<p>Studying exotic hadrons is a challenge against the conventional quark model, providing us with a good platform to deepen our understanding of the strong interaction. An inclusive study of the exotic hadrons in vacuum and at finite temperature is an intriguing approach to shed light on their nature. As a first step, we study the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>Z</mi><mi>c</mi></msub><mo stretchy="false">(</mo><mn>3900</mn><mo stretchy="false">)</mo></math> in both 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></math> hadronic molecular and the triangle singularity pictures, and discuss the behaviors of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>Z</mi><mi>c</mi></msub><mo stretchy="false">(</mo><mn>3900</mn><mo stretchy="false">)</mo></math> at finite temperature in these two different pictures. As a result, we show the properties that its mass becomes smaller and its width becomes larger when the temperature increases, which are seen commonly in the hadronic molecular picture and in the triangle singularity picture. The enhanced widths in hot medium indicate that the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>Z</mi><mi>c</mi></msub><mo stretchy="false">(</mo><mn>3900</mn><mo stretchy="false">)</mo></math> will be dissociated at a sufficiently high temperature. This feature is also reflected by a decrease of the effective couplings in the hadronic molecular picture. It is concluded that, not only in vacuum but also in hot medium, the behaviors of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>Z</mi><mi>c</mi></msub><mo stretchy="false">(</mo><mn>3900</mn><mo stretchy="false">)</mo></math> are similar in the two different interpretations of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>Z</mi><mi>c</mi></msub><mo stretchy="false">(</mo><mn>3900</mn><mo stretchy="false">)</mo></math>.</p>

China

Japan

Ying Zhang

Atsushi Hosaka

Qian Wang

Shigehiro Yasui

<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>Z</mi><mi>c</mi></msub><mo stretchy="false">(</mo><mn>3900</mn><mo stretchy="false">)</mo></math> in a hadronic molecule and a triangle singularity approach at finite temperature

The femtoscopic ϕN correlation function is studied within a hadronic effective Lagrangian approach with coupled channels, based on hidden local symmetry. The results are compared with the data recently reported by the ALICE collaboration. We find that the correlation function has very different features for the ϕN system in the spin 1/2 and 3/2 configurations, with the spin-averaged combination matching well with the experimental data. A strong attraction, leading to the formation of a ϕN bound state or a very prominent cusp is found in the spin 3/2 case. The correlation function for spin 1/2, on the other hand, is strongly impacted by the negative parity <math><msup><mrow><mi>N</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>(</mo><mn>1895</mn><mo>)</mo></math> nucleon resonance.

Brazil

Luciano M. Abreu

Philipp Gubler

K.P. Khemchandani

A. Martínez Torres

A study of the Correlation Function

The ground-breaking discovery of the first fully charmed tetraquark state <math><mi>X</mi><mo>(</mo><mn>6900</mn><mo>)</mo></math> in the <math><mi>J</mi><mo>/</mo><mi>ψ</mi><mi>J</mi><mo>/</mo><mi>ψ</mi></math> invariant mass distribution by the LHCb collaboration has inspired intensive theoretical studies. Various interpretations, such as molecular states, compact tetraquark states, and coupled-channel effects, have been proposed for these states. Of particular interest is the ongoing search for the triple-<math><mi>J</mi><mo>/</mo><mi>ψ</mi></math> state–a fully-charmed hexaquark state. To deepen our understanding of the triple-<math><mi>J</mi><mo>/</mo><mi>ψ</mi></math> state and to guide future experimental searches, we study the triple-<math><mi>J</mi><mo>/</mo><mi>ψ</mi></math> system in this work employing the Gaussian expansion method and the <math><mi>J</mi><mo>/</mo><mi>ψ</mi><mi>J</mi><mo>/</mo><mi>ψ</mi></math> potential parametrized to yield a shallow bound state, as suggested in several theoretical works. Our results support a triple-<math><mi>J</mi><mo>/</mo><mi>ψ</mi></math> bound state, even in cases where the attractive interaction between the two <math><mi>J</mi><mo>/</mo><mi>ψ</mi></math> mesons is very weak. Moreover, our analysis implies the Efimov effect in the triple-<math><mi>J</mi><mo>/</mo><mi>ψ</mi></math> system. In addition, we extend our investigation to the triple-<math><mrow><mi>ϒ</mi><mo>(</mo><mn>1</mn><mi>S</mi><mo>)</mo></mrow></math> system and obtain results similar to those for the triple-<math><mi>J</mi><mo>/</mo><mi>ψ</mi></math> system.

