<p>Dibaryons are the simplest system in which the baryon-baryon interaction, and hence the underlying quark-quark interaction, can be studied in a clear way. Although the only dibaryon known today is the deuteron (and possibly the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>d</mi><mo>*</mo></msup></math>), fully heavy dibaryons are good candidates for bound states because in such systems the kinetic energy is small and the high symmetry of the wave function favors binding. In this study, the possible existence of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ω</mi><mrow><mi>c</mi><mi>c</mi><mi>c</mi></mrow></msub><msub><mi mathvariant="normal">Ω</mi><mrow><mi>c</mi><mi>c</mi><mi>c</mi></mrow></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ω</mi><mrow><mi>b</mi><mi>b</mi><mi>b</mi></mrow></msub><msub><mi mathvariant="normal">Ω</mi><mrow><mi>b</mi><mi>b</mi><mi>b</mi></mrow></msub></math> dibaryons is investigated in the framework of a constituent quark model that satisfactorily describes the deuteron, the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>d</mi><mo>*</mo></msup><mo stretchy="false">(</mo><mn>2380</mn><mo stretchy="false">)</mo></math> and the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi><mi>N</mi></math> interaction. <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><msup><mn>0</mn><mo>+</mo></msup></math> candidates are found in both systems with binding energies of the order of MeV. A <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Ω</mi></math>-dibaryon candidate is also found.</p>

Spain

Pablo Martín-Higueras

David R. Entem

Pablo G. Ortega

Jorge Segovia

Francisco Fernández

Study of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ω</mi><mrow><mi>c</mi><mi>c</mi><mi>c</mi></mrow></msub><msub><mi mathvariant="normal">Ω</mi><mrow><mi>c</mi><mi>c</mi><mi>c</mi></mrow></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Ω</mi><mrow><mi>b</mi><mi>b</mi><mi>b</mi></mrow></msub><msub><mi mathvariant="normal">Ω</mi><mrow><mi>b</mi><mi>b</mi><mi>b</mi></mrow></msub></math> dibaryons in a constituent quark model

Singly, doubly, and fully charmed tetraquark candidates, e.g., <math><msub><mi>T</mi><mrow><mi>c</mi><mover><mi>s</mi><mo>¯</mo></mover></mrow></msub><mo>(</mo><mn>2900</mn><mo>)</mo></math>, <math><msubsup><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow><mo>+</mo></msubsup><mo>(</mo><mn>3875</mn><mo>)</mo></math>, and <math><mi>X</mi><mo>(</mo><mn>6900</mn><mo>)</mo></math> have been recently reported by the LHCb collaboration. Therefore, it is timely to implement a theoretical investigation on triply heavy tetraquark systems; herein, the S-wave triply charm and bottom tetraquarks, <math><mover><mi>Q</mi><mo>¯</mo></mover><mi>Q</mi><mover><mi>q</mi><mo>¯</mo></mover><mi>Q</mi></math> <math><mo>(</mo><mi>q</mi><mo>=</mo><mi>u</mi><mo>,</mo><mi>d</mi><mo>,</mo><mi>s</mi><mo>;</mo><mi>Q</mi><mo>=</mo><mi>c</mi><mo>,</mo><mi>b</mi><mo>)</mo></math>, with spin-parity <math><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><msup><mn>0</mn><mo>+</mo></msup></math>, <math><msup><mn>1</mn><mo>+</mo></msup></math>, and <math><msup><mn>2</mn><mo>+</mo></msup></math>, isospin <math><mi>I</mi><mo>=</mo><mn>0</mn></math> and <math><mfrac><mn>1</mn><mn>2</mn></mfrac></math>, are systematically studied in a constituent quark model. Besides, all tetraquark configurations, i.e., meson-meson, diquark-antidiquark, and K-type arrangements, along with any allowed color structure, are comprehensively considered. The Gaussian expansion method (GEM), in combination with the complex-scaling method (CSM), which is quite ingenious in dealing with either bound or resonances, is the approach adopted in solving the complex scaled Schrödinger equation. This theoretical framework has already been applied in various tetra- and pentaquark systems. In a fully coupled-channel calculation within the <math><mrow><mrow><mi>GEM</mi><mo>+</mo></mrow><mi>CSM</mi></mrow></math>, narrow resonances are found in each <math><mi>I</mi><mo>(</mo><msup><mi>J</mi><mi>P</mi></msup><mo>)</mo></math> channel of the charm and bottom sector. In particular, triply charm and bottom tetraquark resonances are obtained in 5.6–5.9 GeV and 15.3–15.7 GeV, respectively. We provide also some insights of the compositeness of these exotic states, such as the inner quark distance, magnetic moment and dominant wave function component. All this may help to distinguish them in future high energy nuclear and particle experiments.

