The coalescence production of the sexaquark, a hypothetical stable state with quark content <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><mi>u</mi><mi>u</mi><mi>d</mi><mi>d</mi><mi>s</mi><mi>s</mi><mo stretchy="false">)</mo></math>, is investigated using the parton and hadron cascade model PACIAE in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi><mi>p</mi></math> collisions at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>7</mn><mtext> </mtext><mtext> </mtext><mi>TeV</mi></math>. In this work, the compact sexaquark bound state of three diquarks is formed in the final partonic state by a two-step approach, which involves “diquark” formation via partonic coalescence and sexaquark construction with the dynamically constrained phase-space coalescence model successively. The yields, yield ratios, and dependences of the spatial parameters (the size of the diquark <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>D</mi><mn>0</mn></msub></math> and the radius of the sexaquark <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>R</mi><mn>0</mn></msub></math>) of a (anti)sexaquark are predicted. The yields of the hadronic H-dibaryon molecule <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">H</mi><mo stretchy="false">(</mo><mi mathvariant="normal">Λ</mi><mi mathvariant="normal">Λ</mi><mo stretchy="false">)</mo></math> generated in the final hadronic state are also compared. These estimates provide references for future sexaquark searches and other exotic state studies, such as dibaryons.

China

Zhi-Lei She

Norway

An-Ke Lei

Dai-Mei Zhou

Larissa V. Bravina

Russia

Evgeny E. Zabrodin

Chile

Sonia Kabana

Vipul Bairathi

Coalescence production of sexaquark with three diquarks in high-energy nuclear collisions

The pseudorapidity density distributions of charged particles and the transverse-momentum spectra of identified particles in proton-proton (<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>p</mi><mi>p</mi></mrow></math>) collisions at the center-of-mass energies ranging from <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>200</mn></mrow></math> GeV to 13 TeV have been systematically studied using the newly released parton and cascade model paciae 4.0 based on pythia 8.3. The available experimental data are well reproduced across all analyzed aspects. This theoretical method can be easily extended to anywhere the experimental data for <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>p</mi><mi>p</mi></mrow></math> collisions are currently unavailable. Furthermore, since <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>p</mi><mi>p</mi></mrow></math> collisions serve as the baseline for heavy-ion collisions, our results can provide a valuable resource for both experimentalists and theorists.

Zhen Xie

Hua Zheng

Wenchao Zhang

Yu-Liang Yan

Ben-Hao Sa

Pseudorapidity density distributions of charged particles and transverse-momentum spectra of identified particles in <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>p</mi><mi>p</mi></mrow></math> collisions in the PACIAE 4.0 model

