Italy

Switzerland

Luciano Maiani

Charm and hadrons

Steven Weinberg: Philosophy, cosmology and social writings

We study compact hidden charm pentaquarks in the Born–Oppenheimer approximation, previously introduced for tetraquarks, assuming the heavy pair to be in a color octet. We show that Fermi statistics applied to the complex of the three light quarks, also in color octet, requires S-wave pentaquark ground states to consist of three octets of flavour-SU(3)  $$_f$$  <math> <msub> <mrow></mrow> <mi>f</mi> </msub> </math>  , two with spin 1/2 and one with spin 3/2, in line with the observed, strangeness  $$S=0,-1$$  <math> <mrow> <mi>S</mi> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mo>-</mo> <mn>1</mn> </mrow> </math>  , spectrum. Additional lines corresponding to decays into  $$J/\psi +\Sigma $$  <math> <mrow> <mi>J</mi> <mo>/</mo> <mi>ψ</mi> <mo>+</mo> <mi>Σ</mi> </mrow> </math>   and  $$J/\psi +\Xi $$  <math> <mrow> <mi>J</mi> <mo>/</mo> <mi>ψ</mi> <mo>+</mo> <mi>Ξ</mi> </mrow> </math>   are predicted. In the language of non-relativistic SU(6), ground state pentaquarks form either a  $${\varvec{56}}$$  <math> <mrow> <mn>56</mn> </mrow> </math>   or a  $${\varvec{20}}$$  <math> <mrow> <mn>20</mn> </mrow> </math>   representation, distinguished by presence or absence of pentaquarks decaying in the spin 3/2 decuplet, e.g. in  $$J/\psi +\Delta ^{++}$$  <math> <mrow> <mi>J</mi> <mo>/</mo> <mi>ψ</mi> <mo>+</mo> <msup> <mi>Δ</mi> <mrow> <mo>+</mo> <mo>+</mo> </mrow> </msup> </mrow> </math>  . Observation of a strangeness  $$S=-2$$  <math> <mrow> <mi>S</mi> <mo>=</mo> <mo>-</mo> <mn>2</mn> </mrow> </math>   or isospin  $$I=3/2$$  <math> <mrow> <mi>I</mi> <mo>=</mo> <mn>3</mn> <mo>/</mo> <mn>2</mn> </mrow> </math>   pentaquarks would be a clear signature of compact, QCD bound pentaquarks.

Antonio Polosa

Veronica Riquer

The pentaquark spectrum from Fermi statistics

Tetraquarks <math><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></math> are found to be described remarkably well with the Quantum Chromodynamics version of the Hydrogen bond, as treated with the Born-Oppenheimer approximation. We show the robustness of the method by computing the mass of the observed <math><msub><mrow><mi>T</mi></mrow><mrow><mi>c</mi><mi>c</mi></mrow></msub></math> tetraquark following two different paths. Relying on this, we provide a prediction for the mass of the expected <math><msub><mrow><mi>T</mi></mrow><mrow><mi>b</mi><mi>b</mi></mrow></msub></math> particle. The average sizes of tetraquarks are estimated to be approximately 3–<math><mn>5</mn><msup><mrow><mspace width="0.20em"></mspace><mtext>GeV</mtext></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></math>. As a consequence hyperfine separations are not expected to be sizeable. We discussed possible reasons why LHCb has observed only one state in the <math><mi>D</mi><msup><mrow><mi>D</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math> spectrum.

CERN

Alessandro Pilloni

Antonio D. Polosa

Doubly heavy tetraquarks in the Born-Oppenheimer approximation

From a study of the line shape of the <math><mi>X</mi><mo>(</mo><mn>3872</mn><mo>)</mo></math>, the LHCb collaboration measures a sizeable negative effective range. This cannot be reconciled with a shallow <math><mi>D</mi><msup><mover><mi>D</mi><mo>¯</mo></mover><mo>*</mo></msup></math> bound state hypothesis. Based on Weinberg’s compositeness criterion, together with a theorem by Smorodinsky, it follows that the <math><mi>X</mi></math> has to have a compact hidden charm structure interacting with unbound <math><mi>D</mi><msup><mover><mi>D</mi><mo>¯</mo></mover><mo>*</mo></msup></math> pairs via short-distance color forces. This conclusion is strengthened by the general pattern recently emerging from exotic mesons.

