<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

We explore the possible existence of the <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> counterpart of the <math><mi>X</mi><mo>(</mo><mn>3872</mn><mo>)</mo></math> state in a coupled-channels calculation within a constituent quark model, with the aim of confirming the existence of the so-called <math><mover><mrow><mi>X</mi></mrow><mrow><mo>˜</mo></mrow></mover><mo>(</mo><mn>3872</mn><mo>)</mo></math> state observed by the COMPASS Collaboration. Two states are found in the energy region of the <math><mover><mrow><mi>X</mi></mrow><mrow><mo>˜</mo></mrow></mover><mo>(</mo><mn>3872</mn><mo>)</mo></math> signal, both with almost equal mixture of <math><mi>c</mi><mover><mrow><mi>c</mi></mrow><mrow><mo>¯</mo></mrow></mover></math> <math><msup><mrow><mn>2</mn></mrow><mrow><mn>1</mn></mrow></msup><msub><mrow><mi>P</mi></mrow><mrow><mn>1</mn></mrow></msub></math> state and <math><msup><mrow><mi>D</mi></mrow><mrow><mo>⁎</mo></mrow></msup><msup><mrow><mover><mrow><mi>D</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mo>(</mo><mo>⁎</mo><mo>)</mo></mrow></msup></math> channels: One that can be identified as the dressed <math><mi>c</mi><mover><mrow><mi>c</mi></mrow><mrow><mo>¯</mo></mrow></mover></math> <math><msup><mrow><mn>2</mn></mrow><mrow><mn>1</mn></mrow></msup><msub><mrow><mi>P</mi></mrow><mrow><mn>1</mn></mrow></msub></math> and a bound state below the <math><mi>D</mi><msup><mrow><mover><mrow><mi>D</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mo>⁎</mo></mrow></msup></math> threshold. We provide predictions of strong and radiative decays that could help to clarify the existence of such structures.

Does the = 1 Counterpart of the (3872) Exist?

Hidden-charm pentaquark-like <math><msubsup><mrow><mi>P</mi></mrow><mrow><mi>ψ</mi><mi>s</mi></mrow><mrow><mi>Λ</mi></mrow></msubsup><msup><mrow><mo>(</mo><mn>4459</mn><mo>)</mo></mrow><mrow><mn>0</mn></mrow></msup></math> and <math><msubsup><mrow><mi>P</mi></mrow><mrow><mi>ψ</mi><mi>s</mi></mrow><mrow><mi>Λ</mi></mrow></msubsup><mo>(</mo><mn>4338</mn><mo>)</mo></math> resonances are studied in a constituent quark model as molecular meson-baryon structures. Such states are found in the <math><msup><mrow><mi>J</mi></mrow><mrow><mi>P</mi></mrow></msup><mo>(</mo><mi>I</mi><mo>)</mo><mo>=</mo><msup><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow><mrow><mo>−</mo></mrow></msup><mo>(</mo><mn>0</mn><mo>)</mo></math> channel with masses and widths compatible with the experimental measurements in a coupled-channels calculation with all the parameters constrained from previous studies. Other candidates are explored in the <math><msup><mrow><mi>J</mi></mrow><mrow><mi>P</mi></mrow></msup><mo>=</mo><msup><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow><mrow><mo>−</mo></mrow></msup></math>, <math><msup><mrow><mfrac><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow><mrow><mo>−</mo></mrow></msup></math> and <math><msup><mrow><mfrac><mrow><mn>5</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow><mrow><mo>−</mo></mrow></msup></math> channels in the charm and bottom sectors, with isospins 0 (<math><msubsup><mrow><mi>P</mi></mrow><mrow><mi>ψ</mi><mi>s</mi></mrow><mrow><mi>Λ</mi></mrow></msubsup></math> and <math><msubsup><mrow><mi>P</mi></mrow><mrow><mi>ϒ</mi><mi>s</mi></mrow><mrow><mi>Λ</mi></mrow></msubsup></math>) and 1 (<math><msubsup><mrow><mi>P</mi></mrow><mrow><mi>ψ</mi><mi>s</mi></mrow><mrow><mi>Σ</mi></mrow></msubsup></math> and <math><msubsup><mrow><mi>P</mi></mrow><mrow><mi>ϒ</mi><mi>s</mi></mrow><mrow><mi>Σ</mi></mrow></msubsup></math>). Additionally, the formalism is extended to study the <math><msubsup><mrow><mi>P</mi></mrow><mrow><mi>ψ</mi><mi>s</mi><mi>s</mi></mrow><mrow><mi>N</mi></mrow></msubsup></math> (<math><msubsup><mrow><mi>P</mi></mrow><mrow><mi>ϒ</mi><mi>s</mi><mi>s</mi></mrow><mrow><mi>N</mi></mrow></msubsup></math>) pentaquarks, where eight candidates are predicted as <math><msub><mrow><mover><mrow><mi>D</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mi>s</mi></mrow></msub><msub><mrow><mi>Ξ</mi></mrow><mrow><mi>c</mi></mrow></msub></math> molecules in <math><mi>I</mi><mo>=</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></math>, with <math><msup><mrow><mi>J</mi></mrow><mrow><mi>P</mi></mrow></msup><mo>=</mo><msup><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow><mrow><mo>−</mo></mrow></msup></math>, <math><msup><mrow><mfrac><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow><mrow><mo>−</mo></mrow></msup></math> and <math><msup><mrow><mfrac><mrow><mn>5</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow><mrow><mo>−</mo></mrow></msup></math> for the charm sector and nine candidates as <math><msub><mrow><mi>B</mi></mrow><mrow><mi>s</mi></mrow></msub><msub><mrow><mi>Ξ</mi></mrow><mrow><mi>b</mi></mrow></msub></math> for the bottom one.