China

Gang Yang

Jialun Ping

Triply charm and bottom tetraquarks in a constituent quark model

The S-wave   $ \bar{q}q\bar{s}Q \;\; (q=u,\,d;\,Q=c,\,b) $   tetraquarks, with spin-parities   $ \bar{q}q\bar{s}Q \;\; (q=u,\,d;\,Q=c,\,b) $  ,   $ \bar{q}q\bar{s}Q \;\; (q=u,\,d;\,Q=c,\,b) $  , and   $ \bar{q}q\bar{s}Q \;\; (q=u,\,d;\,Q=c,\,b) $  , in both isoscalar and isovector sectors, are systematically studied using a chiral quark model. The meson-meson, diquark-antidiquark, and K-type arrangements of quarks and all possible color wave functions are comprehensively considered. The four-body system is solved using the Gaussian expansion method, a highly efficient computational approach. Additonally, a complex-scaling formulation of the problem is established to disentangle bound, resonance, and scattering states. This theoretical framework has already been successfully applied in various tetra- and penta-quark systems. For the complete coupled channel and within the complex-range formulation, several narrow resonances of   $ \bar{q}q\bar{s}Q \;\; (q=u,\,d;\,Q=c,\,b) $   and   $ \bar{q}q\bar{s}Q \;\; (q=u,\,d;\,Q=c,\,b) $   systems are obtained, in each allowed   $ \bar{q}q\bar{s}Q \;\; (q=u,\,d;\,Q=c,\,b) $  -channel, within the energy regions of   $ \bar{q}q\bar{s}Q \;\; (q=u,\,d;\,Q=c,\,b) $   GeV and   $ \bar{q}q\bar{s}Q \;\; (q=u,\,d;\,Q=c,\,b) $   GeV, respectively. The predicted exotic states, which indicate a richer color structure when going towards multiquark systems beyond mesons and baryons, are expected to be confirmed in future high-energy particle and nuclear experiments.

The Tetraquark System in a Chiral Quark Model  

The lowest-lying charmonium-like tetraquarks  $$c{\bar{c}}q{\bar{q}}$$  <math> <mrow> <mi>c</mi> <mover> <mrow> <mi>c</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> <mi>q</mi> <mover> <mrow> <mi>q</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> </math>    $$(q=u,\,d)$$  <math> <mrow> <mo>(</mo> <mi>q</mi> <mo>=</mo> <mi>u</mi> <mo>,</mo> <mspace width="0.166667em"></mspace> <mi>d</mi> <mo>)</mo> </mrow> </math>   and  $$c{\bar{c}}s{\bar{s}}$$  <math> <mrow> <mi>c</mi> <mover> <mrow> <mi>c</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> <mi>s</mi> <mover> <mrow> <mi>s</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> </math>  , with spin-parity  $$J^P=0^+$$  <math> <mrow> <msup> <mi>J</mi> <mi>P</mi> </msup> <mo>=</mo> <msup> <mn>0</mn> <mo>+</mo> </msup> </mrow> </math>  ,  $$1^+$$  <math> <msup> <mn>1</mn> <mo>+</mo> </msup> </math>   and  $$2^+$$  <math> <msup> <mn>2</mn> <mo>+</mo> </msup> </math>  , and isospin  $$I=0$$  <math> <mrow> <mi>I</mi> <mo>=</mo> <mn>0</mn> </mrow> </math>   and 1, are systematically investigated within the theoretical framework of complex-scaling range for a chiral quark model that has already been successfully applied in former studies of various tetra- and penta-quark systems. A four-body S-wave configuration which includes meson–meson, diquark–antidiquark and K-type arrangements of quarks, along with all possible color wave functions, is comprehensively considered. Several narrow resonances are obtained in each tetraquark channel when a fully coupled-channel computation is performed. We tentatively assign theoretical states to experimentally reported charmonium-like signals such as X(3872),  $$Z_c(3900)$$  <math> <mrow> <msub> <mi>Z</mi> <mi>c</mi> </msub> <mrow> <mo>(</mo> <mn>3900</mn> <mo>)</mo> </mrow> </mrow> </math>  , X(3960), X(4350), X(4685) and X(4700). They can be well identified as hadronic molecules; however, other exotic components which involve, for instance, hidden-color channels or diquark–antidiquark structures play a considerable role. Meanwhile, two resonances are obtained at 4.04 GeV and 4.14 GeV which may be compatible with experimental data in the energy interval 4.0–4.2 GeV. Furthermore, the X(3940) and X(4630) may be identified as color compact tetraquark resonances. Finally, we also find few resonance states in the energy interval from 4.5 to 5.0 GeV, which would be awaiting for discovery in future experiments.