Ya-Wen Pan

Zhi-Wei Liu

Li-Sheng Geng

Xiang Liu

Likely existence of bound states and the Efimov effect in the triple-<math><mi>J</mi><mo>/</mo><mi>ψ</mi></math> system

We study the recently observed <math><mi>Ω</mi><mo>(</mo><mn>2012</mn><mo>)</mo></math> baryon in quantum chromodynamics (QCD) sum rules. We construct the <math><mi>P</mi></math>-wave <math><mi>Ω</mi></math> baryon currents with a covariant derivative, and perform spin projection to obtain the currents with total spin <math><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></math> and <math><mrow><mn>3</mn><mo>/</mo><mn>2</mn></mrow></math>. We then apply the parity-projected QCD sum rules to separate the contributions of the positive and negative parity states. We extract the masses of <math><mrow><msup><mrow><mi>J</mi></mrow><mrow><mi>P</mi></mrow></msup><mo>=</mo><mn>1</mn><mo>/</mo><msup><mrow><mn>2</mn></mrow><mrow><mo>−</mo></mrow></msup></mrow></math> and <math><mn>3</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></math> states to be <math><mrow><msub><mrow><mi>M</mi></mrow><mrow><mn>1</mn><mo>/</mo><msup><mrow><mn>2</mn></mrow><mrow><mo>−</mo></mrow></msup></mrow></msub><mo>=</mo><msubsup><mrow><mn>2.07</mn></mrow><mrow><mo>−</mo><mn>0.07</mn></mrow><mrow><mo>+</mo><mn>0.07</mn></mrow></msubsup><mtext> </mtext><mtext> </mtext><mi>GeV</mi></mrow></math> and <math><mrow><msub><mrow><mi>M</mi></mrow><mrow><mn>3</mn><mo>/</mo><msup><mrow><mn>2</mn></mrow><mrow><mo>−</mo></mrow></msup></mrow></msub><mo>=</mo><msubsup><mrow><mn>2.05</mn></mrow><mrow><mo>−</mo><mn>0.10</mn></mrow><mrow><mo>+</mo><mn>0.09</mn></mrow></msubsup><mtext> </mtext><mtext> </mtext><mi>GeV</mi></mrow></math>. Both results are in good agreement with the experimental result. Therefore, it is likely that the <math><mi>Ω</mi><mo>(</mo><mn>2012</mn><mo>)</mo></math> is a negative parity state, which is interpreted as a <math><mi>P</mi></math>-wave excited state in the quark model. However, its spin is not determined in the present analysis, which can be done by detailed study on its decay properties.

Niu Su

Hua-Xing Chen

Investigation on the <math><mi>Ω</mi><mo>(</mo><mn>2012</mn><mo>)</mo></math> from QCD sum rules

The <math><mi>Ξ</mi><mi>N</mi></math> interaction plays an important role in understanding the long-anticipated <math><mi>H</mi></math> dibaryon. Recent lattice QCD calculations verified the attractive nature of the <math><mi>Ξ</mi><mi>N</mi></math> interaction. On the other hand, whether it is strong enough to generate a bound state remains inconclusive. In this work, assuming it can generate a weakly bound state, we study the yields of the <math><mi>Ξ</mi><mi>N</mi></math> dibaryon for different binding energies in <math><mi>p</mi><mi>p</mi></math> collisions at 7 TeV using the coalescence model and the transport model PACIAE. The yields are estimated first numerically and then analytically, adopting a Yukawa-type wave function. In particular, we find that in the weak binding limit, there exists a universal relation between the yield and the binding energy, valid for <math><mi>p</mi><mi>p</mi></math> collisions.

Tian-Chen Wu

Production of the <math><mrow><mi>Ξ</mi><mi>N</mi></mrow></math> dibaryon as a weakly bound system in <math><mi>p</mi><mi>p</mi></math> collisions

