Charmonium <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>χ</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>χ</mml:mi><mml:mrow><mml:mi>c</mml:mi><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:math> resonances in coupled-channel scattering from lattice QCD

Abstract

In order to explore the spectrum of hidden-charm scalar and tensor resonances, we study meson-meson scattering with <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msup><a:mi>J</a:mi><a:mrow><a:mi>P</a:mi><a:mi>C</a:mi></a:mrow></a:msup><a:mo>=</a:mo><a:msup><a:mn>0</a:mn><a:mrow><a:mo>+</a:mo><a:mo>+</a:mo></a:mrow></a:msup><a:mo>,</a:mo><a:msup><a:mn>2</a:mn><a:mrow><a:mo>+</a:mo><a:mo>+</a:mo></a:mrow></a:msup></a:math> in the charmonium energy region using lattice QCD. Employing a light-quark mass corresponding to <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mrow><c:msub><c:mrow><c:mi>m</c:mi></c:mrow><c:mrow><c:mi>π</c:mi></c:mrow></c:msub><c:mo>≈</c:mo><c:mn>391</c:mn><c:mtext> </c:mtext><c:mtext> </c:mtext><c:mi>MeV</c:mi></c:mrow></c:math>, we determine coupled-channel scattering amplitudes up to around 4100 MeV considering all kinematically relevant channels consisting of a pair of open-charm mesons or a charmonium meson with a light meson. A single isolated scalar resonance near 4000 MeV is found with large couplings to <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>D</e:mi><e:mover accent="true"><e:mi>D</e:mi><e:mo stretchy="false">¯</e:mo></e:mover></e:math>, <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:msub><i:mi>D</i:mi><i:mi>s</i:mi></i:msub><i:msub><i:mover accent="true"><i:mi>D</i:mi><i:mo stretchy="false">¯</i:mo></i:mover><i:mi>s</i:mi></i:msub></i:math> and the kinematically closed <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:msup><m:mi>D</m:mi><m:mo>*</m:mo></m:msup><m:msup><m:mover accent="true"><m:mi>D</m:mi><m:mo stretchy="false">¯</m:mo></m:mover><m:mo>*</m:mo></m:msup></m:math> channel. A single tensor resonance at a similar mass couples strongly to <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:mi>D</q:mi><q:mover accent="true"><q:mi>D</q:mi><q:mo stretchy="false">¯</q:mo></q:mover></q:math>, <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:mi>D</u:mi><u:msup><u:mover accent="true"><u:mi>D</u:mi><u:mo stretchy="false">¯</u:mo></u:mover><u:mo>*</u:mo></u:msup></u:math> and <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"><y:msup><y:mi>D</y:mi><y:mo>*</y:mo></y:msup><y:msup><y:mover accent="true"><y:mi>D</y:mi><y:mo stretchy="false">¯</y:mo></y:mover><y:mo>*</y:mo></y:msup></y:math>. We compare the extracted resonances to contemporary experimental candidate states, previous lattice results and theoretical modeling. In contrast to several other studies, we do not find any significant feature in the scalar amplitudes between the ground state <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"><cb:msub><cb:mi>χ</cb:mi><cb:mrow><cb:mi>c</cb:mi><cb:mn>0</cb:mn></cb:mrow></cb:msub><cb:mo stretchy="false">(</cb:mo><cb:mn>1</cb:mn><cb:mi>P</cb:mi><cb:mo stretchy="false">)</cb:mo></cb:math> and the resonance found around 4000 MeV. Published by the American Physical Society 2024

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