Spectrum of S- and P-wave ccq¯q¯ (q¯,q¯=u¯,d¯,s¯) systems in a chiral SU(3) quark model

Du Wang (School of Nuclear Science and Technology, University of Chinese Academy of Sciences, Beijing 101408, China) ; Ke-Rang Song (School of Nuclear Science and Technology, University of Chinese Academy of Sciences, Beijing 101408, China) ; Wen-Ling Wang (School of Physics, Beihang University, Beijing 100191, China) ; Fei Huang (School of Nuclear Science and Technology, University of Chinese Academy of Sciences, Beijing 101408, China)

Inspired by the resonance Tcc+(3875) recently observed by the LHCb Collaboration, we systematically explore the S- and P-wave ccq¯q¯ (q¯,q¯=u¯,d¯,s¯) systems in a chiral SU(3) quark model. The Hamiltonian contains the kinetic energy, the one-gluon-exchange (OGE) potential, the confinement potential, and the one-boson-exchange (OBE) potential stemming from the coupling of quark and chiral fields. The Schrödinger equation is solved by use of the variational method with the spacial trial wave functions chosen as Gaussian functions. It is found that the lowest state has a mass 3879 MeV, isospin and spin-parity IJP=01+, and quark constituent ccu¯d¯, in agreement with the experimentally observed Tcc+(3875). This state is approximately at the calculated DD* threshold and has a root-mean-square radius of about 0.48 fm. These demonstrate that the Tcc+(3875) can be accommodated as a stable and compact tetraquark sate in the chiral SU(3) quark model. All the other S- and P-wave ccq¯q¯ (q¯,q¯=u¯,d¯,s¯) states lie about 100 to a few hundreds MeV higher than the corresponding meson-meson thresholds and thus are not suggested to be candidates of stable and compact tetraquark states due to their fall-apart decays to two mesons.

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      "title": "Spectrum of <math><mi>S</mi></math>- and <math><mi>P</mi></math>-wave <math><mi>c</mi><mi>c</mi><mover><mi>q</mi><mo>\u00af</mo></mover><msup><mover><mi>q</mi><mo>\u00af</mo></mover><mo>\u2032</mo></msup></math> <math><mo>(</mo><mover><mi>q</mi><mo>\u00af</mo></mover><mo>,</mo><msup><mover><mi>q</mi><mo>\u00af</mo></mover><mo>\u2032</mo></msup><mo>=</mo><mover><mi>u</mi><mo>\u00af</mo></mover><mo>,</mo><mover><mi>d</mi><mo>\u00af</mo></mover><mo>,</mo><mover><mi>s</mi><mo>\u00af</mo></mover><mo>)</mo></math> systems in a chiral SU(3) quark model"
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  "abstracts": [
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      "source": "APS", 
      "value": "Inspired by the resonance <math><msubsup><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow><mo>+</mo></msubsup><mo>(</mo><mn>3875</mn><mo>)</mo></math> recently observed by the LHCb Collaboration, we systematically explore the <math><mi>S</mi></math>- and <math><mi>P</mi></math>-wave <math><mi>c</mi><mi>c</mi><mover><mi>q</mi><mo>\u00af</mo></mover><msup><mover><mi>q</mi><mo>\u00af</mo></mover><mo>\u2032</mo></msup></math> <math><mo>(</mo><mover><mi>q</mi><mo>\u00af</mo></mover><mo>,</mo><msup><mover><mi>q</mi><mo>\u00af</mo></mover><mo>\u2032</mo></msup><mo>=</mo><mover><mi>u</mi><mo>\u00af</mo></mover><mo>,</mo><mover><mi>d</mi><mo>\u00af</mo></mover><mo>,</mo><mover><mi>s</mi><mo>\u00af</mo></mover><mo>)</mo></math> systems in a chiral SU(3) quark model. The Hamiltonian contains the kinetic energy, the one-gluon-exchange (OGE) potential, the confinement potential, and the one-boson-exchange (OBE) potential stemming from the coupling of quark and chiral fields. The Schr\u00f6dinger equation is solved by use of the variational method with the spacial trial wave functions chosen as Gaussian functions. It is found that the lowest state has a mass 3879 MeV, isospin and spin-parity <math><mi>I</mi><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><mn>0</mn><msup><mn>1</mn><mo>+</mo></msup></math>, and quark constituent <math><mi>c</mi><mi>c</mi><mover><mi>u</mi><mo>\u00af</mo></mover><mover><mi>d</mi><mo>\u00af</mo></mover></math>, in agreement with the experimentally observed <math><msubsup><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow><mo>+</mo></msubsup><mo>(</mo><mn>3875</mn><mo>)</mo></math>. This state is approximately at the calculated <math><mi>D</mi><msup><mi>D</mi><mo>*</mo></msup></math> threshold and has a root-mean-square radius of about 0.48 fm. These demonstrate that the <math><msubsup><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow><mo>+</mo></msubsup><mo>(</mo><mn>3875</mn><mo>)</mo></math> can be accommodated as a stable and compact tetraquark sate in the chiral SU(3) quark model. All the other <math><mi>S</mi></math>- and <math><mi>P</mi></math>-wave <math><mi>c</mi><mi>c</mi><mover><mi>q</mi><mo>\u00af</mo></mover><msup><mover><mi>q</mi><mo>\u00af</mo></mover><mo>\u2032</mo></msup></math> <math><mo>(</mo><mover><mi>q</mi><mo>\u00af</mo></mover><mo>,</mo><msup><mover><mi>q</mi><mo>\u00af</mo></mover><mo>\u2032</mo></msup><mo>=</mo><mover><mi>u</mi><mo>\u00af</mo></mover><mo>,</mo><mover><mi>d</mi><mo>\u00af</mo></mover><mo>,</mo><mover><mi>s</mi><mo>\u00af</mo></mover><mo>)</mo></math> states lie about 100 to a few hundreds MeV higher than the corresponding meson-meson thresholds and thus are not suggested to be candidates of stable and compact tetraquark states due to their fall-apart decays to two mesons."
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Published on:
22 April 2024
Publisher:
APS
Published in:
Physical Review D , Volume 109 (2024)
Issue 7
DOI:
https://doi.org/10.1103/PhysRevD.109.074026
arXiv:
2403.15187
Copyrights:
Published by the American Physical Society
Licence:
CC-BY-4.0

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