Exclusive production of a fully heavy tetraquark and a photon in electron-positron collision

The exclusive production of fully heavy tetraquarks ( <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>T</a:mi> <a:mo stretchy="false">(</a:mo> <a:mi>b</a:mi> <a:mi>b</a:mi> <a:mover accent="true"> <a:mi>b</a:mi> <a:mo stretchy="false">¯</a:mo> </a:mover> <a:mover accent="true"> <a:mi>b</a:mi> <a:mo stretchy="false">¯</a:mo> </a:mover> <a:mo stretchy="false">)</a:mo> </a:math> , <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:mi>T</i:mi> <i:mo stretchy="false">(</i:mo> <i:mi>c</i:mi> <i:mi>c</i:mi> <i:mover accent="true"> <i:mi>c</i:mi> <i:mo stretchy="false">¯</i:mo> </i:mover> <i:mover accent="true"> <i:mi>c</i:mi> <i:mo stretchy="false">¯</i:mo> </i:mover> <i:mo stretchy="false">)</i:mo> </i:math> , and <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"> <q:mi>T</q:mi> <q:mo stretchy="false">(</q:mo> <q:mi>b</q:mi> <q:mi>c</q:mi> <q:mover accent="true"> <q:mi>b</q:mi> <q:mo stretchy="false">¯</q:mo> </q:mover> <q:mover accent="true"> <q:mi>c</q:mi> <q:mo stretchy="false">¯</q:mo> </q:mover> <q:mo stretchy="false">)</q:mo> </q:math> ) in association with a hard photon in electron-positron collisions is calculated within the framework of nonrelativistic QCD. Both inner structures of the moleculelike state and compact state with <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"> <y:mi>J</y:mi> <y:mo>=</y:mo> <y:mn>0</y:mn> </y:math> , 1, 2 for the fully heavy tetraquark are discussed. We find that it is dismal to observe any fully heavy tetraquarks in either the compact configuration or the moleculelike configuration through such exclusive processes at either Belle II or future Z factories like the circular electron positron collider and the first stage of the future circular collider.