Strange hidden-charm And Pentaquarks and Additional , And Candidates in a Quark Model Approach

The recent discovery of the <math><msub><mrow><mi>D</mi></mrow><mrow><mi>s</mi><mn>0</mn></mrow></msub><msup><mrow><mo>(</mo><mn>2590</mn><mo>)</mo></mrow><mrow><mo>+</mo></mrow></msup></math> meson by the LHCb Collaboration has stimulated the analysis of meson-meson channels effects in the two-body quark-antiquark meson spectrum. This resonance, assigned to the radial excitation of the pseudoscalar <math><msubsup><mrow><mi>D</mi></mrow><mrow><mi>s</mi></mrow><mrow><mo>+</mo></mrow></msubsup></math> meson, has a mass much lower than the predictions of naive quark models, which could indicate a non-negligible <math><msup><mrow><mi>D</mi></mrow><mrow><mo>(</mo><mo>⁎</mo><mo>)</mo></mrow></msup><msup><mrow><mi>K</mi></mrow><mrow><mo>(</mo><mo>⁎</mo><mo>)</mo></mrow></msup></math> coupling which reduces its mass. Based on the importance of nearby meson-meson thresholds in the dynamics of P-wave <math><msub><mrow><mi>D</mi></mrow><mrow><mi>s</mi></mrow></msub></math> mesons such as the <math><msubsup><mrow><mi>D</mi></mrow><mrow><mi>s</mi><mn>0</mn></mrow><mrow><mo>⁎</mo></mrow></msubsup><msup><mrow><mo>(</mo><mn>2317</mn><mo>)</mo></mrow><mrow><mo>+</mo></mrow></msup></math> and <math><msub><mrow><mi>D</mi></mrow><mrow><mi>s</mi><mn>1</mn></mrow></msub><msup><mrow><mo>(</mo><mn>2460</mn><mo>)</mo></mrow><mrow><mo>+</mo></mrow></msup></math>, in this work we perform a coupled-channels calculation including the <math><msup><mrow><mi>D</mi></mrow><mrow><mo>(</mo><mo>⁎</mo><mo>)</mo></mrow></msup><msup><mrow><mi>K</mi></mrow><mrow><mo>(</mo><mo>⁎</mo><mo>)</mo></mrow></msup></math>, <math><msubsup><mrow><mi>D</mi></mrow><mrow><mi>s</mi></mrow><mrow><mo>(</mo><mo>⁎</mo><mo>)</mo></mrow></msubsup><mi>ω</mi></math> and <math><msubsup><mrow><mi>D</mi></mrow><mrow><mi>s</mi></mrow><mrow><mo>⁎</mo></mrow></msubsup><mi>η</mi></math> channels, and study the impact of incorporating those channels in the mass of the bare <math><mi>c</mi><mover><mrow><mi>s</mi></mrow><mrow><mo>¯</mo></mrow></mover></math>. The coupling between two and four-quark sectors is done by means of the <math><mmultiscripts><mrow><mi>P</mi></mrow><mrow><mn>0</mn></mrow><none></none><mprescripts></mprescripts><none></none><mrow><mn>3</mn></mrow></mmultiscripts></math> mechanism, with all the parameters constrained from previous studies of the heavy meson spectroscopy. The masses, widths and production line shapes of the resulting state are analyzed.

