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.

China

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.

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.

Qing-Fu Song

Qi-Fang Lü

Dian-Yong Chen

Yu-Bing Dong

Predicting hidden bottom molecular tetraquarks with a complex scaling method

We adopt the quark pair creation model to investigate the light meson emissions of several charmonium-like states. The quark pair creation model is applied to four-body systems, and we calculate the pion/kaon emissions of   $ X(4700) $  ,   $ X(4700) $  ,   $ X(4700) $  ,   $ X(4700) $  ,   $ X(4700) $  , and   $ X(4700) $   within compact tetraquark configurations. We find that the pion/kaon decay widths of   $ X(4700) $   and   $ X(4700) $   are relatively small, whereas the partial decay widths of the resonances   $ X(4700) $  ,   $ X(4700) $  ,   $ X(4700) $  , and   $ X(4700) $   are significant. We expect that our exploration of these decay behaviors will provide useful information for future experimental searches and theoretical interpretations.

Ning Li

Hui-Zhen He

Wei Liang

Japan

Light meson emissions of selected charmonium-like states within compact tetraquark configurations  

In this paper, we propose to investigate the   $ d_{N\Omega} $   dibaryon production in the   $ d_{N\Omega} $   process by utilizing a kaon beam with a typical momentum of approximately 10 GeV, which may be available at COMPASS, OKA@U-70, and SPS@CERN. The cross sections for   $ d_{N\Omega} $   are estimated, and in particular, the magnitude of the cross sections is evaluated to be several hundred nanobarns at   $ d_{N\Omega} $   GeV. Considering that the   $ d_{N\Omega} $   dibaryon dominantly decays into   $ d_{N\Omega} $   and   $ d_{N\Omega} $  , we also estimate the cross sections for   $ d_{N\Omega} $   and   $ d_{N\Omega} $     $ d_{N\Omega} $  , where the   $ d_{N\Omega} $   dibaryon can be observed in the invariant mass distributions of   $ d_{N\Omega} $   and   $ d_{N\Omega} $  , respectively.

Jing Liu

Chun-Hua Liu

Production of Dibaryon in Kaon Induced Reactions  

Inspired by the recent observation of a new structure, <math><mi>X</mi><mo>(</mo><mn>4014</mn><mo>)</mo></math>, in the process <math><mi>γ</mi><mi>γ</mi><mo>→</mo><mi>γ</mi><mi>ψ</mi><mo>(</mo><mn>2</mn><mi>S</mi><mo>)</mo></math>, we evaluate the possibility of assigning <math><mi>X</mi><mo>(</mo><mn>4014</mn><mo>)</mo></math> as a <math><msup><mi>D</mi><mo>*</mo></msup><msup><mover><mi>D</mi><mo>¯</mo></mover><mo>*</mo></msup></math> molecular state with <math><mi>I</mi><mo>(</mo><msup><mi>J</mi><mrow><mi>P</mi><mi>C</mi></mrow></msup><mo>)</mo><mo>=</mo><mn>0</mn><mo>(</mo><msup><mn>0</mn><mrow><mo>+</mo><mo>+</mo></mrow></msup><mo>)</mo></math> by investigating the hidden charm decays of <math><mi>X</mi><mo>(</mo><mn>4014</mn><mo>)</mo></math>. The partial widths of <math><mi>J</mi><mo>/</mo><mi>ψ</mi><mi>ω</mi></math>, <math><msub><mi>η</mi><mi>c</mi></msub><mi>η</mi></math> and <math><msub><mi>η</mi><mi>c</mi></msub><msup><mi>η</mi><mo>′</mo></msup></math> channels are evaluated to be about (0.41–5.00), (2.05–7.49) and (0.11–0.51) MeV, respectively. Considering the experimental observation and the present estimations, we proposed to search <math><mi>X</mi><mo>(</mo><mn>4014</mn><mo>)</mo></math> in the <math><mi>γ</mi><mi>γ</mi><mo>→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mi>ω</mi></math> process in Belle II.

Zi-Li Yue

Man-Yu Duan

Hidden charm decays of <math><mi>X</mi><mo>(</mo><mn>4014</mn><mo>)</mo></math> in a <math><msup><mi>D</mi><mo>*</mo></msup><msup><mover><mi>D</mi><mo>¯</mo></mover><mo>*</mo></msup></math> molecule scenario