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

Qing-Fu Song

Qi-Fang Lü

Bottom-charmed baryons in a nonrelativistic quark model

We study the fully strange tetraquark states with the exotic quantum numbers <math><msup><mi>J</mi><mrow><mi>P</mi><mi>C</mi></mrow></msup><mo>=</mo><msup><mn>0</mn><mrow><mo>+</mo><mo>−</mo></mrow></msup></math> and <math><msup><mn>2</mn><mrow><mo>+</mo><mo>−</mo></mrow></msup></math>. We construct their corresponding diquark-antidiquark interpolating currents and apply the QCD sum rule method to calculate both their diagonal and off-diagonal correlation functions. The obtained results are used to construct some mixing currents that are nearly noncorrelated, from which we extract the masses of the lowest-lying states to be <math><msub><mi>M</mi><msup><mn>0</mn><mrow><mo>+</mo><mo>−</mo></mrow></msup></msub><mo>=</mo><mn>2.4</mn><msubsup><mn>7</mn><mrow><mo>−</mo><mn>0.44</mn></mrow><mrow><mo>+</mo><mn>0.33</mn></mrow></msubsup></math> and <math><mrow><msub><mrow><mi>M</mi></mrow><mrow><msup><mrow><mn>2</mn></mrow><mrow><mo>+</mo><mo>−</mo></mrow></msup></mrow></msub><mo>=</mo><mn>3.0</mn><msubsup><mrow><mn>7</mn></mrow><mrow><mo>−</mo><mn>0.33</mn></mrow><mrow><mo>+</mo><mn>0.25</mn></mrow></msubsup><mtext> </mtext><mtext> </mtext><mi>GeV</mi></mrow></math>. We apply the Fierz rearrangement to transform the diquark-antidiquark currents to be the combinations of meson-meson currents, and the obtained Fierz identities indicate that these two states may be searched for in the <math><mi>P</mi></math>-wave <math><mrow><mi>ϕ</mi><mo>(</mo><mn>1020</mn><mo>)</mo><msub><mrow><mi>f</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><mn>1710</mn><mo>)</mo><mo>/</mo><mi>ϕ</mi><mo>(</mo><mn>1020</mn><mo>)</mo><msubsup><mrow><mi>f</mi></mrow><mrow><mn>2</mn></mrow><mrow><mo>′</mo></mrow></msubsup><mo>(</mo><mn>1525</mn><mo>)</mo><mo>(</mo><mo>→</mo><mi>ϕ</mi><mi>K</mi><mover><mrow><mi>K</mi></mrow><mrow><mo>¯</mo></mrow></mover><mo>/</mo><mi>ϕ</mi><mi>π</mi><mi>π</mi><mo>)</mo></mrow></math> channels.

Hong-Zhou Xi

Yi-Wei Jiang

Fully strange tetraquark states with the exotic quantum numbers <math><mrow><msup><mrow><mi>J</mi></mrow><mrow><mi>P</mi><mi>C</mi></mrow></msup><mo>=</mo><msup><mrow><mn>0</mn></mrow><mrow><mo>+</mo><mo>−</mo></mrow></msup></mrow></math> and <math><mrow><msup><mrow><mn>2</mn></mrow><mrow><mo>+</mo><mo>−</mo></mrow></msup></mrow></math>

The recent discoveries and observations of pentaquarks and tetraquarks by high-energy accelerator facilities have accumulated evidence of the existence of multiquark hadrons with heavy quarks, as discussed from the early stage of the prediction of quarks. We construct a coupled-channel model for the hidden-charm pentaquarks with strangeness whose quark content is <math><mi>u</mi><mi>d</mi><mi>s</mi><mi>c</mi><mover><mi>c</mi><mo>¯</mo></mover></math>, <math><msub><mi>P</mi><mrow><mi>c</mi><mi>s</mi></mrow></msub></math>, described as <math><mrow><msub><mrow><mi>Λ</mi></mrow><mrow><mi>c</mi></mrow></msub><msubsup><mrow><mover><mrow><mi>D</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mi>s</mi></mrow><mrow><mo>(</mo><mo>*</mo><mo>)</mo></mrow></msubsup></mrow></math>, <math><mrow><msubsup><mrow><mi>Ξ</mi></mrow><mrow><mi>c</mi></mrow><mrow><msup><mrow><mo>(</mo></mrow><mrow><mo>′</mo></mrow></msup><mo>*</mo><mo>)</mo></mrow></msubsup><msup><mrow><mover><mrow><mi>D</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mo>(</mo><mo>*</mo><mo>)</mo></mrow></msup></mrow></math> molecules, produced by the cooperation of the heavy quark and chiral symmetries, coupled to a five-quark core. We reproduce the experimental mass of <math><msub><mi>P</mi><mrow><mi>c</mi><mi>s</mi></mrow></msub></math>, of which LHCb has announced the discovery. Furthermore, our result supports the quantum numbers that are preferred by the experiment. Our predictions indicate the existence of additional <math><msub><mi>P</mi><mrow><mi>c</mi><mi>s</mi></mrow></msub></math>’s in proximity to molecular threshold regions, which can be further investigated by LHCb.