Inspired by the BESIII observation of exotic hadron <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>G</mi><mo stretchy="false">(</mo><mn>3900</mn><mo stretchy="false">)</mo></math> 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><mo stretchy="false">→</mo><mi>D</mi><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover></math> process [M. Ablikim et al. (BESIII Collaboration), <a href="http://dx.doi.org/10.1103/PhysRevLett.133.081901">Phys. Rev. Lett. 133, 081901 (2024)</a>], we use the parton and hadron cascade model PACIAE to simulate the productions of charmonium-like exotic hadrons, including <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>, <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><msup><mo stretchy="false">)</mo><mn>0</mn></msup></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>G</mi><mo stretchy="false">(</mo><mn>3900</mn><mo stretchy="false">)</mo></math> 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> annihilations at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>4.95</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>. The charmonium-like candidates are recombined by the dynamically constrained phase-space coalescence model using component mesons <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover></math> [for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>G</mi><mo stretchy="false">(</mo><mn>3900</mn><mo stretchy="false">)</mo></math>] or <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><mo>/</mo><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><msup><mi>D</mi><mo>*</mo></msup></math> [for <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>, <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><msup><mo stretchy="false">)</mo><mn>0</mn></msup></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>G</mi><mo stretchy="false">(</mo><mn>3900</mn><mo stretchy="false">)</mo></math>] in the PACIAE simulated final hadronic state. We then calculate, for the first time, the charmonium-like candidate’s orbital angular momentum quantum number in its rest frame and perform the spectral classification for each of the above candidates. For <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>G</mi><mo stretchy="false">(</mo><mn>3900</mn><mo stretchy="false">)</mo></math>, as its <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>J</mi><mrow><mi>P</mi><mi>C</mi></mrow></msup></math> is <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>1</mn><mrow><mo>−</mo><mo>−</mo></mrow></msup></math>, it is identified as the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>P</mi></math>-wave <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover></math> or <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><mo>/</mo><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><msup><mi>D</mi><mo>*</mo></msup></math> state. Meanwhile, for <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> 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>3900</mn><msup><mo stretchy="false">)</mo><mn>0</mn></msup></math>, as their <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>J</mi><mrow><mi>P</mi><mi>C</mi></mrow></msup><mrow><mi mathvariant="normal">s</mi></mrow></math> are, respectively, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>1</mn><mrow><mo>+</mo><mo>+</mo></mrow></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>1</mn><mrow><mo>+</mo><mo>−</mo></mrow></msup></math>, they are identified as the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi></math>-wave <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><mo>/</mo><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><msup><mi>D</mi><mo>*</mo></msup></math> candidates. It is observed that the yield of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>P</mi></math>-wave <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>G</mi><mo stretchy="false">(</mo><mn>3900</mn><mo stretchy="false">)</mo></math> composed of <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><mo>/</mo><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><msup><mi>D</mi><mo>*</mo></msup></math> is significantly larger than that composed of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover></math>. Moreover, in the <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><mo>/</mo><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><msup><mi>D</mi><mo>*</mo></msup></math> channel, the yield of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>P</mi></math>-wave <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>G</mi><mo stretchy="false">(</mo><mn>3900</mn><mo stretchy="false">)</mo></math> is around three times as large as the yield of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi></math>-wave <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><msup><mo stretchy="false">)</mo><mn>0</mn></msup></math>, and it is around two orders of magnitude as large as the yield of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi></math>-wave <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>. Finally, significant discrepancies are observed in the transverse momentum spectra and the rapidity distributions among 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>, <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><msup><mo stretchy="false">)</mo><mn>0</mn></msup></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>G</mi><mo stretchy="false">(</mo><mn>3900</mn><mo stretchy="false">)</mo></math> states. These discrepancies are proposed as valuable criteria for identifying the different charmonium-like exotic hadrons from each other.

Jian Cao

Wen-Chao Zhang

Jin-Peng Zhang

Zhong-Qi Wang

Charmonium-like exotic hadron productions in <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> collisions at the BESIII energy with the PACIAE model

Inspired by the BESIII newest observation of X(2370) glueball-like particle, we search its productions in both <math><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup></math> collisions at <math><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>4.95</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math> and proton-proton (pp) collisions at <math><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>13</mn><mtext> </mtext><mtext> </mtext><mi>TeV</mi></math> with a parton and hadron cascade model PACIAE. In this model, the final partonic state (FPS) and the final hadronic state (FHS) are consecutively simulated and recorded. The X(2370) glueball- or tetraquark-state is then, respectively, recombined by two gluons or four quarks <math><mi>s</mi><mi>s</mi><mover><mi>s</mi><mo>¯</mo></mover><mover><mi>s</mi><mo>¯</mo></mover></math> in the FPS using the quantum statistical mechanics inspired dynamically constrained phase-space coalescence (DCPC) model. The X(2370) molecular-state is recombined by the baryon-antibaryon of <math><mrow><mi>Λ</mi><mtext>−</mtext><mover><mrow><mi>Λ</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow></math> or <math><mrow><mi>Σ</mi><mtext>−</mtext><mover><mrow><mi>Σ</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow></math>, or by three mesons of <math><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><msup><mi>η</mi><mo>′</mo></msup></math>, <math><msup><mi>K</mi><mo>+</mo></msup><msup><mi>K</mi><mo>−</mo></msup><msup><mi>η</mi><mo>′</mo></msup></math>, or <math><msubsup><mi>K</mi><mi>S</mi><mn>0</mn></msubsup><msubsup><mi>K</mi><mi>S</mi><mn>0</mn></msubsup><msup><mi>η</mi><mo>′</mo></msup></math> in the FHS using DCPC model. In both <math><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup></math> and pp collisions, significant discrepancies in the yields, the transverse momentum spectra and the rapidity distributions among the X(2370) glueball-, tetraquark-, and molecular-state are observed. These discrepancies are proposed as valuable criteria identifying the X(2370) different states from each other. Our results not only support the BESIII observation of glueball-like particle X(2370) production in <math><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup></math> collisions, but also serve as a prediction for the X(2370) production in pp collisions. We strongly suggest the experimental measurement of the X(2370) glueball-like particle production in pp collisions at the LHC energies.