Charmoniumlike tetraquarks in a chiral quark model

We construct a contact interaction model for the <math><mi>η</mi></math> and <math><msup><mi>η</mi><mo>′</mo></msup></math> mesons in the SDE-BSE approach to QCD and compute several static properties of these mesons and their transition form factors. We find that this model gives an excellent description of the <math><mi>η</mi></math> and <math><msup><mi>η</mi><mo>′</mo></msup></math> static properties, namely, their masses, decay width, and decay constants. However, a contact interaction disagrees with experimental data for <math><msup><mi>Q</mi><mn>2</mn></msup></math> greater than <math><mn>2</mn><mtext> </mtext><mtext> </mtext><msup><mi>GeV</mi><mn>2</mn></msup></math>, and produces transition form factors in conflict with perturbative QCD prediction. This is not surprising and the reasons for this are explained.

Mexico

Bilgai Almeida Zamora

Enrique Carreon Martínez

J. J. Cobos-Martínez

Contact interaction model for the <math><mrow><mi>η</mi></mrow></math> and <math><msup><mi>η</mi><mo>′</mo></msup></math> mesons in a Schwinger-Dyson-Bethe-Salpeter approach to QCD: Masses, decay widths, and transition form factors

The low-lying bottomoniumlike tetraquarks <math><mrow><mi>b</mi><mover><mrow><mi>b</mi></mrow><mrow><mo>¯</mo></mrow></mover><mi>q</mi><mover><mrow><mi>q</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow></math> (<math><mrow><mi>q</mi><mo>=</mo><mi>u</mi></mrow></math>, <math><mrow><mi>d</mi></mrow></math>, <math><mrow><mi>s</mi></mrow></math>) with spin-parity <math><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><msup><mn>0</mn><mo>+</mo></msup></math>, <math><msup><mn>1</mn><mo>+</mo></msup></math>, and <math><msup><mn>2</mn><mo>+</mo></msup></math>, and isospin <math><mi>I</mi><mo>=</mo><mn>0</mn></math>, 1, or <math><mfrac><mn>1</mn><mn>2</mn></mfrac></math>, are systematically investigated within the theoretical framework of real- and complex-scaling range of a chiral quark model, which has already been successfully applied in analysis of several multiquark systems. A complete four-body <math><mi>S</mi></math>-wave function, which includes meson-meson, diquark-antidiquark and K-type arrangements of quarks, along with all possible color configurations are considered. In the <math><mrow><mi>b</mi><mover><mrow><mi>b</mi></mrow><mrow><mo>¯</mo></mrow></mover><mi>q</mi><mover><mrow><mi>q</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow></math> (<math><mrow><mi>q</mi><mo>=</mo><mi>u</mi></mrow></math>, <math><mrow><mi>d</mi></mrow></math>) tetraquark system, we found resonance states of <math><mrow><msup><mrow><mi>B</mi></mrow><mrow><mo>(</mo><mo>*</mo><mo>)</mo></mrow></msup><msup><mrow><mover><mrow><mi>B</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mo>(</mo><mo>*</mo><mo>)</mo></mrow></msup></mrow></math>, <math><mi>ϒ</mi><mi>ω</mi></math>, <math><mi>ϒ</mi><mi>ρ</mi></math>, and <math><msub><mi>η</mi><mi>b</mi></msub><mi>ρ</mi></math> nature with all possible <math><mi>I</mi><mo>(</mo><msup><mi>J</mi><mi>P</mi></msup><mo>)</mo></math> quantum numbers. Their masses are generally located in the energy range 11.0–11.3 GeV and their widths are less than 10 MeV. In addition, extremely narrow resonances, with two-meson strong decay widths less than 1.5 MeV, are obtained in both <math><mrow><mi>b</mi><mover><mrow><mi>b</mi></mrow><mrow><mo>¯</mo></mrow></mover><mi>u</mi><mover><mrow><mi>s</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow></math> and <math><mrow><mi>b</mi><mover><mrow><mi>b</mi></mrow><mrow><mo>¯</mo></mrow></mover><mi>s</mi><mover><mrow><mi>s</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow></math> tetraquark systems. Particularly, four radial excitations of <math><mrow><mi>ϒ</mi><msup><mrow><mi>K</mi></mrow><mrow><mo>*</mo></mrow></msup></mrow></math> and <math><mrow><msub><mrow><mi>η</mi></mrow><mrow><mi>b</mi></mrow></msub><msup><mrow><mi>K</mi></mrow><mrow><mo>*</mo></mrow></msup></mrow></math> are found at <math><mrow><mo>∼</mo><mn>11.1</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></mrow></math> in <math><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><msup><mn>0</mn><mo>+</mo></msup></math>, <math><msup><mn>1</mn><mo>+</mo></msup></math>, and <math><msup><mn>2</mn><mo>+</mo></msup></math> channels of <math><mi>b</mi><mover><mi>b</mi><mo>¯</mo></mover><mi>u</mi><mover><mi>s</mi><mo>¯</mo></mover></math> system. One <math><mi>ϒ</mi><mo>(</mo><mn>1</mn><mi>S</mi><mo>)</mo><mi>ϕ</mi><mo>(</mo><mn>2</mn><mi>S</mi><mo>)</mo></math> resonance state is obtained at 11.28 GeV in the <math><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><msup><mn>1</mn><mo>+</mo></msup></math> sector.

