup><msubsup><mrow><mi>Λ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup></mrow></math> reaction is on the order of 1.0 pb, which is accessible at the proposed the Electron-Ion Collider in China [Front. Phys. (Beijing) 16, 64701 (2021)] or the U.S. [Eur. Phys. J. A 52, 268 (2016)] due to the higher luminosity. If measured and confirmed in the future experiments, the predicted total cross sections can be used to verify the (molecular) nature of the <math><msubsup><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow><mo>+</mo></msubsup></math>.

South Korea

Li-Sheng Geng

Production of <math><mrow><msubsup><mrow><mi>T</mi></mrow><mrow><mi>c</mi><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup></mrow></math> exotic state in the <math><mrow><mi>γ</mi><mi>p</mi><mo>→</mo><msup><mrow><mi>D</mi></mrow><mrow><mo>+</mo></mrow></msup><msubsup><mrow><mover><mrow><mi>T</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mi>c</mi><mi>c</mi></mrow><mrow><mo>−</mo></mrow></msubsup><msubsup><mrow><mi>Λ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup></mrow></math> reaction

We investigate the possibility of studying the strange hidden-charm pentaquark state <math><msub><mi>P</mi><mrow><mi>c</mi><mi>s</mi></mrow></msub><mo>(</mo><mn>4459</mn><mo>)</mo></math> by photon-induced reactions on a proton target in an effective Lagrangian approach. The production process is described by the <math><mi>t</mi></math>-channel <math><msup><mi>K</mi><mo>−</mo></msup></math> exchange, the <math><mi>u</mi></math>-channel <math><mi>Λ</mi></math> exchange, the contract term, and the <math><mi>s</mi></math>- channel nucleon pole. Our theoretical approach is based on the assumption that <math><msub><mi>P</mi><mrow><mi>c</mi><mi>s</mi></mrow></msub><mo>(</mo><mn>4459</mn><mo>)</mo></math> with <math><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></math> or <math><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><mn>3</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></math> can be interpreted as a molecule composed of <math><msup><mover><mi>D</mi><mo>¯</mo></mover><mo>*</mo></msup><msub><mi>Ξ</mi><mi>c</mi></msub></math>. Using the coupling constants of the <math><msubsup><mi>P</mi><mrow><mi>c</mi><mi>s</mi></mrow><msup><mi>J</mi><mi>P</mi></msup></msubsup></math> to <math><mi>γ</mi><mi>Λ</mi></math> and <math><msup><mi>K</mi><mo>−</mo></msup><mi>p</mi></math> channels obtained from molecule picture of the <math><msubsup><mi>P</mi><mrow><mi>c</mi><mi>s</mi></mrow><msup><mi>J</mi><mi>P</mi></msup></msubsup><mo>(</mo><mn>4459</mn><mo>)</mo></math>, the total cross-sections of the process <math><mi>γ</mi><mi>p</mi><mo>→</mo><msubsup><mi>P</mi><mrow><mi>c</mi><mi>s</mi></mrow><msup><mi>J</mi><mi>P</mi></msup></msubsup><msup><mi>K</mi><mo>+</mo></msup></math> is evaluated. Our calculation indicates that the cross-section for <math><mi>γ</mi><mi>p</mi><mo>→</mo><msubsup><mi>P</mi><mrow><mi>c</mi><mi>s</mi></mrow><mrow><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></mrow></msubsup><msup><mi>K</mi><mo>+</mo></msup></math> and <math><mi>γ</mi><mi>p</mi><mo>→</mo><msubsup><mi>P</mi><mrow><mi>c</mi><mi>s</mi></mrow><mrow><mn>3</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></mrow></msubsup><msup><mi>K</mi><mo>+</mo></msup></math> are of the order of 10.0 pb and 5.0 pb, respectively. In addition, we compute the cross section by assuming <math><msub><mi>P</mi><mrow><mi>c</mi><mi>s</mi></mrow></msub><mo>(</mo><mn>4459</mn><mo>)</mo></math> as a compact pentaquark and find it is quite different from the results of <math><msup><mover><mi>D</mi><mo>¯</mo></mover><mo>*</mo></msup><msub><mi>Ξ</mi><mi>c</mi></msub></math> molecule. Those results can be measured in future experiments, such as the Electron-Ion Collider in China and the United States, and can be used to test the nature of the <math><msub><mi>P</mi><mrow><mi>c</mi><mi>s</mi></mrow></msub></math>.