Italy

Poland

Alessandro Giachino

Elena Santopinto

Sachiko Takeuchi

Makoto Takizawa

Yasuhiro Yamaguchi

Rich structure of the hidden-charm pentaquarks near threshold regions

Spectrum of the doubly heavy tetraquarks is studied in a constituent quark model including one-pion exchange (OPE) potential. Central and tensor forces induced by OPE between two light quarks are considered. Our results show that <math><mi>I</mi><mo>(</mo><msup><mrow><mi>J</mi></mrow><mrow><mi>P</mi></mrow></msup><mo>)</mo><mo>=</mo><mn>0</mn><mo>(</mo><msup><mrow><mn>1</mn></mrow><mrow><mo>+</mo></mrow></msup><mo>)</mo></math> compact bound states are shifted up because of the repulsive central force between <math><mover><mrow><mi>q</mi></mrow><mrow><mo>¯</mo></mrow></mover><mover><mrow><mi>q</mi></mrow><mrow><mo>¯</mo></mrow></mover></math>. This effect possibly leads to the small binding energy in <math><msub><mrow><mi>T</mi></mrow><mrow><mi>c</mi><mi>c</mi></mrow></msub></math>. In addition, a <math><mi>I</mi><mo>(</mo><msup><mrow><mi>J</mi></mrow><mrow><mi>P</mi></mrow></msup><mo>)</mo><mo>=</mo><mn>1</mn><mo>(</mo><msup><mrow><mn>1</mn></mrow><mrow><mo>+</mo></mrow></msup><mo>)</mo></math> resonant state is reported with <math><mi>E</mi><mo>=</mo><mn>10641</mn><mspace width="0.25em"></mspace><mtext>MeV</mtext><mo>,</mo><mi>Γ</mi><mo>=</mo><mn>15</mn><mspace width="0.25em"></mspace><mtext>MeV</mtext></math> and <math><mi>E</mi><mo>=</mo><mn>10640</mn><mtext> MeV</mtext><mo>,</mo><mi>Γ</mi><mo>=</mo><mn>15</mn><mtext> MeV</mtext></math>, without and with including OPE potential, respectively. The repulsive central force and attractive tensor force almost cancel with each other and leave a small energy difference when OPE potential is included.

Qi Meng

Emiko Hiyama

Makoto Oka

Chang Xu

Doubly heavy tetraquarks including one-pion exchange potential

Effects of the <math><mi>U</mi><mo>(</mo><mn>1</mn><msub><mo>)</mo><mi>A</mi></msub></math> axial anomaly on the mass spectrum of singly heavy baryons (SHBs) is studied in terms of the chiral effective theory based on the chiral linear representation for light flavors. We consider SHBs made of both three quarks (<math><mi>Q</mi><mi>q</mi><mi>q</mi></math>) and five quarks (<math><mi>Q</mi><mi>q</mi><mi>q</mi><mi>q</mi><mover><mi>q</mi><mo>¯</mo></mover></math>). For the three-quark SHBs, we prove that the inverse mass hierarchy for the negative-parity <math><msub><mi>Λ</mi><mi>c</mi></msub></math> and <math><msub><mi>Ξ</mi><mi>c</mi></msub></math> is realized only when the <math><mi>U</mi><mo>(</mo><mn>1</mn><msub><mo>)</mo><mi>A</mi></msub></math> anomaly is present. For the five-quark SHBs, in contrast, it is found that the <math><mi>U</mi><mo>(</mo><mn>1</mn><msub><mo>)</mo><mi>A</mi></msub></math> anomaly does not change the mass spectrum at the leading order, and accordingly, their decay properties induced by emitting a pseudoscalar meson are not affected by the anomaly. Moreover, taking into account small mixings between the three-quark and five-quark SHBs, we find that the observed <math><msub><mi>Ξ</mi><mi>c</mi></msub></math> excited state, either <math><msub><mi>Ξ</mi><mi>c</mi></msub><mo>(</mo><mn>2923</mn><mo>)</mo></math> or <math><msub><mi>Ξ</mi><mi>c</mi></msub><mo>(</mo><mn>2930</mn><mo>)</mo></math>, can be consistently regarded as a negative-parity SHB that is dominated by the five-quark component. We also predict a new negative-parity five-quark dominant <math><msub><mi>Λ</mi><mi>c</mi></msub></math>, whose mass is around 2700 MeV and the decay width is of order a few MeV, which provides useful information for future experiments to check our description.

Hiroto Takada

Daiki Suenaga

Masayasu Harada

Axial anomaly effect on three-quark and five-quark singly heavy baryons