Singly heavy tetraquark resonant states with multiple strange quarks

We systematically investigate the S-wave singly heavy tetraquark systems containing two or three strange quarks, <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>s</a:mi> <a:mo stretchy="false">¯</a:mo> </a:mover> <a:mover accent="true"> <a:mi>s</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:mi>Q</g:mi> <g:mi>n</g:mi> <g:mover accent="true"> <g:mi>s</g:mi> <g:mo stretchy="false">¯</g:mo> </g:mover> <g:mover accent="true"> <g:mi>s</g:mi> <g:mo stretchy="false">¯</g:mo> </g:mover> </g:math> , and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:mi>Q</m:mi> <m:mi>s</m:mi> <m:mover accent="true"> <m:mi>s</m:mi> <m:mo stretchy="false">¯</m:mo> </m:mover> <m:mover accent="true"> <m:mi>n</m:mi> <m:mo stretchy="false">¯</m:mo> </m:mover> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mi>Q</m:mi> <m:mo>=</m:mo> <m:mi>c</m:mi> <m:mo>,</m:mo> <m:mi>b</m:mi> <m:mo>,</m:mo> <m:mi>n</m:mi> <m:mo>=</m:mo> <m:mi>u</m:mi> <m:mo>,</m:mo> <m:mi>d</m:mi> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:math> , within the constituent quark potential model. We solve the four-body Schrödinger equation using the Gaussian expansion method and identify resonances via the complex scaling method. There are no bound states below the lowest two-meson thresholds. We obtain several compact resonances with <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"> <u:msup> <u:mi>J</u:mi> <u:mi>P</u:mi> </u:msup> <u:mo>=</u:mo> <u:msup> <u:mn>0</u:mn> <u:mo>+</u:mo> </u:msup> <u:mo>,</u:mo> <u:msup> <u:mn>2</u:mn> <u:mo>+</u:mo> </u:msup> </u:math> in <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"> <w:mi>Q</w:mi> <w:mi>s</w:mi> <w:mover accent="true"> <w:mi>s</w:mi> <w:mo stretchy="false">¯</w:mo> </w:mover> <w:mover accent="true"> <w:mi>s</w:mi> <w:mo stretchy="false">¯</w:mo> </w:mover> </w:math> , and <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"> <cb:msup> <cb:mi>J</cb:mi> <cb:mi>P</cb:mi> </cb:msup> <cb:mo>=</cb:mo> <cb:msup> <cb:mn>2</cb:mn> <cb:mo>+</cb:mo> </cb:msup> </cb:math> in <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"> <eb:mi>Q</eb:mi> <eb:mi>n</eb:mi> <eb:mover accent="true"> <eb:mi>s</eb:mi> <eb:mo stretchy="false">¯</eb:mo> </eb:mover> <eb:mover accent="true"> <eb:mi>s</eb:mi> <eb:mo stretchy="false">¯</eb:mo> </eb:mover> </eb:math> and <kb:math xmlns:kb="http://www.w3.org/1998/Math/MathML" display="inline"> <kb:mi>Q</kb:mi> <kb:mi>s</kb:mi> <kb:mover accent="true"> <kb:mi>s</kb:mi> <kb:mo stretchy="false">¯</kb:mo> </kb:mover> <kb:mover accent="true"> <kb:mi>n</kb:mi> <kb:mo stretchy="false">¯</kb:mo> </kb:mover> </kb:math> . The pole positions are mainly distributed around 7.0–7.2 GeV (bottom) and 3.7–3.9 GeV (charm), with widths from a few to several tens of MeV. These resonances decay into <qb:math xmlns:qb="http://www.w3.org/1998/Math/MathML" display="inline"> <qb:msub> <qb:mi>D</qb:mi> <qb:mi>s</qb:mi> </qb:msub> <qb:msup> <qb:mi>η</qb:mi> <qb:mo>′</qb:mo> </qb:msup> <qb:mo>,</qb:mo> <qb:msubsup> <qb:mi>D</qb:mi> <qb:mrow> <qb:mo stretchy="false">(</qb:mo> <qb:mi>s</qb:mi> <qb:mo stretchy="false">)</qb:mo> </qb:mrow> <qb:mo>*</qb:mo> </qb:msubsup> <qb:mi>ϕ</qb:mi> <qb:mo>,</qb:mo> <qb:msup> <qb:msub> <qb:mi>D</qb:mi> <qb:mi>s</qb:mi> </qb:msub> <qb:mo>*</qb:mo> </qb:msup> <qb:msup> <qb:mi>K</qb:mi> <qb:mo>*</qb:mo> </qb:msup> </qb:math> , and <ub:math xmlns:ub="http://www.w3.org/1998/Math/MathML" display="inline"> <ub:msubsup> <ub:mi>D</ub:mi> <ub:mi>s</ub:mi> <ub:mo>*</ub:mo> </ub:msubsup> <ub:msup> <ub:mover accent="true"> <ub:mi>K</ub:mi> <ub:mo stretchy="false">¯</ub:mo> </ub:mover> <ub:mo>*</ub:mo> </ub:msup> </ub:math> (and their bottom counterparts), providing targets for future experimental searches.