A non-relativistic model for the [cc] [cc] tetraquark

  • We use a non-relativistic model to study the spectroscopy of a tetraquark composed of [cc] [cc] 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 cc 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 cc 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.
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V. R. Debastiani and F. S. Navarra. A non-relativistic model for the [cc] [cc] tetraquark[J]. Chinese Physics C, 2019, 43(1): 013105. doi: 10.1088/1674-1137/43/1/013105
V. R. Debastiani and F. S. Navarra. A non-relativistic model for the [cc] [cc] tetraquark[J]. Chinese Physics C, 2019, 43(1): 013105.  doi: 10.1088/1674-1137/43/1/013105 shu
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Received: 2018-06-27
Revised: 2018-08-20
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    The 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)

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A non-relativistic model for the [cc] [cc] tetraquark

  • 1. Departamento de Física Teórica and IFIC, Centro Mixto Universidad de Valencia-CSIC Institutos deInvestigación de Paterna, Aptdo. 22085, 46071 Valencia, Spain;
  • 2. Instituto de Física, Universidade de São Paulo, C. P. 66318, 05389-970 São Paulo, SP, Brazil;
  • 3. Institut de Physique Théorique, Université Paris Saclay, CEA, CNRS, F-91191, Gif-sur-Yvette, France
Fund Project:  The 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)

Abstract: We use a non-relativistic model to study the spectroscopy of a tetraquark composed of [cc] [cc] 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 cc 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 cc 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.

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