Toward the quark mass dependence of Tcc+ from lattice QCD

The <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>D</a:mi><a:msup><a:mi>D</a:mi><a:mo>*</a:mo></a:msup></a:math> scattering phase shifts in the <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msubsup><c:mi>T</c:mi><c:mrow><c:mi>c</c:mi><c:mi>c</c:mi></c:mrow><c:mo>+</c:mo></c:msubsup><c:mo>=</c:mo><c:mi>c</c:mi><c:mi>c</c:mi><c:mover accent="true"><c:mi>u</c:mi><c:mo stretchy="false">¯</c:mo></c:mover><c:mover accent="true"><c:mi>d</c:mi><c:mo stretchy="false">¯</c:mo></c:mover></c:math> channel are extracted from lattice QCD for five different charm quark masses and a fixed light-quark mass corresponding to <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:msub><i:mi>m</i:mi><i:mi>π</i:mi></i:msub><i:mo>≃</i:mo><i:mn>280</i:mn><i:mtext> </i:mtext><i:mtext> </i:mtext><i:mi>MeV</i:mi></i:math>. The phase shifts are analyzed employing two approaches: effective range expansion and Lippmann-Schwinger equation derived in the effective field theory. In the latter case, the results imply an attraction at short range parametrized by contact terms and a slight repulsion at long range mediated by one-pion exchange with <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:msub><k:mi>m</k:mi><k:mi>π</k:mi></k:msub><k:mo>></k:mo><k:msub><k:mi>m</k:mi><k:msup><k:mi>D</k:mi><k:mo>*</k:mo></k:msup></k:msub><k:mo>−</k:mo><k:msub><k:mi>m</k:mi><k:mi>D</k:mi></k:msub></k:math>. The poles in the amplitude across the complex energy plane are extracted and their trajectories are discussed as the charm quark mass is varied. Two complex conjugate poles corresponding to a resonance below threshold are found for <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:msub><m:mi>m</m:mi><m:mi>c</m:mi></m:msub></m:math> close to the physical value. They turn into a pair of virtual states at the largest <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:msub><o:mi>m</o:mi><o:mi>c</o:mi></o:msub></o:math> studied. With further increasing <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:msub><q:mi>m</q:mi><q:mi>c</q:mi></q:msub></q:math>, one virtual pole representing <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:msubsup><s:mi>T</s:mi><s:mrow><s:mi>c</s:mi><s:mi>c</s:mi></s:mrow><s:mo>+</s:mo></s:msubsup></s:math> is expected to move towards the two-body threshold and turn into a bound state. The light-quark mass dependence of the <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:msubsup><u:mi>T</u:mi><u:mrow><u:mi>c</u:mi><u:mi>c</u:mi></u:mrow><u:mo>+</u:mo></u:msubsup></u:math> pole is briefly discussed using the data on <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:mi>D</w:mi><w:msup><w:mi>D</w:mi><w:mo>*</w:mo></w:msup></w:math> scattering from other lattice collaborations. Published by the American Physical Society 2024