Fully heavy tetraquark resonant states with different flavors

We use the quark potential model to calculate the mass spectrum of the S-wave fully heavy tetraquark systems with different flavors, including the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>b</a:mi><a:mi>c</a:mi><a:mover accent="true"><a:mi>b</a:mi><a:mo stretchy="false">¯</a:mo></a:mover><a:mover accent="true"><a:mi>c</a:mi><a:mo stretchy="false">¯</a:mo></a:mover><a:mo>,</a:mo><a:mi>b</a:mi><a:mi>b</a:mi><a:mover accent="true"><a:mi>c</a:mi><a:mo stretchy="false">¯</a:mo></a:mover><a:mover accent="true"><a:mi>c</a:mi><a:mo stretchy="false">¯</a:mo></a:mover><a:mo>,</a:mo><a:mi>c</a:mi><a:mi>c</a:mi><a:mover accent="true"><a:mi>c</a:mi><a:mo stretchy="false">¯</a:mo></a:mover><a:mover accent="true"><a:mi>b</a:mi><a:mo stretchy="false">¯</a:mo></a:mover></a:math>, and <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mi>b</o:mi><o:mi>b</o:mi><o:mover accent="true"><o:mi>b</o:mi><o:mo stretchy="false">¯</o:mo></o:mover><o:mover accent="true"><o:mi>c</o:mi><o:mo stretchy="false">¯</o:mo></o:mover></o:math> systems. We employ the Gaussian expansion method to solve the four-body Schrödinger equation, and the complex scaling method to identify resonant states. The <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:mi>b</u:mi><u:mi>c</u:mi><u:mover accent="true"><u:mi>b</u:mi><u:mo stretchy="false">¯</u:mo></u:mover><u:mover accent="true"><u:mi>c</u:mi><u:mo stretchy="false">¯</u:mo></u:mover><u:mo>,</u:mo><u:mi>b</u:mi><u:mi>b</u:mi><u:mover accent="true"><u:mi>c</u:mi><u:mo stretchy="false">¯</u:mo></u:mover><u:mover accent="true"><u:mi>c</u:mi><u:mo stretchy="false">¯</u:mo></u:mover><u:mo>,</u:mo><u:mi>c</u:mi><u:mi>c</u:mi><u:mover accent="true"><u:mi>c</u:mi><u:mo stretchy="false">¯</u:mo></u:mover><u:mover accent="true"><u:mi>b</u:mi><u:mo stretchy="false">¯</u:mo></u:mover></u:math>, and <ib:math xmlns:ib="http://www.w3.org/1998/Math/MathML" display="inline"><ib:mi>b</ib:mi><ib:mi>b</ib:mi><ib:mover accent="true"><ib:mi>b</ib:mi><ib:mo stretchy="false">¯</ib:mo></ib:mover><ib:mover accent="true"><ib:mi>c</ib:mi><ib:mo stretchy="false">¯</ib:mo></ib:mover></ib:math> resonant states are obtained in the mass regions of (13.2, 13.5), (13.3, 13.6), (10.0, 10.3), (16.5, 16.7) GeV, respectively. Among these states, the <ob:math xmlns:ob="http://www.w3.org/1998/Math/MathML" display="inline"><ob:mi>b</ob:mi><ob:mi>c</ob:mi><ob:mover accent="true"><ob:mi>b</ob:mi><ob:mo stretchy="false">¯</ob:mo></ob:mover><ob:mover accent="true"><ob:mi>c</ob:mi><ob:mo stretchy="false">¯</ob:mo></ob:mover></ob:math> tetraquark states are the most promising ones to be discovered in the near future. We recommend the experimental exploration of the <ub:math xmlns:ub="http://www.w3.org/1998/Math/MathML" display="inline"><ub:msup><ub:mn>1</ub:mn><ub:mrow><ub:mo>+</ub:mo><ub:mo>+</ub:mo></ub:mrow></ub:msup></ub:math> and <wb:math xmlns:wb="http://www.w3.org/1998/Math/MathML" display="inline"><wb:mrow><wb:msup><wb:mrow><wb:mn>2</wb:mn></wb:mrow><wb:mrow><wb:mo>+</wb:mo><wb:mo>+</wb:mo></wb:mrow></wb:msup><wb:mtext> </wb:mtext><wb:mi>b</wb:mi><wb:mi>c</wb:mi><wb:mover accent="true"><wb:mrow><wb:mi>b</wb:mi></wb:mrow><wb:mrow><wb:mo stretchy="false">¯</wb:mo></wb:mrow></wb:mover><wb:mover accent="true"><wb:mrow><wb:mi>c</wb:mi></wb:mrow><wb:mrow><wb:mo stretchy="false">¯</wb:mo></wb:mrow></wb:mover></wb:mrow></wb:math> states with masses near 13.3 GeV in the <cc:math xmlns:cc="http://www.w3.org/1998/Math/MathML" display="inline"><cc:mi>J</cc:mi><cc:mo>/</cc:mo><cc:mi>ψ</cc:mi><cc:mi mathvariant="normal">ϒ</cc:mi></cc:math> channel. From the root-mean-square radii, we find that all the resonant states we have identified are compact tetraquark states. Published by the American Physical Society 2024