The (2590) As the Dressed Meson in a Coupled-channels Calculation

The <math><mrow><msub><mrow><mi>Z</mi></mrow><mrow><mi>b</mi></mrow></msub><mo>(</mo><mn>10610</mn><msup><mrow><mo>)</mo></mrow><mrow><mo>±</mo></mrow></msup></mrow></math> and <math><msub><mi>Z</mi><mi>b</mi></msub><mo>(</mo><mn>10650</mn><msup><mo>)</mo><mo>±</mo></msup></math> are two bottomoniumlike structures discovered in the <math><mrow><mi>π</mi><msub><mrow><mi>h</mi></mrow><mrow><mi>b</mi></mrow></msub><mo>(</mo><mi>m</mi><mi>P</mi><mo>)</mo></mrow></math>, <math><mrow><mi>π</mi><mi>ϒ</mi><mo>(</mo><mi>n</mi><mi>S</mi><mo>)</mo></mrow></math> and <math><mrow><msup><mrow><mi>B</mi></mrow><mrow><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><mo>+</mo><mi>H</mi><mo>.</mo><mi>c</mi><mo>.</mo></mrow></math> invariant mass spectra, where <math><mi>m</mi><mo>=</mo><mo>{</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>}</mo></math> and <math><mi>n</mi><mo>=</mo><mo>{</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>}</mo></math>. Their nature is puzzling due to their charge, which forces its minimal quark content to be <math><mi>b</mi><mover><mi>b</mi><mo>¯</mo></mover><mi>u</mi><mover><mi>d</mi><mo>¯</mo></mover></math> (<math><mrow><mi>b</mi><mover><mrow><mi>b</mi></mrow><mrow><mo>¯</mo></mrow></mover><mi>d</mi><mover><mrow><mi>u</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow></math>). Thus, it is necessary to explore four-quark systems in order to understand their inner structure. Additionally, their strong coupling to channels such as <math><mi>π</mi><mi>ϒ</mi></math> and the closeness of their mass to <math><mrow><msup><mrow><mi>B</mi></mrow><mrow><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> thresholds stimulates a molecular interpretation. Within the framework of a constituent quark model which satisfactorily describes a wide range of properties of (non)conventional hadrons containing heavy quarks, we perform a coupled-channels calculation of the <math><mrow><msup><mrow><mi>I</mi></mrow><mrow><mi>G</mi></mrow></msup><mo>(</mo><msup><mrow><mi>J</mi></mrow><mrow><mi>P</mi><mi>C</mi></mrow></msup><mo>)</mo><mo>=</mo><msup><mrow><mn>1</mn></mrow><mrow><mo>+</mo></mrow></msup><mo>(</mo><msup><mrow><mn>1</mn></mrow><mrow><mo>+</mo><mo>−</mo></mrow></msup><mo>)</mo></mrow></math> hidden-bottom sector including <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></mrow></msup><mo>+</mo><mi>H</mi><mo>.</mo><mi>c</mi><mo>.</mo></mrow></math>, <math><mi>π</mi><msub><mi>h</mi><mi>b</mi></msub></math>, <math><mi>π</mi><mi>ϒ</mi></math>, and <math><mi>ρ</mi><msub><mi>η</mi><mi>b</mi></msub></math> channels. We analyze the line shapes in the different channels, describing the <math><mrow><mi>ϒ</mi><mo>(</mo><mn>5</mn><mi>S</mi><mo>)</mo><mo>→</mo><mi>π</mi><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> by means of the <math><mrow><mmultiscripts><mrow><msub><mrow><mi>P</mi></mrow><mrow><mn>0</mn></mrow></msub></mrow><mprescripts></mprescripts><none></none><mrow><mn>3</mn></mrow></mmultiscripts></mrow></math> model. Since our description of the line shapes is promising, we perform the same coupled-channels calculation for the <math><msub><mi>Z</mi><mi>b</mi></msub></math>’s with <math><msup><mi>J</mi><mrow><mo>−</mo><mo>−</mo></mrow></msup></math>, where <math><mi>J</mi><mo>=</mo><mo>{</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>}</mo></math>. This allows us to obtain a fair description of the corresponding line shapes. The study of the analytic structure of the <math><mi>S</mi></math>-matrix suggests that the experimental <math><msub><mi>Z</mi><mi>b</mi></msub></math> structures arise as a combination of several poles with <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>, <math><msup><mn>1</mn><mrow><mo>±</mo><mo>−</mo></mrow></msup></math> and <math><msup><mn>2</mn><mrow><mo>−</mo><mo>−</mo></mrow></msup></math> quantum numbers nearby the <math><mi>B</mi><msup><mover><mi>B</mi><mo>¯</mo></mover><mo>*</mo></msup></math> and <math><msup><mi>B</mi><mo>*</mo></msup><msup><mover><mi>B</mi><mo>¯</mo></mover><mo>*</mo></msup></math> thresholds.