In this paper, we adopt an extended relativized quark model to investigate the triply-heavy tetraquarks systematically. The mass spectra are obtained by solving the four-body relativized Hamiltonian including the Coulomb potential, confining potential, spin-spin interactions, and relativistic corrections. We find that all of the triply-heavy tetraquarks lie above the corresponding meson-meson thresholds, and thus no stable one exists. In particular, besides the spin-spin interactions, the Coulomb and confining potentials also contribute to the mass splittings in the <math><mrow><mi>c</mi><mi>b</mi><mover><mrow><mi>c</mi></mrow><mrow><mo>¯</mo></mrow></mover><mover><mrow><mi>q</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow></math> and <math><mrow><mi>c</mi><mi>b</mi><mover><mrow><mi>b</mi></mrow><mrow><mo>¯</mo></mrow></mover><mover><mrow><mi>q</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow></math> systems. Moreover, the whole mass spectra for triply heavy tetraquarks show quite similar patterns, which preserve the light flavor SU(3) symmetry and heavy quark symmetry well. Through the fall-apart mechanism, the triply-heavy tetraquarks may easily decay into the heavy quarkonium plus heavy-light mesons, which are good candidates for investigation in future experiments.

Italy

Elena Santopinto

Triply-heavy tetraquarks in an extended relativized quark model

In this work, we investigate the decays of the fully open-flavor tetraquark state <math><msub><mi>X</mi><mn>0</mn></msub><mo>(</mo><mn>2900</mn><mo>)</mo></math> which was observed by the LHCb collaboration very recently. By using an effective Lagrangian approach, the partial widths of <math><msub><mi>X</mi><mn>0</mn></msub><mo>(</mo><mn>2900</mn><mo>)</mo></math> are estimated, where <math><msub><mi>X</mi><mn>0</mn></msub><mo>(</mo><mn>2900</mn><mo>)</mo></math> is assumed to be an <math><mi>S</mi></math>-wave <math><msup><mover><mi>D</mi><mo>¯</mo></mover><mo>*</mo></msup><msup><mi>K</mi><mo>*</mo></msup></math> hadronic molecule with <math><mi>I</mi><mo>=</mo><mn>0</mn></math>. It is found that the estimated results are in agreement with the experimental observations. Moreover, we also predict the decay behaviors of the other unobserved <math><msub><mover><mi>X</mi><mo>˜</mo></mover><mrow><mi>J</mi><mo>(</mo><mi>J</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></mrow></msub></math>, which are the spin partners of the <math><msub><mi>X</mi><mn>0</mn></msub><mo>(</mo><mn>2900</mn><mo>)</mo></math> in the <math><mi>S</mi></math>-wave <math><msup><mover><mi>D</mi><mo>¯</mo></mover><mo>*</mo></msup><msup><mi>K</mi><mo>*</mo></msup></math> picture. It is pointed out that the <math><msub><mover><mi>X</mi><mo>˜</mo></mover><mn>1</mn></msub></math> state with <math><mi>I</mi><mo>=</mo><mn>0</mn></math> is a broad state with the width more than 100 MeV, while another <math><msub><mover><mi>X</mi><mo>˜</mo></mover><mn>2</mn></msub></math> state with <math><mi>I</mi><mo>=</mo><mn>0</mn></math> is a narrow state with the width approaching half of that for the <math><msub><mi>X</mi><mn>0</mn></msub><mo>(</mo><mn>2900</mn><mo>)</mo></math>. In addition, our results also show that the <math><msup><mover><mi>D</mi><mo>¯</mo></mover><mo>*</mo></msup><mi>K</mi></math> mode is expected to be the dominant decay mode for both <math><msub><mover><mi>X</mi><mo>˜</mo></mover><mn>1</mn></msub></math> and <math><msub><mover><mi>X</mi><mo>˜</mo></mover><mn>2</mn></msub></math>. Searching for those unobserved <math><msub><mover><mi>X</mi><mo>˜</mo></mover><mrow><mi>J</mi><mo>(</mo><mi>J</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></mrow></msub></math> in the future experiments might be helpful to understand the nature of <math><msub><mi>X</mi><mn>0</mn></msub><mo>(</mo><mn>2900</mn><mo>)</mo></math>.

Cheng-Jian Xiao

Guang-Wei Meng

Study of the decays of <math><mi>S</mi></math>-wave <math><msup><mover><mi>D</mi><mo>¯</mo></mover><mo>*</mo></msup><msup><mi>K</mi><mo>*</mo></msup></math> hadronic molecules: The scalar <math><msub><mi>X</mi><mn>0</mn></msub><mo>(</mo><mn>2900</mn><mo>)</mo></math> and its spin partners <math><mrow><msub><mrow><mover><mrow><mi>X</mi></mrow><mrow><mo>˜</mo></mrow></mover></mrow><mrow><mi>J</mi><mo>(</mo><mi>J</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></mrow></msub></mrow></math>

