Unified description of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>Q</mml:mi><mml:mi>s</mml:mi><mml:mover accent="true"><mml:mrow><mml:mi>q</mml:mi></mml:mrow><mml:mrow><mml:mo stretchy="false">¯</mml:mo></mml:mrow></mml:mover><mml:mover accent="true"><mml:mrow><mml:mi>q</mml:mi></mml:mrow><mml:mrow><mml:mo stretchy="false">¯</mml:mo></mml:mrow></mml:mover></mml:mrow></mml:math> molecular bound states, molecular resonances, and compact tetraquark states in the quark potential model

Abstract

We calculate the mass spectrum of the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>Q</a:mi><a:mi>s</a:mi><a:mover accent="true"><a:mi>q</a:mi><a:mo stretchy="false">¯</a:mo></a:mover><a:mover accent="true"><a:mi>q</a:mi><a:mo stretchy="false">¯</a:mo></a:mover></a:math> (<g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mrow><g:mi>Q</g:mi><g:mo>=</g:mo><g:mi>c</g:mi></g:mrow></g:math>, <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mrow><i:mi>b</i:mi></i:mrow></i:math>) tetraquark states with <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:msup><k:mi>J</k:mi><k:mi>P</k:mi></k:msup><k:mo>=</k:mo><k:mo stretchy="false">(</k:mo><k:mn>0</k:mn><k:mo>,</k:mo><k:mn>1</k:mn><k:mo>,</k:mo><k:mn>2</k:mn><k:msup><k:mo stretchy="false">)</k:mo><k:mo>+</k:mo></k:msup></k:math> using the AL1 quark potential model, which successfully describes the conventional hadron spectrum. We employ the Gaussian expansion method to solve the four-body Schrödinger equation and use the complex scaling method to identify the resonances. With the notation <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:msubsup><o:mi>T</o:mi><o:mrow><o:mi>Q</o:mi><o:mi>s</o:mi><o:mo>,</o:mo><o:mi>I</o:mi><o:mo stretchy="false">(</o:mo><o:mi>J</o:mi><o:mo stretchy="false">)</o:mo></o:mrow><o:mrow><o:mi>Theo</o:mi><o:mo>.</o:mo></o:mrow></o:msubsup><o:mo stretchy="false">(</o:mo><o:mi>M</o:mi><o:mo stretchy="false">)</o:mo></o:math>, we find several near-threshold bound states and resonances, including <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:mrow><u:msubsup><u:mrow><u:mi>T</u:mi></u:mrow><u:mrow><u:mi>c</u:mi><u:mi>s</u:mi><u:mo>,</u:mo><u:mn>0</u:mn><u:mo stretchy="false">(</u:mo><u:mn>0</u:mn><u:mo stretchy="false">)</u:mo></u:mrow><u:mrow><u:mi>Theo</u:mi><u:mo>.</u:mo></u:mrow></u:msubsup><u:mo stretchy="false">(</u:mo><u:mn>2350</u:mn><u:mo stretchy="false">)</u:mo></u:mrow></u:math>, <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"><ab:msubsup><ab:mi>T</ab:mi><ab:mrow><ab:mi>c</ab:mi><ab:mi>s</ab:mi><ab:mo>,</ab:mo><ab:mn>0</ab:mn><ab:mo stretchy="false">(</ab:mo><ab:mn>0</ab:mn><ab:mo stretchy="false">)</ab:mo></ab:mrow><ab:mrow><ab:mi>Theo</ab:mi><ab:mo>.</ab:mo></ab:mrow></ab:msubsup><ab:mo stretchy="false">(</ab:mo><ab:mn>2906</ab:mn><ab:mo stretchy="false">)</ab:mo></ab:math>, <gb:math xmlns:gb="http://www.w3.org/1998/Math/MathML" display="inline"><gb:msubsup><gb:mi>T</gb:mi><gb:mrow><gb:mi>b</gb:mi><gb:mi>s</gb:mi><gb:mo>,</gb:mo><gb:mn>0</gb:mn><gb:mo stretchy="false">(</gb:mo><gb:mn>0</gb:mn><gb:mo stretchy="false">)</gb:mo></gb:mrow><gb:mrow><gb:mi>Theo</gb:mi><gb:mo>.</gb:mo></gb:mrow></gb:msubsup><gb:mo stretchy="false">(</gb:mo><gb:mn>5781</gb:mn><gb:mo stretchy="false">)</gb:mo></gb:math>, <mb:math xmlns:mb="http://www.w3.org/1998/Math/MathML" display="inline"><mb:msubsup><mb:mi>T</mb:mi><mb:mrow><mb:mi>b</mb:mi><mb:mi>s</mb:mi><mb:mo>,</mb:mo><mb:mn>0</mb:mn><mb:mo stretchy="false">(</mb:mo><mb:mn>1</mb:mn><mb:mo stretchy="false">)</mb:mo></mb:mrow><mb:mrow><mb:mi>Theo</mb:mi><mb:mo>.