Jia-Hao Shi

Zhi-Ying Qin

X(2370) glueball-like particle productions in <math><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup></math> collisions at the BESIII energy and in pp collisions at the LHC energy with the PACIAE model

The production of exotic hadron <math><mrow><mi>X</mi><mo>(</mo><mn>3872</mn><mo>)</mo></mrow></math> in <math><mrow><mi>p</mi><mi>p</mi></mrow></math> collisions at <math><mrow><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>2.76</mn><mspace width="0.16em"></mspace><mi>TeV</mi></mrow></math> is investigated by the parton and hadron cascade model PACIAE in this work. In the simulation the final partonic state (quark matter, QM) and the final hadronic state (hadron matter, HM) are continuously processed and recorded. The <math><mrow><mi>X</mi><mo>(</mo><mn>3872</mn><mo>)</mo></mrow></math> compact tetraquark state and loose molecular state are, respectively, coalesced and recombined in the QM and HM with the quantum statistical mechanics inspired dynamically constrained phase-space coalescence model. The formation time, velocity, and temperature of QM (tetraquark state) and HM (molecular state) are proposed as identifying criteria between the two states. Our results in transverse momentum spectrum and rapidity distribution, etc. show a significant discrepancy between the two states and confirm that they are also valuable criteria identifying the <math><mrow><mi>X</mi><mo>(</mo><mn>3872</mn><mo>)</mo></mrow></math> compact tetraquark state or molecular state.

Liang Zheng

Yi-Long Xie

Gang Chen

Identifying an <math><mtext>X(3872)</mtext></math> tetraquark state versus a molecular state by formation time, velocity, and temperature in relativistic nuclear collisions

In this work we investigate the <math><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></math> production in proton-proton collisions at the center-of-mass energy <math><mo>(</mo><msqrt><mi>s</mi></msqrt><mo>)</mo></math> equal to 2.76, 5.02, 7, 8, and 13 TeV with the parton and hadron cascade model PACIAE 2.2a. It is based on PYTHIA but extended considering the partonic and hadronic rescatterings before and after hadronization, respectively. In the PYTHIA sector the <math><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></math> production quantum chromodynamics processes are selected specially and a bias factor is proposed correspondingly. The calculated total cross sections, the transverse momentum differential, and the rapidity differential cross sections of <math><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></math> in the forward rapidity region reproduce the corresponding experimental measurements reasonably well. In the mid-rapidity region, the double-differential cross sections at <math><mrow><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>5.02</mn></mrow></math>, 7, and 13 TeV are also in a good agreement with the experimental data. Moreover, we interpolate the double-differential cross section as well as the total cross section of <math><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></math> in the mid-rapidity region at <math><mrow><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>8</mn></mrow></math> TeV, which could be validated if the experimental data are available.