In this work we systematically calculate the mass spectra of open charm and bottom tetraquarks <math><mi>q</mi><mi>q</mi><mover><mi>q</mi><mo>¯</mo></mover><mover><mi>Q</mi><mo>¯</mo></mover></math> within an extended relativized quark model. The four-body relativized Hamiltonians including the Coulomb potential, confining potential, spin-spin interactions, and relativistic corrections are solved by using the variational method. We find that the predicted masses of four <math><mrow><msup><mrow><mn>0</mn></mrow><mrow><mo>+</mo></mrow></msup><mtext> </mtext><mtext> </mtext><mi>u</mi><mi>d</mi><mover><mrow><mi>s</mi></mrow><mrow><mo>¯</mo></mrow></mover><mover><mrow><mi>c</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow></math> states are 2765, 3065, 3152, and 3396 MeV, which disfavor the assignment of the newly observed <math><msub><mi>X</mi><mn>0</mn></msub><mo>(</mo><mn>2900</mn><mo>)</mo></math> as a compact tetraquark. Moreover, the mass spectra of the open charm and bottom tetraquarks show quite similar patterns, which preserve the light flavor SU(3) symmetry and heavy quark symmetry well. In addition, our results suggest that the flavor-exotic states <math><mi>n</mi><mi>n</mi><mover><mi>s</mi><mo>¯</mo></mover><mover><mi>c</mi><mo>¯</mo></mover></math>, <math><mi>n</mi><mi>n</mi><mover><mi>s</mi><mo>¯</mo></mover><mover><mi>b</mi><mo>¯</mo></mover></math>, <math><mi>s</mi><mi>s</mi><mover><mi>n</mi><mo>¯</mo></mover><mover><mi>c</mi><mo>¯</mo></mover></math>, and <math><mi>s</mi><mi>s</mi><mover><mi>n</mi><mo>¯</mo></mover><mover><mi>b</mi><mo>¯</mo></mover></math> and their antiparticles can be searched for in the heavy-light meson plus kaon final states by future experiments. More theoretical and experimental efforts are needed to investigate these singly heavy tetraquarks.

Open charm and bottom tetraquarks in an extended relativized quark model

Inspired by recent measurement of possible fully charmed tetraquarks in LHCb Collaboration, we investigate the mass spectra of fully heavy tetraquarks  $$QQ {\bar{Q}} {\bar{Q}}$$  <math> <mrow> <mi>Q</mi> <mi>Q</mi> <mover> <mrow> <mi>Q</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> <mover> <mrow> <mi>Q</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> </math>   in an extended relativized quark model. Our estimations indicate that the broad structure around 6.4 GeV should contain one or more ground states for  $$cc {\bar{c}} {\bar{c}}$$  <math> <mrow> <mi>c</mi> <mi>c</mi> <mover> <mrow> <mi>c</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> <mover> <mrow> <mi>c</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> </math>   tetraquarks, while the narrow structure near 6.9 GeV can be categorized as the first radial excitation of  $$cc {\bar{c}} {\bar{c}}$$  <math> <mrow> <mi>c</mi> <mi>c</mi> <mover> <mrow> <mi>c</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> <mover> <mrow> <mi>c</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> </math>   system. Moreover, with the wave functions of the tetraquarks and mesons, the strong decays of tetraquarks into heavy quarkonium pair are qualitatively discussed, which can be further checked by the LHCb and CMS Collaborations.

Masses of fully heavy tetraquarks  $$QQ {\bar{Q}} {\bar{Q}}$$  <math> <mrow> <mi>Q</mi> <mi>Q</mi> <mover> <mrow> <mi>Q</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> <mover> <mrow> <mi>Q</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> </math>   in an extended relativized quark model

In the present work, the mass spectra of doubly heavy tetraquarks <math><msub><mi>T</mi><mrow><mi>Q</mi><msup><mi>Q</mi><mo>′</mo></msup></mrow></msub></math> are systematically investigated in a relativized quark model. The four-body systems including the Coulomb potential, confining potential, spin-spin interactions, and relativistic corrections are solved within the variational method. Our results suggest that the <math><mi>I</mi><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><mn>0</mn><msup><mn>1</mn><mo>+</mo></msup><mtext> </mtext><mtext> </mtext><mi>b</mi><mi>b</mi><mover><mi>u</mi><mo>¯</mo></mover><mover><mi>d</mi><mo>¯</mo></mover></math> state is 54 MeV below the relevant <math><mover><mi>B</mi><mo>¯</mo></mover><msup><mover><mi>B</mi><mo>¯</mo></mover><mo>*</mo></msup></math> thresholds, which indicates that both strong and electromagnetic decays are forbidden, and thus this state can be a stable one. Its large hidden color component and small root mean square radius demonstrate that it is a compact tetraquark rather than a loosely bound molecule or pointlike diquark-antidiquark structure. Our predictions of the doubly heavy tetraquarks may provide valuable information for future experimental searches.

Masses of doubly heavy tetraquarks <math><msub><mi>T</mi><mrow><mi>Q</mi><msup><mi>Q</mi><mo>′</mo></msup></mrow></msub></math> in a relativized quark model