Spectrum of S - and P -wave ccq¯q<mml:mo …

Inspired by the resonance <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msubsup><a:mi>T</a:mi><a:mrow><a:mi>c</a:mi><a:mi>c</a:mi></a:mrow><a:mo>+</a:mo></a:msubsup><a:mo stretchy="false">(</a:mo><a:mn>3875</a:mn><a:mo stretchy="false">)</a:mo></a:math> recently observed by the LHCb Collaboration, we systematically explore the <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>S</e:mi></e:math>- and <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>P</g:mi></g:math>-wave <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>c</i:mi><i:mi>c</i:mi><i:mover accent="true"><i:mi>q</i:mi><i:mo stretchy="false">¯</i:mo></i:mover><i:msup><i:mover accent="true"><i:mi>q</i:mi><i:mo stretchy="false">¯</i:mo></i:mover><i:mo>′</i:mo></i:msup></i:math> <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mo stretchy="false">(</o:mo><o:mover accent="true"><o:mi>q</o:mi><o:mo stretchy="false">¯</o:mo></o:mover><o:mo>,</o:mo><o:msup><o:mover accent="true"><o:mi>q</o:mi><o:mo stretchy="false">¯</o:mo></o:mover><o:mo>′</o:mo></o:msup><o:mo>=</o:mo><o:mover accent="true"><o:mi>u</o:mi><o:mo stretchy="false">¯</o:mo></o:mover><o:mo>,</o:mo><o:mover accent="true"><o:mi>d</o:mi><o:mo stretchy="false">¯</o:mo></o:mover><o:mo>,</o:mo><o:mover accent="true"><o:mi>s</o:mi><o:mo stretchy="false">¯</o:mo></o:mover><o:mo stretchy="false">)</o:mo></o: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 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 <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"><cb:mi>I</cb:mi><cb:msup><cb:mi>J</cb:mi><cb:mi>P</cb:mi></cb:msup><cb:mo>=</cb:mo><cb:mn>0</cb:mn><cb:msup><cb:mn>1</cb:mn><cb:mo>+</cb:mo></cb:msup></cb:math>, and quark constituent <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"><eb:mi>c</eb:mi><eb:mi>c</eb:mi><eb:mover accent="true"><eb:mi>u</eb:mi><eb:mo stretchy="false">¯</eb:mo></eb:mover><eb:mover accent="true"><eb:mi>d</eb:mi><eb:mo stretchy="false">¯</eb:mo></eb:mover></eb:math>, in agreement with the experimentally observed <kb:math xmlns:kb="http://www.w3.org/1998/Math/MathML" display="inline"><kb:msubsup><kb:mi>T</kb:mi><kb:mrow><kb:mi>c</kb:mi><kb:mi>c</kb:mi></kb:mrow><kb:mo>+</kb:mo></kb:msubsup><kb:mo stretchy="false">(</kb:mo><kb:mn>3875</kb:mn><kb:mo stretchy="false">)</kb:mo></kb:math>. This state is approximately at the calculated <ob:math xmlns:ob="http://www.w3.org/1998/Math/MathML" display="inline"><ob:mi>D</ob:mi><ob:msup><ob:mi>D</ob:mi><ob:mo>*</ob:mo></ob:msup></ob:math> threshold and has a root-mean-square radius of about 0.48 fm. These demonstrate that the <qb:math xmlns:qb="http://www.w3.org/1998/Math/MathML" display="inline"><qb:msubsup><qb:mi>T</qb:mi><qb:mrow><qb:mi>c</qb:mi><qb:mi>c</qb:mi></qb:mrow><qb:mo>+</qb:mo></qb:msubsup><qb:mo stretchy="false">(</qb:mo><qb:mn>3875</qb:mn><qb:mo stretchy="false">)</qb:mo></qb:math> can be accommodated as a stable and compact tetraquark sate in the chiral SU(3) quark model. All the other <ub:math xmlns:ub="http://www.w3.org/1998/Math/MathML" display="inline"><ub:mi>S</ub:mi></ub:math>- and <wb:math xmlns:wb="http://www.w3.org/1998/Math/MathML" display="inline"><wb:mi>P</wb:mi></wb:math>-wave <yb:math xmlns:yb="http://www.w3.org/1998/Math/MathML" display="inline"><yb:mi>c</yb:mi><yb:mi>c</yb:mi><yb:mover accent="true"><yb:mi>q</yb:mi><yb:mo stretchy="false">¯</yb:mo></yb:mover><yb:msup><yb:mover accent="true"><yb:mi>q</yb:mi><yb:mo stretchy="false">¯</yb:mo></yb:mover><yb:mo>′</yb:mo></yb:msup></yb:math> <ec:math xmlns:ec="http://www.w3.org/1998/Math/MathML" display="inline"><ec:mo stretchy="false">(</ec:mo><ec:mover accent="true"><ec:mi>q</ec:mi><ec:mo stretchy="false">¯</ec:mo></ec:mover><ec:mo>,</ec:mo><ec:msup><ec:mover accent="true"><ec:mi>q</ec:mi><ec:mo stretchy="false">¯</ec:mo></ec:mover><ec:mo>′</ec:mo></ec:msup><ec:mo>=</ec:mo><ec:mover accent="true"><ec:mi>u</ec:mi><ec:mo stretchy="false">¯</ec:mo></ec:mover><ec:mo>,</ec:mo><ec:mover accent="true"><ec:mi>d</ec:mi><ec:mo stretchy="false">¯</ec:mo></ec:mover><ec:mo>,</ec:mo><ec:mover accent="true"><ec:mi>s</ec:mi><ec:mo stretchy="false">¯</ec:mo></ec:mover><ec:mo stretchy="false">)</ec:mo></ec: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. Published by the American Physical Society 2024