We use a non-relativistic model to study the spectroscopy of a tetraquark composed of in a diquark-antidiquark configuration. By numerically solving the Schrödinger equation with a Cornell-inspired potential, we separate the four-body problem into three two-body problems. Spin-dependent terms (spin-spin, spin-orbit and tensor) are used to describe the splitting structure of the spectrum and are also extended to the interaction between diquarks. Recent experimental data on charmonium states are used to fix the parameters of the model and a satisfactory description of the spectrum is obtained. We find that the spin-dependent interaction is sizable in the diquark-antidiquark system, despite the heavy diquark mass, and also that the diquark has a finite size if treated in the same way as the systems. We find that the lowest S-wave T4c tetraquarks might be below their thresholds of spontaneous dissociation into low-lying charmonium pairs, while orbital and radial excitations would be mostly above the corresponding charmonium pair thresholds. Finally, we repeat the calculations without the confining part of the potential and obtain bound diquarks and bound tetraquarks. This might be relevant to the study of exotic charmonium in the quark-gluon plasma. The T4c states could be investigated in the forthcoming experiments at the LHC and Belle II.

Spain

Brazil

V.R. Debastiani

France

F.S. Navarra

A non-relativistic model for the tetraquarkThe authors acknowledge the support received from the brazilian funding agencies FAPESP (contract 12/50984-4), CNPq and CAPES. V. R. Debastiani also acknowledges the support from Generalitat Valenciana in the Program Santiago Grisolia (Exp. GRISOLIA/2015/005)

Motivated by the experimental measurements of D0 radiative decay modes, we have proposed a model to study the decay, by establishing a link with (V=ρ0, ω) decays through the vector meson dominance hypothesis. In order to do this properly, we have used the Lagrangians from the local hidden gauge symmetry approach to account for Vγ conversion. As a result, we have found the branching ratio , which is in fair agreement with the experimental values reported by the Belle and BaBar collaborations.

China

J.M. Dias

Ju-Jun Xie

E. Oset

The radiative decay with vector meson dominanceJ. M. Dias would like to thank the Brazilian funding agency FAPESP for the financial support (2016/22561-2), V. R. Debastiani wishes to acknowledge the support from the Programa Santiago Grisolia of Generalitat Valenciana (Exp. GRISOLIA/2015/005). This work is also partly supported by the Spanish Ministerio de Economia y Competitividad and European FEDER funds (FIS2014-57026- REDT, FIS2014-51948-C2-1-P, FIS2014-51948-C2-2-P), and the Generalitat Valenciana in the program Prometeo II-2014/068. This work is partly supported by the National Natural Science Foundation of China (11475227, 11735003) and the Youth Innovation Promotion Association CAS (2016367)

Motivated by the recent finding of five <math><msub><mrow><mi>Ω</mi></mrow><mrow><mi>c</mi></mrow></msub></math> states by the LHCb collaboration, and the successful reproduction of three of them in a recent approach searching for molecular states of meson–baryon with the quantum numbers of <math><msub><mrow><mi>Ω</mi></mrow><mrow><mi>c</mi></mrow></msub></math>, we extend these ideas and make predictions for the interaction of meson–baryon in the beauty sector, searching for poles in the scattering matrix that correspond to physical states. We find several <math><msub><mrow><mi>Ω</mi></mrow><mrow><mi>b</mi></mrow></msub></math> states: two states with masses 6405 MeV and 6465 MeV for <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>; two more states with masses 6427 MeV and 6665 MeV for <math><msup><mrow><mfrac><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow><mrow><mo>−</mo></mrow></msup></math>; and three states between 6500 and 6820 MeV, degenerate 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><mo>,</mo><mspace width="0.2em"></mspace><msup><mrow><mfrac><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow><mrow><mo>−</mo></mrow></msup></math>, stemming from the interaction of vector–baryon in the beauty sector.

Wei-Hong Liang

Molecular Ω States

We study the isospin breaking in the reactions χc1→π0π+π− and χc1→π0π0η and its relation to the a0(980)−f0(980) mixing, which was measured by the BESIII Collaboration. We show that the same theoretical model previously developed to study the χc1→ηπ+π− reaction (also measured by BESIII), and further explored in the predictions to the ηc→ηπ+π− , can be successfully employed in the present study. We assume that the χc1 behaves as an SU(3) singlet to find the weight in which trios of pseudoscalars are created, followed by the final state interaction of pairs of mesons to describe how the a0(980) and f0(980) are dynamically generated, using the chiral unitary approach in coupled channels. The isospin violation is introduced through the use of different masses for the charged and neutral kaons, either in the propagators of pairs of mesons created in the χc1 decay, or in the propagators inside the T matrix, constructed through the unitarization of the scattering and transition amplitudes of pairs of pseudoscalar mesons. We find that violating isospin inside the T matrix makes the π0η→π+π− amplitude nonzero, which gives an important contribution and also enhances the effect of the KK¯ term. We also find that the most important effect in the total amplitude is the isospin breaking inside the T matrix, due to the constructive sum of π0η→π+π− and KK¯→π+π− , which is essential to get a good agreement with the experimental measurement of the mixing.

Türkiye

M. Bayar

A 0 (980)â f 0 (980) Mixing in ï c 1 â ï 0 f 0 (980)â ï 0 ï + ï â and ï c 1 â ï 0 a 0 (980)â ï 0 ï 0 î·