</mb:mo></mb:mrow></mb:msubsup><mb:mo stretchy="false">(</mb:mo><mb:mn>5840</mb:mn><mb:mo stretchy="false">)</mb:mo></mb:math>, and <sb:math xmlns:sb="http://www.w3.org/1998/Math/MathML" display="inline"><sb:msubsup><sb:mi>T</sb:mi><sb:mrow><sb:mi>b</sb:mi><sb:mi>s</sb:mi><sb:mo>,</sb:mo><sb:mn>0</sb:mn><sb:mo stretchy="false">(</sb:mo><sb:mn>0</sb:mn><sb:mo stretchy="false">)</sb:mo></sb:mrow><sb:mrow><sb:mi>Theo</sb:mi><sb:mo>.</sb:mo></sb:mrow></sb:msubsup><sb:mo stretchy="false">(</sb:mo><sb:mn>6240</sb:mn><sb:mo stretchy="false">)</sb:mo></sb:math>, which are close to the <yb:math xmlns:yb="http://www.w3.org/1998/Math/MathML" display="inline"><yb:mi>D</yb:mi><yb:mover accent="true"><yb:mi>K</yb:mi><yb:mo stretchy="false">¯</yb:mo></yb:mover></yb:math>, <cc:math xmlns:cc="http://www.w3.org/1998/Math/MathML" display="inline"><cc:msup><cc:mi>D</cc:mi><cc:mo>*</cc:mo></cc:msup><cc:msup><cc:mover accent="true"><cc:mi>K</cc:mi><cc:mo stretchy="false">¯</cc:mo></cc:mover><cc:mo>*</cc:mo></cc:msup></cc:math>, <gc:math xmlns:gc="http://www.w3.org/1998/Math/MathML" display="inline"><gc:mover accent="true"><gc:mi>B</gc:mi><gc:mo stretchy="false">¯</gc:mo></gc:mover><gc:mover accent="true"><gc:mi>K</gc:mi><gc:mo stretchy="false">¯</gc:mo></gc:mover></gc:math>, <mc:math xmlns:mc="http://www.w3.org/1998/Math/MathML" display="inline"><mc:msup><mc:mover accent="true"><mc:mi>B</mc:mi><mc:mo stretchy="false">¯</mc:mo></mc:mover><mc:mo>*</mc:mo></mc:msup><mc:mover accent="true"><mc:mi>K</mc:mi><mc:mo stretchy="false">¯</mc:mo></mc:mover></mc:math>, and <sc:math xmlns:sc="http://www.w3.org/1998/Math/MathML" display="inline"><sc:msup><sc:mover accent="true"><sc:mi>B</sc:mi><sc:mo stretchy="false">¯</sc:mo></sc:mover><sc:mo>*</sc:mo></sc:msup><sc:msup><sc:mover accent="true"><sc:mi>K</sc:mi><sc:mo stretchy="false">¯</sc:mo></sc:mover><sc:mo>*</sc:mo></sc:msup></sc:math> thresholds, respectively. Furthermore, their spatial structures clearly support their molecular natures. The resonance <yc:math xmlns:yc="http://www.w3.org/1998/Math/MathML" display="inline"><yc:msubsup><yc:mi>T</yc:mi><yc:mrow><yc:mi>c</yc:mi><yc:mi>s</yc:mi><yc:mo>,</yc:mo><yc:mn>0</yc:mn><yc:mo stretchy="false">(</yc:mo><yc:mn>0</yc:mn><yc:mo stretchy="false">)</yc:mo></yc:mrow><yc:mrow><yc:mi>Theo</yc:mi><yc:mo>.</yc:mo></yc:mrow></yc:msubsup><yc:mo stretchy="false">(</yc:mo><yc:mn>2906</yc:mn><yc:mo stretchy="false">)</yc:mo></yc:math> with a mass of 2906 MeV, a width of 20 MeV, and quantum numbers <ed:math xmlns:ed="http://www.w3.org/1998/Math/MathML" display="inline"><ed:mi>I</ed:mi><ed:mo stretchy="false">(</ed:mo><ed:msup><ed:mi>J</ed:mi><ed:mi>P</ed:mi></ed:msup><ed:mo stretchy="false">)</ed:mo><ed:mo>=</ed:mo><ed:mn>0</ed:mn><ed:mo stretchy="false">(</ed:mo><ed:msup><ed:mn>0</ed:mn><ed:mo>+</ed:mo></ed:msup><ed:mo stretchy="false">)</ed:mo></ed:math> may serve as a good candidate for the experimental <kd:math xmlns:kd="http://www.w3.org/1998/Math/MathML" display="inline"><kd:msub><kd:mi>T</kd:mi><kd:mrow><kd:mi>c</kd:mi><kd:mi>s</kd:mi><kd:mn>0</kd:mn></kd:mrow></kd:msub><kd:mo stretchy="false">(</kd:mo><kd:mn>2900</kd:mn><kd:mo stretchy="false">)</kd:mo></kd:math> state. We strongly urge the experimental search of the predicted states. Published by the American Physical Society 2024

Topics & Concepts