<math><msub><mi>Z</mi><mi>b</mi></msub></math> structures in a constituent quark model coupled-channels calculation

The discovery of a new charged structure in the <math><msup><mrow><mi>K</mi></mrow><mrow><mo>+</mo></mrow></msup></math> recoil-mass spectrum near the <math><msubsup><mrow><mi>D</mi></mrow><mrow><mi>s</mi></mrow><mrow><mo>−</mo></mrow></msubsup><msup><mrow><mi>D</mi></mrow><mrow><mo>⁎</mo><mn>0</mn></mrow></msup><mo>/</mo><msubsup><mrow><mi>D</mi></mrow><mrow><mi>s</mi></mrow><mrow><mo>⁎</mo><mo>−</mo></mrow></msubsup><msup><mrow><mi>D</mi></mrow><mrow><mn>0</mn></mrow></msup></math> threshold, dubbed <math><msub><mrow><mi>Z</mi></mrow><mrow><mi>c</mi><mi>s</mi></mrow></msub><msup><mrow><mo>(</mo><mn>3985</mn><mo>)</mo></mrow><mrow><mo>−</mo></mrow></msup></math>, reinforce the idea that the structure of hadrons goes beyond the naive qqq and the <math><mi>q</mi><mover><mrow><mi>q</mi></mrow><mrow><mo>¯</mo></mrow></mover></math> structures.The existence of this state, with quark content <math><mi>c</mi><mover><mrow><mi>c</mi></mrow><mrow><mo>¯</mo></mrow></mover><mi>s</mi><mover><mrow><mi>u</mi></mrow><mrow><mo>¯</mo></mrow></mover></math>, can be expected from the well-established <math><msub><mrow><mi>Z</mi></mrow><mrow><mi>c</mi></mrow></msub><msup><mrow><mo>(</mo><mn>3900</mn><mo>)</mo></mrow><mrow><mo>±</mo></mrow></msup></math> and <math><msub><mrow><mi>Z</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>(</mo><mn>4020</mn><mo>)</mo></math> states using SU(3) flavor symmetry. The <math><msub><mrow><mi>Z</mi></mrow><mrow><mi>c</mi></mrow></msub></math> structures have been explained using the chiral constituent quark model in a coupled-channels calculation and, in this work, we undertake the study of the <math><msub><mrow><mi>Z</mi></mrow><mrow><mi>c</mi><mi>s</mi></mrow></msub><msup><mrow><mo>(</mo><mn>3985</mn><mo>)</mo></mrow><mrow><mo>−</mo></mrow></msup></math> using the same model.We are able to reproduce the <math><msup><mrow><mi>K</mi></mrow><mrow><mo>+</mo></mrow></msup></math> recoil-mass spectrum without any fine tuning of the model parameters. The study of the analytical structure of the S-matrix allows us to conclude that the structure is due to the presence of one virtual pole. A second state, the SU(3) flavor partner of the <math><msub><mrow><mi>Z</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>(</mo><mn>4020</mn><mo>)</mo></math> is predicted at ∼4110 MeV/<math><msup><mrow><mi>c</mi></mrow><mrow><mn>2</mn></mrow></msup></math>. New states in the hidden bottom strange sector are also predicted.