United States

Angelo Esposito

Verónica Riquer

From the line shape of the <math><mi>X</mi><mo>(</mo><mn>3872</mn><mo>)</mo></math> to its structure

We discuss a method to construct hadronic scattering and decay amplitudes from Euclidean correlators, by combining the approach of a regulated inverse Laplace transform with the work of Maiani and Testa [1]. Revisiting the original result of ref. [1], we observe that the key observation, i.e. that only threshold scattering information can be extracted at large separations, can be understood by interpreting the correlator as a spectral function, ρ(ω), convoluted with the Euclidean kernel, e  −ωt , which is sharply peaked at threshold. We therefore consider a modification in which a smooth step function, equal to one above a target energy, is inserted in the spectral decomposition. This can be achieved either through Backus-Gilbert-like methods or more directly using the variational approach. The result is a shifted resolution function, such that the large t limit projects onto scattering or decay amplitudes above threshold. The utility of this method is highlighted through large t expansions of both three- and four-point functions that include leading terms proportional to the real and imaginary parts (separately) of the target observable. This work also presents new results relevant for the un-modified correlator at threshold, including expressions for extracting the Nπ scattering length from four-point functions and a new strategy to organize the large t expansion that exhibits better convergence than the expansion in powers of 1/t.

M. Bruno

United Kingdom

M. Hansen

Variations on the Maiani-Testa approach and the inverse problem

We discuss how the latest data on <math><mi>X</mi><mo>(</mo><mn>3872</mn><mo>)</mo></math> in <math><mi>B</mi></math> and <math><msub><mi>B</mi><mi>s</mi></msub></math> decays speak about its tetraquark nature. The established decay pattern, including the up-to-date observations by CMS, are explained by the mixing of two quasidegenerate, unresolvable neutral states. The same mechanism also explains isospin violations in <math><mi>X</mi></math> decays and strongly suggests that the lurking charged partners are required to have very small branching fractions in <math><mi>J</mi><mo>/</mo><mi>ψ</mi><msup><mi>ρ</mi><mo>±</mo></msup></math>, well below the current experimental limits. In addition, a new prediction on the decay into <math><mi>J</mi><mo>/</mo><mi>ψ</mi><mi>ω</mi></math> final states is attained. The newest experimental observations are found to give thrust to the simplest tetraquark picture and call for a definitive, in-depth study of final states with charged <math><mi>ρ</mi></math> mesons.

<math><mi>X</mi><mo>(</mo><mn>3872</mn><mo>)</mo></math> tetraquarks in <math><mi>B</mi></math> and <math><msub><mi>B</mi><mi>s</mi></msub></math> decays