Kai-Fan Ye

Qiang Wang

Energy dependence of <math><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></math> production in <math><mrow><mi>p</mi><mi>p</mi></mrow></math> collisions from the PACIAE model

We develop a parton and hadron cascade model paciae 3.0 based on pythia 6.428 and the paciae 2.2 program series for nuclear collisions. The original simulation framework composed of the initial partonic state, the partonic rescattering stage, hadronization stage, and the hadronic rescattering stage, is renamed a C-simulation framework for high-energy (<math><mrow><msqrt><msub><mi>s</mi><mrow><mi>N</mi><mi>N</mi></mrow></msub></msqrt><mo>≥</mo><mn>3</mn></mrow></math> GeV) nuclear collisions. A B-simulation framework without partonic rescattering is designed for the high-energy nuclear collisions, too. In addition, an A-simulation framework is introduced for the low-energy (<math><mrow><msqrt><msub><mi>s</mi><mrow><mi>N</mi><mi>N</mi></mrow></msub></msqrt><mo>&lt;</mo><mn>3</mn></mrow></math> GeV) nuclear collisions, which is developed in the hadronic degree of freedom only. In the C-simulation framework, the parton-parton inelastic-scattering processes are implemented, the single-string structure and multiple-string interaction mechanisms are proposed to investigate the strangeness enhancement, and the phenomenological coalescence hadronization model is modified. With the model, the particle yield, transverse momentum distribution, and rapidity distribution resulted from A-simulation framework well reproduce the data measured at the FOPI and E895 experiments, and the results from B- and C-simulation frameworks are well consistent with the data measured at the energies of the BNL Relativistic Heavy Ion Collider and the Large Hadron Collider.

Gao-Chan Yong

Xiao-Mei Li

Xu Cai

Introduction to the parton and hadron cascade model PACIAE 3.0

A dynamically constrained phase-space coalescence (dcpc) model was introduced to study the exotic state <math><msub><mi>χ</mi><mrow><mi>c</mi><mn>1</mn></mrow></msub><mo>(</mo><mn>3872</mn><mo>)</mo></math> yield for three possible structures: tetraquark state, nuclearlike state, and molecular state respectively, where the hadronic final states generated by the parton and hadron cascade model (paciae). The <math><mrow><msub><mrow><mi>χ</mi></mrow><mrow><mi>c</mi><mn>1</mn></mrow></msub><mo>(</mo><mn>3872</mn><mo>)</mo><mo>/</mo><mi>ψ</mi><mo>(</mo><mn>2</mn><mi>S</mi><mo>)</mo></mrow></math> cross-section ratio from beauty-hadron decays (nonprompt) based on the <math><mrow><msub><mrow><mi>χ</mi></mrow><mrow><mi>c</mi><mn>1</mn></mrow></msub><mo>(</mo><mn>3872</mn><mo>)</mo></mrow></math> or <math><mrow><mi>ψ</mi><mo>(</mo><mn>2</mn><mi>S</mi><mo>)</mo><mo>→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><msup><mrow><mi>π</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mo>−</mo></mrow></msup></mrow></math> bound state in the decay chains as a function of charged-particle multiplicity and transverse momentum in <math><mi>p</mi><mi>p</mi></math> collisions at <math><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>8</mn><mtext> </mtext><mtext> </mtext><mi>TeV</mi></math> are calculated. A tetraquark state scenario from paciae<math><mrow><mo>+</mo></mrow></math>dcpc model shows better agreement with the LHCb and ATLAS measurements for the nonprompt <math><mrow><msub><mrow><mi>χ</mi></mrow><mrow><mi>c</mi><mn>1</mn></mrow></msub><mo>(</mo><mn>3872</mn><mo>)</mo><mo>/</mo><mi>ψ</mi><mo>(</mo><mn>2</mn><mi>S</mi><mo>)</mo></mrow></math> cross-section ratio distributions, indicating that the <math><msub><mi>χ</mi><mrow><mi>c</mi><mn>1</mn></mrow></msub><mo>(</mo><mn>3872</mn><mo>)</mo></math> is more likely to be a compact tetraquark state.