The strange partner of the Structures in a Coupled-channels Model

The bottom-charmed ($$B_c$$ <math><msub><mi>B</mi><mi>c</mi></msub></math> ) mesons are more stable than their charmonium ($$c{{\bar{c}}}$$ <math><mrow><mi>c</mi><mover><mrow><mi>c</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow></math> ) and bottomium ($$b{{\bar{b}}}$$ <math><mrow><mi>b</mi><mover><mrow><mi>b</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow></math> ) partners because they cannot annihilate into gluons. However, the low production cross-sections and signal-to-background ratios avoided until now their clear identification. The recent experimental results reported by CMS and LHCb at CERN open the possibility of having a $$B_c$$ <math><msub><mi>B</mi><mi>c</mi></msub></math>  spectrum as complete as the ones of charmonium and bottomonium. Motivated by this expectation, we compute bottom-charmed meson masses in the region energies in which decay meson–meson thresholds are opened, looking for the analogs to the X(3872) in the $$B_c$$ <math><msub><mi>B</mi><mi>c</mi></msub></math>  spectroscopy. We use a constituent quark model in which quark–antiquark degrees of freedom are complemented by four-body Fock states configurations. The model has been applied to a wide range of hadronic observables, in particular to the X(3872), and thus the model parameters are completely constrained. No extra states are found in the $$J^P=0^+$$ <math><mrow><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><msup><mn>0</mn><mo>+</mo></msup></mrow></math>  and $$J^P=1^+$$ <math><mrow><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><msup><mn>1</mn><mo>+</mo></msup></mrow></math>  sectors. However, in the $$J^P=2^+$$ <math><mrow><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><msup><mn>2</mn><mo>+</mo></msup></mrow></math>  sector we found an additional state very close to the $$D^*B^*$$ <math><mrow><msup><mi>D</mi><mo>∗</mo></msup><msup><mi>B</mi><mo>∗</mo></msup></mrow></math>  threshold which could be experimentally detected.

Pablo Ortega

David Entem

Spectroscopy of $$\mathbf {B_c}$$ <math><msub><mi>B</mi><mi>c</mi></msub></math>  mesons and the possibility of finding exotic $$\mathbf {B_c}$$ <math><msub><mi>B</mi><mi>c</mi></msub></math> -like structures

In recent years, the discovery in quarkonium spectrum of several states not predicted by the naive quark model has awakened a lot of interest. A possible description of such states requires the enlargement of the quark model by introducing quark-antiquark pair creation or continuum coupling effects. The unquenching of the quark models is a way to take these new components into account. In the spirit of the Cornell Model, this is usually done by coupling perturbatively a quark-antiquark state with definite quantum numbers to the meson-meson channel with the closest threshold. In this work we present a method to coupled quark-antiquark states with meson-meson channels, taking into account effectively the nonperturbative coupling to all quark-antiquark states with the same quantum numbers. The method will be applied to the study of the X(3872) resonance and a comparison with the perturbative calculation will be performed.