Recently, the Belle Collaboration has updated the analysis of the cross sections for the processes <math><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo></mrow></msup><mo>→</mo><mi>ϒ</mi><mo>(</mo><mi>n</mi><mi>S</mi><mo>)</mo><mspace width="0.2em"></mspace><msup><mrow><mi>π</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mo>−</mo></mrow></msup></math> (<math><mi>n</mi><mo>=</mo><mn>1</mn><mo>,</mo><mspace width="0.2em"></mspace><mn>2</mn><mo>,</mo><mspace width="0.2em"></mspace><mn>3</mn></math>) in the <math><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo></mrow></msup></math> center-of-mass energy range from 10.52 to 11.02 GeV. A new structure, called here <math><msub><mrow><mi>Y</mi></mrow><mrow><mi>b</mi></mrow></msub><mo>(</mo><mn>10750</mn><mo>)</mo></math>, with the mass <math><mi>M</mi><mo>(</mo><msub><mrow><mi>Y</mi></mrow><mrow><mi>b</mi></mrow></msub><mo>)</mo><mo>=</mo><mo>(</mo><mn>10752.7</mn><mo>±</mo><msubsup><mrow><mn>5.9</mn></mrow><mrow><mo>−</mo><mn>1.1</mn></mrow><mrow><mo>+</mo><mn>0.7</mn></mrow></msubsup><mo>)</mo></math> MeV and the Breit-Wigner width <math><mi>Γ</mi><mo>(</mo><msub><mrow><mi>Y</mi></mrow><mrow><mi>b</mi></mrow></msub><mo>)</mo><mo>=</mo><mo>(</mo><msubsup><mrow><mn>35.5</mn></mrow><mrow><mo>−</mo><mn>11.3</mn><mo>−</mo><mn>3.3</mn></mrow><mrow><mo>+</mo><mn>17.6</mn><mo>+</mo><mn>3.9</mn></mrow></msubsup><mo>)</mo></math> MeV was observed [1]. We interpret <math><msub><mrow><mi>Y</mi></mrow><mrow><mi>b</mi></mrow></msub><mo>(</mo><mn>10750</mn><mo>)</mo></math> as a compact <math><msup><mrow><mi>J</mi></mrow><mrow><mi>P</mi><mi>C</mi></mrow></msup><mo>=</mo><msup><mrow><mn>1</mn></mrow><mrow><mo>−</mo><mo>−</mo></mrow></msup></math> state with a dominant tetraquark component. The mass eigenstate <math><msub><mrow><mi>Y</mi></mrow><mrow><mi>b</mi></mrow></msub><mo>(</mo><mn>10750</mn><mo>)</mo></math> is treated as a linear combination of the diquark-antidiquark and <math><mi>b</mi><mover><mrow><mi>b</mi></mrow><mrow><mo>¯</mo></mrow></mover></math> components due to the mixing via gluonic exchanges shown recently to arise in the limit of large number of quark colors. The mixing angle between <math><msub><mrow><mi>Y</mi></mrow><mrow><mi>b</mi></mrow></msub></math> and <math><mi>ϒ</mi><mo>(</mo><mn>5</mn><mi>S</mi><mo>)</mo></math> can be estimated from the electronic width, recently determined to be <math><msub><mrow><mi>Γ</mi></mrow><mrow><mi>e</mi><mi>e</mi></mrow></msub><mo>(</mo><msub><mrow><mi>Y</mi></mrow><mrow><mi>b</mi></mrow></msub><mo>)</mo><mo>=</mo><mo>(</mo><mn>13.7</mn><mo>±</mo><mn>1.8</mn><mo>)</mo></math> eV. The mixing provides a plausible mechanism for <math><msub><mrow><mi>Y</mi></mrow><mrow><mi>b</mi></mrow></msub><mo>(</mo><mn>10750</mn><mo>)</mo></math> production in high energy collisions from its <math><mi>b</mi><mover><mrow><mi>b</mi></mrow><mrow><mo>¯</mo></mrow></mover></math> component and we work out the Drell-Yan and prompt production cross sections for <math><mi>p</mi><mi>p</mi><mo>→</mo><msub><mrow><mi>Y</mi></mrow><mrow><mi>b</mi></mrow></msub><mo>(</mo><mn>10750</mn><mo>)</mo><mo>→</mo><mi>ϒ</mi><mo>(</mo><mi>n</mi><mi>S</mi><mo>)</mo><mspace width="0.2em"></mspace><msup><mrow><mi>π</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mo>−</mo></mrow></msup></math> at the LHC. The resonant part of the dipion invariant mass spectrum in <math><msub><mrow><mi>Y</mi></mrow><mrow><mi>b</mi></mrow></msub><mo>(</mo><mn>10750</mn><mo>)</mo><mo>→</mo><mi>ϒ</mi><mo>(</mo><mn>1</mn><mi>S</mi><mo>)</mo><mspace width="0.2em"></mspace><msup><mrow><mi>π</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mo>−</mo></mrow></msup></math> and the corresponding angular distribution of <math><msup><mrow><mi>π</mi></mrow><mrow><mo>+</mo></mrow></msup></math>-meson in the dipion rest frame are presented as an example.

Germany

Ahmed Ali

China

Russia

Alexander Ya. Parkhomenko

Wei Wang

Interpretation of (10750) as a Tetraquark and its Production Mechanism

In this paper we present in greater detail previous work on the Born-Oppenheimer approximation to treat the hydrogen bond of QCD, and add a similar treatment of doubly heavy baryons. Doubly heavy exotic resonances <math><mi>X</mi></math> and <math><mi>Z</mi></math> can be described as color molecules of two-quark lumps, the analogue of the <math><msub><mi>H</mi><mn>2</mn></msub></math> molecule, and doubly heavy baryons as the analog of the <math><msubsup><mi>H</mi><mn>2</mn><mo>+</mo></msubsup></math> ion, except that the two heavy quarks attract each other. We compare our results with constituent quark model and lattice QCD calculations and find further evidence in support of this upgraded picture of compact tetraquarks and baryons.

Hydrogen bond of QCD in doubly heavy baryons and tetraquarks

Using the Born-Oppenheimer approximation, we show that exotic resonances, <math><mrow><mi>X</mi></mrow></math> and <math><mi>Z</mi></math>, may emerge as QCD molecular objects made of colored two-quark lumps, states with heavy-light diquarks spatially separated from antidiquarks. With the same method we confirm that doubly heavy tetraquarks are stable against strong decays. Tetraquarks described here provide a new picture of exotic hadrons, as formed by the QCD analog of the hydrogen bond of molecular physics.