Feng Yang

Searching for strange hidden-charm pentaquark state <math><msub><mi>P</mi><mrow><mi>c</mi><mi>s</mi></mrow></msub><mo>(</mo><mn>4459</mn><mo>)</mo></math> in <math><mi>γ</mi><mi>p</mi><mo>→</mo><msup><mi>K</mi><mo>+</mo></msup><msub><mi>P</mi><mrow><mi>c</mi><mi>s</mi></mrow></msub><mo>(</mo><mn>4459</mn><mo>)</mo></math> reaction

In this work, we report on a theoretical study of possible pentaquark states <math><msubsup><mi>Λ</mi><mi>b</mi><mn>0</mn></msubsup><mo>(</mo><mn>5912</mn><mo>)</mo></math> and <math><msubsup><mi>Λ</mi><mi>b</mi><mn>0</mn></msubsup><mo>(</mo><mn>5920</mn><mo>)</mo></math> in the <math><mrow><mi>γ</mi><mi>p</mi><mo>→</mo><msubsup><mrow><mi>Λ</mi></mrow><mrow><mi>b</mi></mrow><mrow><mn>0</mn><mo>(</mo><mo>*</mo><mo>)</mo></mrow></msubsup><msup><mrow><mi>B</mi></mrow><mrow><mo>+</mo></mrow></msup></mrow></math> reactions within an effective Lagrangian approach. In addition to the contributions from the <math><mi>s</mi></math>-channel nucleon pole and <math><mi>t</mi></math>-channel <math><mrow><msup><mrow><mover><mrow><mi>B</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mo>*</mo><mo>−</mo></mrow></msup></mrow></math> exchange, the contact term contribution is also included. Our theoretical approach is based on the chiral unitary theory where the <math><msubsup><mi>Λ</mi><mi>b</mi><mn>0</mn></msubsup><mo>(</mo><mn>5912</mn><mo>)</mo></math> and <math><msubsup><mi>Λ</mi><mi>b</mi><mn>0</mn></msubsup><mo>(</mo><mn>5920</mn><mo>)</mo></math> resonances are dynamically generated. Within the coupling constants of the <math><msubsup><mi>Λ</mi><mi>b</mi><mn>0</mn></msubsup><mo>(</mo><mn>5912</mn><mo>)</mo></math> and <math><msubsup><mi>Λ</mi><mi>b</mi><mn>0</mn></msubsup><mo>(</mo><mn>5920</mn><mo>)</mo></math> to <math><mover><mi>B</mi><mo>¯</mo></mover><mi>p</mi></math> and <math><msup><mover><mi>B</mi><mo>¯</mo></mover><mo>*</mo></msup><mi>p</mi></math> channels obtained from chiral unitary theory, the total and differential cross sections of the <math><mi>γ</mi><mi>p</mi><mo>→</mo><msubsup><mi>Λ</mi><mi>b</mi><mrow><mn>0</mn><mo>(</mo><mo>*</mo><mo>)</mo></mrow></msubsup><msup><mi>B</mi><mo>+</mo></msup></math> are evaluated. Our calculation indicates that the cross section for <math><mi>γ</mi><mi>p</mi><mo>→</mo><msubsup><mi>Λ</mi><mi>b</mi><mn>0</mn></msubsup><mo>(</mo><mn>5912</mn><mo>)</mo><msup><mi>B</mi><mo>+</mo></msup></math> and <math><mi>γ</mi><mi>p</mi><mo>→</mo><msubsup><mi>Λ</mi><mi>b</mi><mn>0</mn></msubsup><mo>(</mo><mn>5920</mn><mo>)</mo><msup><mi>B</mi><mo>+</mo></msup></math> reactions are of the order of 0.0164 and 0.00527 nb, respectively. If measured in future experiments, such as the Electron-Ion Collider in China or the United States, then the predicted total cross sections and specific features of the angular distributions can be used to test the (molecular) nature of the <math><msubsup><mi>Λ</mi><mi>b</mi><mn>0</mn></msubsup><mo>(</mo><mn>5912</mn><mo>)</mo></math> and <math><msubsup><mi>Λ</mi><mi>b</mi><mn>0</mn></msubsup><mo>(</mo><mn>5920</mn><mo>)</mo></math> that they may be pentaquark states.

