Global coupled-channel analysis of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msup> <mml:mi>e</mml:mi> <mml:mo>+</mml:mo> </mml:msup> <mml:msup> <mml:mi>e</mml:mi> <mml:mo>−</mml:mo> </mml:msup> <mml:mo stretchy="false">→</mml:mo> <mml:mi>c</mml:mi> <mml:mover accent="true"> <mml:mi>c</mml:mi> <mml:mo stretchy="false">¯</mml:mo> </mml:mover> </mml:math> processes in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mrow> <mml:msqrt> <mml:mrow> <mml:mi>s</mml:mi> </mml:mrow> </mml:msqrt> <mml:mo>=</mml:mo> </mml:mrow> <mml:mn>3.75</mml:mn> <mml:mtext> </mml:mtext> <mml:mi>to</mml:mi> <mml:mtext> </mml:mtext> <mml:mn>4.7</mml:mn> <mml:mtext>  </mml:mtext> <mml:mi>GeV</mml:mi> </mml:mrow> </mml:math>

Abstract

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.

Topics & Concepts