Unquenching the Quark Model in a Nonperturbative Scheme

Along the years, the Cornell model has been extraordinarily successful in describing hadronic phenomenology, in particular in physical situations for which an effective theory of the strong interactions such as NRQCD cannot be applied. As a consequence of its achievements, a relevant question is whether its model parameters can somehow be related to fundamental constants of QCD. We shall give a first answer in this article by comparing the predictions of both approaches. Building on results from a previous study on heavy meson spectroscopy, we calibrate the Cornell model employing NRQCD predictions for the lowest-lying bottomonium states up to $$\hbox {N}^3\hbox {LO}$$ <math><mrow><msup><mtext>N</mtext><mn>3</mn></msup><mtext>LO</mtext></mrow></math> , in which the bottom mass is varied within a wide range. We find that the Cornell model mass parameter can be identified, within perturbative uncertainties, with the MSR mass at the scale $$R = 1\,\hbox {GeV}$$ <math><mrow><mi>R</mi><mo>=</mo><mn>1</mn><mspace width="0.166667em"></mspace><mtext>GeV</mtext></mrow></math> . This identification holds for any value of $$\alpha _s$$ <math><msub><mi>α</mi><mi>s</mi></msub></math>  or the bottom mass, and for all perturbative orders investigated. Furthermore, we show that: (a) the “string tension” parameter is independent of the bottom mass, and (b) the Coulomb strength $$\kappa $$ <math><mi>κ</mi></math>  of the Cornell model can be related to the QCD strong coupling constant $$\alpha _s$$ <math><msub><mi>α</mi><mi>s</mi></msub></math>  at a characteristic non-relativistic scale. We also show how to remove the $$u=1/2$$ <math><mrow><mi>u</mi><mo>=</mo><mn>1</mn><mo>/</mo><mn>2</mn></mrow></math>  renormalon of the static QCD potential and sum-up large logs related to the renormalon subtraction by switching to the low-scale, short-distance MSR mass, and using R-evolution. Our R-improved expression for the static potential remains independent of the heavy quark mass value and agrees with lattice QCD results for values of the radius as large as $$0.8\,\hbox {fm}$$ <math><mrow><mn>0.8</mn><mspace width="0.166667em"></mspace><mtext>fm</mtext></mrow></math> , and with the Cornell model potential at long distances. Finally we show that for moderate values of r, the R-improved NRQCD and Cornell static potentials are in head-on agreement.