Photoproduction of possible pentaquark states <math><mrow><msubsup><mrow><mi>Λ</mi></mrow><mrow><mi>b</mi></mrow><mrow><mn>0</mn></mrow></msubsup><mo>(</mo><mn>5912</mn><mo>)</mo></mrow></math> and <math><msubsup><mi>Λ</mi><mi>b</mi><mn>0</mn></msubsup><mo>(</mo><mn>5920</mn><mo>)</mo></math> in the <math><mrow><mi>γ</mi><mi>p</mi><mo>→</mo><msubsup><mrow><mi>Λ</mi></mrow><mrow><mi>b</mi></mrow><mrow><mn>0</mn><mo>(</mo><mo>*</mo><mo>)</mo></mrow></msubsup><msup><mrow><mi>B</mi></mrow><mrow><mo>+</mo></mrow></msup></mrow></math> reactions

Last year, the   $ \Xi(1620) $   state, which is cataloged in the Particle Data Group (PDG) with only one star, was reported again in the   $ \Xi(1620) $   final state by the Belle Collaboration. Its properties, such as the spectroscopy and decay width, cannot be simply explained in the context of conventional constituent quark models. This inspires an active discussion on the structure of this resonance. In this paper, we study the radiative decays of the newly observed   $ \Xi(1620) $   assuming that it is a meson-baryon molecular state of   $ \Xi(1620) $   and   $ \Xi(1620) $   with spin-parity   $ \Xi(1620) $   developed in our previous study. The partial decay widths of the   $ \Xi(1620) $   molecular state into   $ \Xi(1620) $   and   $ \Xi(1620) $   final states through hadronic loops are evaluated using effective Lagrangians. The partial widths for   $ \Xi(1620) $   is evaluated to be approximately   $ \Xi(1620) $   keV, which may be accessible for the LHCb experiment. If   $ \Xi(1620) $   is a   $ \Xi(1620) $   molecule, the radiative transition strength   $ \Xi(1620) $   is considerably small and the decay width is of the order of 0.01 eV. Future experimental measurements of these processes can be useful to test the molecule interpretations of the   $ \Xi(1620) $  .