Bottomoniumlike tetraquarks in a chiral quark model

The fully charm and bottom pentaquarks, i.e., <math><mi>c</mi><mi>c</mi><mi>c</mi><mi>c</mi><mover><mi>c</mi><mo>¯</mo></mover></math> and <math><mi>b</mi><mi>b</mi><mi>b</mi><mi>b</mi><mover><mi>b</mi><mo>¯</mo></mover></math>, with spin-parity quantum numbers <math><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><msup><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>−</mo></msup></math>, <math><mrow><msup><mrow><mfrac><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow><mrow><mo>−</mo></mrow></msup></mrow></math>, and <math><msup><mfrac><mn>5</mn><mn>2</mn></mfrac><mo>−</mo></msup></math>, are investigated within a lattice-QCD inspired quark model, which has already successfully described the recently announced fully charm tetraquark candidate <math><mi>X</mi><mo>(</mo><mn>6900</mn><mo>)</mo></math> and has also predicted several other fully heavy tetraquarks. A powerful computational technique, based on the Gaussian expansion method combined with a complex-scaling range approach, is employed to predict, and distinguish, bound, resonance, and scattering states of the mentioned five-body system. Both baryon-meson and diquark-diquark-antiquark configurations, along with all of their possible color channels are comprehensively considered. Narrow resonances are obtained in each spin-parity channel for the fully charm and bottom systems. Moreover, most of them seem to be compact multiquarks whose wave functions are dominated by either hidden-color baryon-meson or diquark-diquark-antiquark structure or by the coupling between them.

Fully charm and bottom pentaquarks in a lattice-QCD inspired quark model

A Poincaré-covariant <math><mrow><mi>quark</mi><mo>+</mo><mi>diquark</mi></mrow></math> Faddeev equation is used to develop insights into the structure of the four lightest <math><mo>(</mo><mi>I</mi><mo>,</mo><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><mfrac><mn>3</mn><mn>2</mn></mfrac><mo>,</mo><msup><mfrac><mn>3</mn><mn>2</mn></mfrac><mo>±</mo></msup><mo>)</mo></math> baryon multiplets. While these systems can contain isovector-axialvector and isovector-vector diquarks, one may neglect the latter and still arrive at a reliable description. The <math><mo>(</mo><mfrac><mn>3</mn><mn>2</mn></mfrac><mo>,</mo><msup><mfrac><mn>3</mn><mn>2</mn></mfrac><mo>+</mo></msup><mo>)</mo></math> states are the simpler systems, with features that bear some resemblance to quark model pictures, e.g., their most prominent rest-frame orbital angular momentum component is <math><mi>S</mi></math>-wave and the <math><mrow><mi>Δ</mi><mo>(</mo><mn>1600</mn><mo>)</mo><msup><mrow><mfrac><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow><mrow><mo>+</mo></mrow></msup></mrow></math> may reasonably be viewed as a radial excitation of the <math><mi>Δ</mi><mo>(</mo><mn>1232</mn><mo>)</mo><msup><mfrac><mn>3</mn><mn>2</mn></mfrac><mo>+</mo></msup></math>. The <math><mo>(</mo><mfrac><mn>3</mn><mn>2</mn></mfrac><mo>,</mo><msup><mfrac><mn>3</mn><mn>2</mn></mfrac><mo>−</mo></msup><mo>)</mo></math> states are more complex: the <math><mi>Δ</mi><mo>(</mo><mn>1940</mn><mo>)</mo><msup><mfrac><mn>3</mn><mn>2</mn></mfrac><mo>−</mo></msup></math> expresses little of the character of a radial excitation of the <math><mi>Δ</mi><mo>(</mo><mn>1700</mn><mo>)</mo><msup><mfrac><mn>3</mn><mn>2</mn></mfrac><mo>−</mo></msup></math>; and while the rest-frame wave function of the latter is predominantly <math><mi>P</mi></math>-wave, the leading piece in the <math><mi>Δ</mi><mo>(</mo><mn>1940</mn><mo>)</mo><msup><mfrac><mn>3</mn><mn>2</mn></mfrac><mo>−</mo></msup></math> wave function is <math><mi>S</mi></math>-wave, in conflict with quark model expectations. Experiments that can test these predictions, such as large momentum transfer resonance electroexcitation, may shed light on the nature of emergent hadron mass.

