Global coupled-channel analysis of e+e−→cc¯ processes in <…

Recent high-precision <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msup><a:mi>e</a:mi><a:mo>+</a:mo></a:msup><a:msup><a:mi>e</a:mi><a:mo>−</a:mo></a:msup><a:mo stretchy="false">→</a:mo><a:mi>c</a:mi><a:mover accent="true"><a:mi>c</a:mi><a:mo stretchy="false">¯</a:mo></a:mover></a:math> data from BESIII and Belle are highly useful to understand vector charmonium (<f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:mi>ψ</f:mi></f:math>) pole structures and puzzling line shapes due to the exotic hadron candidates <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:mi>Y</h:mi></h:math>. We, thus, perform a global coupled-channel analysis of most of the available data (ten two-body, nine three-body, and one four-body final states) in <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"><j:mrow><j:mrow><j:mrow><j:msqrt><j:mrow><j:mi>s</j:mi></j:mrow></j:msqrt><j:mo>=</j:mo></j:mrow><j:mn>3.75</j:mn><j:mtext> </j:mtext><j:mo>−</j:mo><j:mn>4.7</j:mn></j:mrow><j:mtext> </j:mtext><j:mi>GeV</j:mi></j:mrow></j:math>. Not only cross sections, but also invariant-mass distributions of subsystems are fitted. The <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"><l:msup><l:mi>e</l:mi><l:mo>+</l:mo></l:msup><l:msup><l:mi>e</l:mi><l:mo>−</l:mo></l:msup><l:mo stretchy="false">→</l:mo><l:msup><l:mi>μ</l:mi><l:mo>+</l:mo></l:msup><l:msup><l:mi>μ</l:mi><l:mo>−</l:mo></l:msup></l:math> cross sections are also predicted. Our model includes dozens of (quasi-)two-body states that nonperturbatively couple with each other through bare <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mi>ψ</o:mi></o:math> excitations, particle-exchange, and short-range mechanisms; approximate three-body unitarity is considered. The amplitudes obtained from the fit are analytically continued to <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:mi>ψ</q:mi></q:math> and <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:msub><s:mi>Z</s:mi><s:mi>c</s:mi></s:msub></s:math> poles. We find <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:mi>ψ</u:mi></u:math> states similar to those in the Particle Data Group listing and <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:mi>Y</w:mi><w:mo stretchy="false">(</w:mo><w:mn>4320</w:mn><w:mo stretchy="false">)</w:mo></w:math>. Moreover, several <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"><ab:mi>ψ</ab:mi></ab:math> states, including new ones, are found close to open-charm thresholds. Trajectories and compositeness of the near-threshold poles suggest dominant hadron-molecule contents in their internal structures. Two <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"><cb:msub><cb:mi>Z</cb:mi><cb:mi>c</cb:mi></cb:msub></cb:math> poles are found as virtual states <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"><eb:mo>∼</eb:mo><eb:mn>40</eb:mn><eb:mtext> </eb:mtext><eb:mtext> </eb:mtext><eb:mi>MeV</eb:mi></eb:math> below the <gb:math xmlns:gb="http://www.w3.org/1998/Math/MathML" display="inline"><gb:msup><gb:mi>D</gb:mi><gb:mo>*</gb:mo></gb:msup><gb:msup><gb:mover accent="true"><gb:mi>D</gb:mi><gb:mo stretchy="false">¯</gb:mo></gb:mover><gb:mrow><gb:mo stretchy="false">(</gb:mo><gb:mo>*</gb:mo><gb:mo stretchy="false">)</gb:mo></gb:mrow></gb:msup></gb:math> thresholds, consistent with lattice QCD results. This work presents the first global analysis to determine <mb:math xmlns:mb="http://www.w3.org/1998/Math/MathML" display="inline"><mb:mi>ψ</mb:mi></mb:math> and <ob:math xmlns:ob="http://www.w3.org/1998/Math/MathML" display="inline"><ob:msub><ob:mi>Z</ob:mi><ob:mi>c</ob:mi></ob:msub></ob:math> poles, thereby paving the way to extracting detailed properties of the prominent exotic hadron candidates from data.