Analysis of bound and resonant states of doubly heavy tetraquarks with spin <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>J</mml:mi><mml:mo>≤</mml:mo><mml:mn>2</mml:mn></mml:math>

Recently, a number of exotic hadrons have been reported in the experiments, and most of these states lie slightly below the threshold. Therefore, these states are considered to be hadronic molecules composed of mesons or baryons. In 2022, the doubly charmed tetraquark <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mi>T</a:mi><a:mrow><a:mi>c</a:mi><a:mi>c</a:mi></a:mrow></a:msub></a:math> was reported by the LHCb experiment, which is considered to be composed of two heavy quarks and two light antiquarks, and located slightly below the <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>D</c:mi><c:msup><c:mi>D</c:mi><c:mo>*</c:mo></c:msup></c:math> threshold. The observation motivates us to study the bound and resonant states of the doubly heavy tetraquarks as two meson systems. We employ the one boson exchange potential as an interaction between two mesons, where one free parameter has been determined to reproduce <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msub><e:mi>T</e:mi><e:mrow><e:mi>c</e:mi><e:mi>c</e:mi></e:mrow></e:msub></e:math> reported by the LHCb experiment. In our previous work, bound states of <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msup><g:mi>D</g:mi><g:mrow><g:mo stretchy="false">(</g:mo><g:mo>*</g:mo><g:mo stretchy="false">)</g:mo></g:mrow></g:msup><g:msup><g:mi>D</g:mi><g:mrow><g:mo stretchy="false">(</g:mo><g:mo>*</g:mo><g:mo stretchy="false">)</g:mo></g:mrow></g:msup></g:math> and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:msup><m:mi>B</m:mi><m:mrow><m:mo stretchy="false">(</m:mo><m:mo>*</m:mo><m:mo stretchy="false">)</m:mo></m:mrow></m:msup><m:msup><m:mi>B</m:mi><m:mrow><m:mo stretchy="false">(</m:mo><m:mo>*</m:mo><m:mo stretchy="false">)</m:mo></m:mrow></m:msup></m:math> molecules were studied, where we respected the heavy quark spin symmetry (HQS). Using the same framework, we study not only bound but also resonant states with <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:mi>J</s:mi><s:mo>≤</s:mo><s:mn>2</s:mn></s:math> in this paper. Furthermore, we discuss the HQS partner structures of <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:msub><u:mi>T</u:mi><u:mrow><u:mi>c</u:mi><u:mi>c</u:mi></u:mrow></u:msub></u:math> and <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:msub><w:mi>T</w:mi><w:mrow><w:mi>b</w:mi><w:mi>b</w:mi></w:mrow></w:msub></w:math> obtained in our study by introducing the light cloud basis.