Langtian Liu

Chen Chen

Ya Lu

Craig D. Roberts

Composition of low-lying <math><mrow><mi>J</mi><mo>=</mo><msup><mrow><mfrac><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow><mrow><mo>±</mo></mrow></msup></mrow></math> <math><mrow><mi>Δ</mi></mrow></math>-baryons

We use a continuum <math><mrow><mi>quark</mi><mo>+</mo><mi>diquark</mi></mrow></math> approach to the nucleon bound-state problem in relativistic quantum field theory to deliver parameter-free predictions for the nucleon axial and induced pseudoscalar form factors, <math><msub><mi>G</mi><mi>A</mi></msub></math> and <math><msub><mi>G</mi><mi>P</mi></msub></math>, and unify them with the pseudoscalar form factor <math><msub><mi>G</mi><mn>5</mn></msub></math> or, equivalently, the pion-nucleon form factor <math><msub><mi>G</mi><mrow><mi>π</mi><mi>N</mi><mi>N</mi></mrow></msub></math>. We explain how partial conservation of the axial-vector current and the associated Goldberger-Treiman relation are satisfied once all necessary couplings of the external current to the building blocks of the nucleon are constructed consistently; in particular, we fully resolve the seagull couplings to the diquark-quark vertices associated with the axial-vector and pseudoscalar currents. Among the results we describe, the following are worth highlighting. A dipole form factor defined by an axial charge <math><msub><mi>g</mi><mi>A</mi></msub><mo>=</mo><msub><mi>G</mi><mi>A</mi></msub><mo>(</mo><mn>0</mn><mo>)</mo><mo>=</mo><mn>1.25</mn><mo>(</mo><mn>3</mn><mo>)</mo></math> and a mass scale <math><msub><mi>M</mi><mi>A</mi></msub><mo>=</mo><mn>1.23</mn><mo>(</mo><mn>3</mn><mo>)</mo><msub><mi>m</mi><mi>N</mi></msub></math>, where <math><msub><mi>m</mi><mi>N</mi></msub></math> is the nucleon mass, can accurately describe the pointwise behavior of <math><msub><mi>G</mi><mi>A</mi></msub></math>. Concerning <math><msub><mi>G</mi><mi>P</mi></msub></math>, we obtain the pseudoscalar charge <math><msubsup><mi>g</mi><mi>p</mi><mo>*</mo></msubsup><mo>=</mo><mn>8.80</mn><mo>(</mo><mn>23</mn><mo>)</mo></math>, and find that the pion pole dominance approach delivers a reliable estimate of the directly computed result. Our computed value of the pion-nucleon coupling constant, <math><msub><mi>g</mi><mrow><mi>π</mi><mi>N</mi><mi>N</mi></mrow></msub><mo>/</mo><msub><mi>m</mi><mi>N</mi></msub><mo>=</mo><mn>14.02</mn><mo>(</mo><mn>33</mn><mo>)</mo><mo>/</mo><mi>GeV</mi></math> is consistent with recent precision determinations.

Germany

Christian S. Fischer

Nucleon axial-vector and pseudoscalar form factors and PCAC relations

We introduce a new family of generalized parton distribution models able to fulfill by construction all the theoretical properties imposed by QCD. These models are built on standard parton distribution functions and extended to off-forward kinematics through a well-defined procedure. We apply this strategy on the pion, first handling a simple but insightful algebraic model, and then exploiting state-of-the-art computations obtained in continuum QCD. We compare these models with a more standard one relying on an xFitter extraction of the pion parton distribution functions. The results for both quark and gluon generalized parton distributions are presented and exploited for calculation of electromagnetic, gravitational, and Compton form factors. Results on the latter highlight the relevance of next-to-leading-order corrections, even in the so-called valence region.