Vicent Mateu

Calibrating the naïve Cornell model with NRQCD

The $$Z_{c}(3900)^\pm /Z_c(3885)^\pm $$ <math><mrow><msub><mi>Z</mi><mi>c</mi></msub><msup><mrow><mo>(</mo><mn>3900</mn><mo>)</mo></mrow><mo>±</mo></msup><mo>/</mo><msub><mi>Z</mi><mi>c</mi></msub><msup><mrow><mo>(</mo><mn>3885</mn><mo>)</mo></mrow><mo>±</mo></msup></mrow></math>  and $$Z_{c}(4020)^\pm $$ <math><mrow><msub><mi>Z</mi><mi>c</mi></msub><msup><mrow><mo>(</mo><mn>4020</mn><mo>)</mo></mrow><mo>±</mo></msup></mrow></math>  are two charmonium-like structures discovered in the $$\pi J/\psi $$ <math><mrow><mi>π</mi><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></math>  and $$D^*\bar{D}^{(*)}+h.c.$$ <math><mrow><msup><mi>D</mi><mo>∗</mo></msup><msup><mrow><mover><mrow><mi>D</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mo>(</mo><mrow></mrow><mo>∗</mo><mo>)</mo></mrow></msup><mo>+</mo><mi>h</mi><mo>.</mo><mi>c</mi><mo>.</mo></mrow></math>  invariant mass spectra. Their nature is puzzling due to their charge, which forces its minimal quark content to be $$c\bar{c} u\bar{d}$$ <math><mrow><mi>c</mi><mover><mrow><mi>c</mi></mrow><mrow><mo>¯</mo></mrow></mover><mi>u</mi><mover><mrow><mi>d</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow></math>  ($$c\bar{c} d\bar{u}$$ <math><mrow><mi>c</mi><mover><mrow><mi>c</mi></mrow><mrow><mo>¯</mo></mrow></mover><mi>d</mi><mover><mrow><mi>u</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow></math> ). Thus, it is necessary to explore four-quark systems in order to understand their inner structure. Additionally, their strong coupling to channels such as $$\pi J/\psi $$ <math><mrow><mi>π</mi><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></math>  and the closeness of their mass to $$D^*\bar{D}^{(*)}$$ <math><mrow><msup><mi>D</mi><mo>∗</mo></msup><msup><mrow><mover><mrow><mi>D</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mo>(</mo><mrow></mrow><mo>∗</mo><mo>)</mo></mrow></msup></mrow></math> -thresholds stimulates both a molecular interpretation or a coupled-channels threshold effect. In this work we perform a coupled-channels calculation of the $$I^G(J^{PC})=1^+(1^{+-})$$ <math><mrow><msup><mi>I</mi><mi>G</mi></msup><mrow><mo>(</mo><msup><mi>J</mi><mrow><mi>PC</mi></mrow></msup><mo>)</mo></mrow><mo>=</mo><msup><mn>1</mn><mo>+</mo></msup><mrow><mo>(</mo><msup><mn>1</mn><mrow><mo>+</mo><mo>-</mo></mrow></msup><mo>)</mo></mrow></mrow></math>  sector including $$D^{(*)}\bar{D}^{*}+h.c.$$ <math><mrow><msup><mi>D</mi><mrow><mo>(</mo><mrow></mrow><mo>∗</mo><mo>)</mo></mrow></msup><msup><mrow><mover><mrow><mi>D</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mrow></mrow><mo>∗</mo></mrow></msup><mo>+</mo><mi>h</mi><mo>.</mo><mi>c</mi><mo>.</mo></mrow></math> , $$\pi J/\psi $$ <math><mrow><mi>π</mi><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></math>  and $$\rho \eta _c$$ <math><mrow><mi>ρ</mi><msub><mi>η</mi><mi>c</mi></msub></mrow></math>  channels in the framework of a constituent quark model which satisfactorily describes a wide range of properties of (non-)conventional hadrons containing heavy quarks. The meson–meson interactions are dominated by the non-diagonal $$\pi J/\psi -D^*\bar{D}^{(*)}$$ <math><mrow><mi>π</mi><mi>J</mi><mo>/</mo><mi>ψ</mi><mo>-</mo><msup><mi>D</mi><mo>∗</mo></msup><msup><mrow><mover><mrow><mi>D</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mo>(</mo><mrow></mrow><mo>∗</mo><mo>)</mo></mrow></msup></mrow></math>  and $$\rho \eta _c-D^*\bar{D}^{(*)}$$ <math><mrow><mi>ρ</mi><msub><mi>η</mi><mi>c</mi></msub><mo>-</mo><msup><mi>D</mi><mo>∗</mo></msup><msup><mrow><mover><mrow><mi>D</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mo>(</mo><mrow></mrow><mo>∗</mo><mo>)</mo></mrow></msup></mrow></math>  couplings which indicates that the $$Z_{c}(3900)^\pm /Z_c(3885)^\pm $$ <math><mrow><msub><mi>Z</mi><mi>c</mi></msub><msup><mrow><mo>(</mo><mn>3900</mn><mo>)</mo></mrow><mo>±</mo></msup><mo>/</mo><msub><mi>Z</mi><mi>c</mi></msub><msup><mrow><mo>(</mo><mn>3885</mn><mo>)</mo></mrow><mo>±</mo></msup></mrow></math>  and $$Z_{c}(4020)^\pm $$ <math><mrow><msub><mi>Z</mi><mi>c</mi></msub><msup><mrow><mo>(</mo><mn>4020</mn><mo>)</mo></mrow><mo>±</mo></msup></mrow></math>  are unusual structures. The study of the analytic structure of the S-matrix allows us to conclude that the point-wise behavior of the line shapes in the $$\pi J/\psi $$ <math><mrow><mi>π</mi><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></math>  and $$D\bar{D}^*$$ <math><mrow><mi>D</mi><msup><mrow><mover><mrow><mi>D</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mo>∗</mo></msup></mrow></math>  invariant mass distributions is due to the presence of two virtual states that produce the $$Z_c$$ <math><msub><mi>Z</mi><mi>c</mi></msub></math>  peaks.