Chun-tai Wu

Xin-Ye Peng

Xiao-Lin Kang

Hong-Ge Xu

Study on the structure of exotic states <math><mrow><msub><mrow><mi>χ</mi></mrow><mrow><mi>c</mi><mn>1</mn></mrow></msub><mo>(</mo><mn>3872</mn><mo>)</mo></mrow></math> via beauty-hadron decays in <math><mi>p</mi><mi>p</mi></math> collisions at <math><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>8</mn><mtext> </mtext><mtext> </mtext><mi>TeV</mi></math>

The exotic resonant states <math><msubsup><mi>P</mi><mi>c</mi><mo>±</mo></msubsup><mo>(</mo><mn>4312</mn><mo>)</mo></math>, <math><msubsup><mi>P</mi><mi>c</mi><mo>±</mo></msubsup><mo>(</mo><mn>4440</mn><mo>)</mo></math>, and <math><msubsup><mi>P</mi><mi>c</mi><mo>±</mo></msubsup><mo>(</mo><mn>4457</mn><mo>)</mo></math> are studied using the constrained phase-space coalescence model plus the parton and hadron cascade (paciae) model in <math><mi>p</mi><mi>p</mi></math> collisions at <math><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>7</mn></math>, 13 TeV, respectively. The pentaquark states, the nucleuslike states, and the hadronic molecular states are considered as their possible structures based on the <math><msubsup><mi>P</mi><mi>c</mi><mo>±</mo></msubsup><mo>→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mi>p</mi><mrow><mo>(</mo><mover><mi>p</mi><mo>¯</mo></mover><mo>)</mo></mrow></math> bound state. The predictions about the yield, the normalized <math><msub><mi>p</mi><mi>T</mi></msub></math>-differential yield, and the normalized rapidity-differential yield are presented for the aforementioned scenarios. The results indicate a hierarchy of the yields for different possible structures; they are all on the order of <math><msup><mn>10</mn><mrow><mo>−</mo><mn>6</mn></mrow></msup></math>. These predictions can be tested by future experimental measurements.

Chun-hui Chen

Hong-ge Xu

Zhen Zhang

Exotic states <math><msub><mi>P</mi><mi>c</mi></msub><mo>(</mo><mn>4312</mn><mo>)</mo></math>, <math><msub><mi>P</mi><mi>c</mi></msub><mo>(</mo><mn>4440</mn><mo>)</mo></math>, and <math><msub><mi>P</mi><mi>c</mi></msub><mo>(</mo><mn>4457</mn><mo>)</mo></math> in <math><mi>p</mi><mi>p</mi></math> collisions at <math><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>7</mn></math>, 13 TeV

We have used the dynamically constrained phase space coalescence model to study the production of the exotic state X(3872) based on the hadronic final states generated by the parton and hadron cascade model (PACIAE) with $$|y|&lt;1$$ <math> <mrow> <mo>|</mo> <mi>y</mi> <mo>|</mo> <mo>&lt;</mo> <mn>1</mn> </mrow> </math> and $$p_T &lt; 15.5$$ <math> <mrow> <msub> <mi>p</mi> <mi>T</mi> </msub> <mo>&lt;</mo> <mn>15.5</mn> </mrow> </math> GeV/c in pp collisions at $$\sqrt{s}=7$$ <math> <mrow> <msqrt> <mi>s</mi> </msqrt> <mo>=</mo> <mn>7</mn> </mrow> </math> and 13 TeV, respectively. Here the X(3872) is assumed to consist of bound state $$D\bar{D^*}$$ <math> <mrow> <mi>D</mi> <mover> <mrow> <msup> <mi>D</mi> <mo>∗</mo> </msup> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> </math> , which can form three possible structures for the tetraquark state, the nucleus-like state, and the molecular state. The yields of three different structures X(3872) were predicted. The transverse momentum distribution and the rapidity distribution of three different structures X(3872) are also presented. Sizable difference can be found in the transverse momentum and rapidity distributions for the three different X(3872) structures.

Investigation of exotic state X(3872) in pp collisions at $$\sqrt{s}=7$$ <math> <mrow> <msqrt> <mi>s</mi> </msqrt> <mo>=</mo> <mn>7</mn> </mrow> </math> , 13 TeV