Light tetraquark states with exotic quantum numbers JPC=2+−

We study the masses of light tetraquark states <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>u</a:mi><a:mi>d</a:mi><a:mover accent="true"><a:mi>u</a:mi><a:mo stretchy="false">¯</a:mo></a:mover><a:mover accent="true"><a:mi>d</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>u</g:mi><g:mi>s</g:mi><g:mover accent="true"><g:mi>u</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>s</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>s</m:mi><m:mo stretchy="false">¯</m:mo></m:mover></m:math> with exotic quantum numbers <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:mrow><s:msup><s:mrow><s:mi>J</s:mi></s:mrow><s:mrow><s:mi>P</s:mi><s:mi>C</s:mi></s:mrow></s:msup><s:mo>=</s:mo><s:msup><s:mn>2</s:mn><s:mrow><s:mo>+</s:mo><s:mo>−</s:mo></s:mrow></s:msup></s:mrow></s:math> using the method of QCD sum rules. It is found that there is no tetraquark operator with two Lorentz indices coupling to the <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:msup><u:mn>2</u:mn><u:mrow><u:mo>+</u:mo><u:mo>−</u:mo></u:mrow></u:msup></u:math> quantum numbers. To investigate such tetraquark states, we construct the interpolating tetraquark currents with three Lorentz indices and without a derivative operator. We calculate the correlation functions up to dimension-ten condensates and extract the <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:msup><w:mn>2</w:mn><w:mrow><w:mo>+</w:mo><w:mo>−</w:mo></w:mrow></w:msup></w:math> invariant functions via the projector operator. Our results show that the masses of the <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"><y:mi>u</y:mi><y:mi>d</y:mi><y:mover accent="true"><y:mi>u</y:mi><y:mo stretchy="false">¯</y:mo></y:mover><y:mover accent="true"><y:mi>d</y:mi><y:mo stretchy="false">¯</y:mo></y:mover></y:math>, <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"><eb:mi>u</eb:mi><eb:mi>s</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>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>s</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>s</kb:mi><kb:mo stretchy="false">¯</kb:mo></kb:mover></kb:math> tetraquark states with <qb:math xmlns:qb="http://www.w3.org/1998/Math/MathML" display="inline"><qb:mrow><qb:msup><qb:mrow><qb:mi>J</qb:mi></qb:mrow><qb:mrow><qb:mi>P</qb:mi><qb:mi>C</qb:mi></qb:mrow></qb:msup><qb:mo>=</qb:mo><qb:msup><qb:mrow><qb:mn>2</qb:mn></qb:mrow><qb:mrow><qb:mo>+</qb:mo><qb:mo>−</qb:mo></qb:mrow></qb:msup></qb:mrow></qb:math> are about 3.3–3.5, 3.5–3.7, and 3.67 GeV, respectively. We further discuss the strong decays of these light tetraquarks into the two-meson and baryon-antibaryon final states and suggest to search for them in the <sb:math xmlns:sb="http://www.w3.org/1998/Math/MathML" display="inline"><sb:mrow><sb:mi>ρ</sb:mi><sb:mi>π</sb:mi></sb:mrow></sb:math>, <ub:math xmlns:ub="http://www.w3.org/1998/Math/MathML" display="inline"><ub:mrow><ub:mi>ω</ub:mi><ub:mi>π</ub:mi></ub:mrow></ub:math>, <wb:math xmlns:wb="http://www.w3.org/1998/Math/MathML" display="inline"><wb:mrow><wb:mi>ϕ</wb:mi><wb:mi>π</wb:mi></wb:mrow></wb:math>, <yb:math xmlns:yb="http://www.w3.org/1998/Math/MathML" display="inline"><yb:msub><yb:mi>b</yb:mi><yb:mn>1</yb:mn></yb:msub><yb:mi>π</yb:mi></yb:math>, <ac:math xmlns:ac="http://www.w3.org/1998/Math/MathML" display="inline"><ac:msub><ac:mi>h</ac:mi><ac:mn>1</ac:mn></ac:msub><ac:mi>π</ac:mi></ac:math>, <cc:math xmlns:cc="http://www.w3.org/1998/Math/MathML" display="inline"><cc:mrow><cc:mi>K</cc:mi><cc:msup><cc:mrow><cc:mover accent="true"><cc:mrow><cc:mi>K</cc:mi></cc:mrow><cc:mrow><cc:mo stretchy="false">¯</cc:mo></cc:mrow></cc:mover></cc:mrow><cc:mrow><cc:mo>*</cc:mo></cc:mrow></cc:msup></cc:mrow></cc:math>, <gc:math xmlns:gc="http://www.w3.org/1998/Math/MathML" display="inline"><gc:mrow><gc:mi>K</gc:mi><gc:msub><gc:mrow><gc:mover accent="true"><gc:mrow><gc:mi>K</gc:mi></gc:mrow><gc:mrow><gc:mo stretchy="false">¯</gc:mo></gc:mrow></gc:mover></gc:mrow><gc:mn>1</gc:mn></gc:msub></gc:mrow></gc:math>, <kc:math xmlns:kc="http://www.w3.org/1998/Math/MathML" display="inline"><kc:mi mathvariant="normal">Δ</kc:mi><kc:mover accent="true"><kc:mi mathvariant="normal">Δ</kc:mi><kc:mo stretchy="false">¯</kc:mo></kc:mover></kc:math>, <qc:math xmlns:qc="http://www.w3.org/1998/Math/MathML" display="inline"><qc:msup><qc:mi mathvariant="normal">Σ</qc:mi><qc:mo>*</qc:mo></qc:msup><qc:msup><qc:mover accent="true"><qc:mi mathvariant="normal">Σ</qc:mi><qc:mo stretchy="false">¯</qc:mo></qc:mover><qc:mo>*</qc:mo></qc:msup></qc:math>, <wc:math xmlns:wc="http://www.w3.org/1998/Math/MathML" display="inline"><wc:msup><wc:mi mathvariant="normal">Ξ</wc:mi><wc:mo>*</wc:mo></wc:msup><wc:msup><wc:mover accent="true"><wc:mi mathvariant="normal">Ξ</wc:mi><wc:mo stretchy="false">¯</wc:mo></wc:mover><wc:mo>*</wc:mo></wc:msup></wc:math>, and <cd:math xmlns:cd="http://www.w3.org/1998/Math/MathML" display="inline"><cd:mi mathvariant="normal">Ω</cd:mi><cd:mover accent="true"><cd:mi mathvariant="normal">Ω</cd:mi><cd:mo stretchy="false">¯</cd:mo></cd:mover></cd:math> channels in the future.