HongQiang Zhu

Radiative decay of the Ξ(1620) in a hadronic molecule picture  

Very recently, three new structures  $$\Xi _c(2923)^0$$  <math> <mrow> <msub> <mi>Ξ</mi> <mi>c</mi> </msub> <msup> <mrow> <mo>(</mo> <mn>2923</mn> <mo>)</mo> </mrow> <mn>0</mn> </msup> </mrow> </math>  ,  $$\Xi _c(2938)^0$$  <math> <mrow> <msub> <mi>Ξ</mi> <mi>c</mi> </msub> <msup> <mrow> <mo>(</mo> <mn>2938</mn> <mo>)</mo> </mrow> <mn>0</mn> </msup> </mrow> </math>  , and  $$\Xi _c(2964)^0$$  <math> <mrow> <msub> <mi>Ξ</mi> <mi>c</mi> </msub> <msup> <mrow> <mo>(</mo> <mn>2964</mn> <mo>)</mo> </mrow> <mn>0</mn> </msup> </mrow> </math>   at the invariant mass spectrum of  $$\Lambda _c^{+}K^{-}$$  <math> <mrow> <msubsup> <mi>Λ</mi> <mi>c</mi> <mo>+</mo> </msubsup> <msup> <mi>K</mi> <mo>-</mo> </msup> </mrow> </math>   observed by the LHCb Collaboration trigger a hot discussion about their inner structure. In this work, we study the strong decay mode of the newly observed  $$\Xi ^0_c$$  <math> <msubsup> <mi>Ξ</mi> <mi>c</mi> <mn>0</mn> </msubsup> </math>   assuming that the  $$\Xi ^0_c$$  <math> <msubsup> <mi>Ξ</mi> <mi>c</mi> <mn>0</mn> </msubsup> </math>   is a  $$\bar{D}\Lambda -\bar{D}\Sigma $$  <math> <mrow> <mover> <mrow> <mi>D</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> <mi>Λ</mi> <mo>-</mo> <mover> <mrow> <mi>D</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> <mi>Σ</mi> </mrow> </math>   molecular state. With the possible quantum numbers  $$J^p=1/2^{\pm }$$  <math> <mrow> <msup> <mi>J</mi> <mi>p</mi> </msup> <mo>=</mo> <mn>1</mn> <mo>/</mo> <msup> <mn>2</mn> <mo>±</mo> </msup> </mrow> </math>   and  $$3/2^{\pm }$$  <math> <mrow> <mn>3</mn> <mo>/</mo> <msup> <mn>2</mn> <mo>±</mo> </msup> </mrow> </math>  , the partial decay widths of the  $$\bar{D}\Lambda -\bar{D}\Sigma $$  <math> <mrow> <mover> <mrow> <mi>D</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> <mi>Λ</mi> <mo>-</mo> <mover> <mrow> <mi>D</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> <mi>Σ</mi> </mrow> </math>   molecular state into the  $$\Lambda _c^{+}K^{-}$$  <math> <mrow> <msubsup> <mi>Λ</mi> <mi>c</mi> <mo>+</mo> </msubsup> <msup> <mi>K</mi> <mo>-</mo> </msup> </mrow> </math>  ,  $$\Sigma _c^{+}K^{-}$$  <math> <mrow> <msubsup> <mi>Σ</mi> <mi>c</mi> <mo>+</mo> </msubsup> <msup> <mi>K</mi> <mo>-</mo> </msup> </mrow> </math>  ,and  $$\Xi _c^{+}\pi ^{-}$$  <math> <mrow> <msubsup> <mi>Ξ</mi> <mi>c</mi> <mo>+</mo> </msubsup> <msup> <mi>π</mi> <mo>-</mo> </msup> </mrow> </math>   final states through hadronic loop are calculated with the help of the effective Lagrangians. By comparison with the LHCb observation, the current results of total decay width support the  $$\Xi _c(2923)^0$$  <math> <mrow> <msub> <mi>Ξ</mi> <mi>c</mi> </msub> <msup> <mrow> <mo>(</mo> <mn>2923</mn> <mo>)</mo> </mrow> <mn>0</mn> </msup> </mrow> </math>   as  $$\bar{D}\Lambda -\bar{D}\Sigma $$  <math> <mrow> <mover> <mrow> <mi>D</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> <mi>Λ</mi> <mo>-</mo> <mover> <mrow> <mi>D</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> <mi>Σ</mi> </mrow> </math>   molecule while the decay width of the  $$\Xi _c(2938)^0$$  <math> <mrow> <msub> <mi>Ξ</mi> <mi>c</mi> </msub> <msup> <mrow> <mo>(</mo> <mn>2938</mn> <mo>)</mo> </mrow> <mn>0</mn> </msup> </mrow> </math>   and  $$\Xi _c(2964)^0$$  <math> <mrow> <msub> <mi>Ξ</mi> <mi>c</mi> </msub> <msup> <mrow> <mo>(</mo> <mn>2964</mn> <mo>)</mo> </mrow> <mn>0</mn> </msup> </mrow> </math>   can not be well reproduced in the molecular state picture. In addition, the calculated partial decay widths with S wave  $$\bar{D}\Lambda -\bar{D}\Sigma $$  <math> <mrow> <mover> <mrow> <mi>D</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> <mi>Λ</mi> <mo>-</mo> <mover> <mrow> <mi>D</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> <mi>Σ</mi> </mrow> </math>   molecular state picture indicate that allowed decay mode,  $$\Xi _c^{+}\pi ^{-}$$  <math> <mrow> <msubsup> <mi>Ξ</mi> <mi>c</mi> <mo>+</mo> </msubsup> <msup> <mi>π</mi> <mo>-</mo> </msup> </mrow> </math>  , may have the biggest branching ratio for the  $$\Xi _c(2923)^0$$  <math> <mrow> <msub> <mi>Ξ</mi> <mi>c</mi> </msub> <msup> <mrow> <mo>(</mo> <mn>2923</mn> <mo>)</mo> </mrow> <mn>0</mn> </msup> </mrow> </math>  . The experimental measurements for this strong decay process could be a crucial test for the molecule interpretation of the  $$\Xi _c(2923)^0$$  <math> <mrow> <msub> <mi>Ξ</mi> <mi>c</mi> </msub> <msup> <mrow> <mo>(</mo> <mn>2923</mn> <mo>)</mo> </mrow> <mn>0</mn> </msup> </mrow> </math>  .