Production of meson molecules in ultraperipheral heavy ion collisons

In this work we present a calculation of exotic charmonium production in ultraperipheral collisions, in which the exotic state is explicitly treated as a meson molecule. Our formalism is general, but we focus on the lightest possible exotic charmonium state: a <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:msup><a:mrow><a:mi>D</a:mi></a:mrow><a:mrow><a:mo>+</a:mo></a:mrow></a:msup><a:msup><a:mrow><a:mi>D</a:mi></a:mrow><a:mrow><a:mo>−</a:mo></a:mrow></a:msup></a:mrow></a:math> molecular bound state. It was proposed some time ago, and it has been an object of experimental searches. Here we study the production of the open charm pair in the process <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>γ</c:mi><c:mi>γ</c:mi><c:mo stretchy="false">→</c:mo><c:msup><c:mi>D</c:mi><c:mo>+</c:mo></c:msup><c:msup><c:mi>D</c:mi><c:mo>−</c:mo></c:msup></c:math>. Then we use a prescription to project the free pair <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:mo stretchy="false">|</f:mo><f:msup><f:mi>D</f:mi><f:mo>+</f:mo></f:msup><f:msup><f:mi>D</f:mi><f:mo>−</f:mo></f:msup><f:mo stretchy="false">⟩</f:mo></f:math> onto a bound state at the amplitude level and compute the cross section of the process <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"><j:mi>γ</j:mi><j:mi>γ</j:mi><j:mo stretchy="false">→</j:mo><j:mi>B</j:mi></j:math> (where <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mi>B</m:mi></m:math> is the bound state). Finally, we convolute this last cross section with the equivalent photon distributions coming from the projectile and target in an ultraperipheral collision and find the <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mi>A</o:mi><o:mi>A</o:mi><o:mo stretchy="false">→</o:mo><o:mi>A</o:mi><o:mi>A</o:mi><o:mi>B</o:mi></o:math> cross section, which, for <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"><r:mi>P</r:mi><r:mi>b</r:mi><r:mo>−</r:mo><r:mi>P</r:mi><r:mi>b</r:mi></r:math> collisions at <t:math xmlns:t="http://www.w3.org/1998/Math/MathML" display="inline"><t:msqrt><t:msub><t:mi>s</t:mi><t:mrow><t:mi>N</t:mi><t:mi>N</t:mi></t:mrow></t:msub></t:msqrt><t:mo>=</t:mo><t:mn>5.02</t:mn><t:mtext> </t:mtext><t:mtext> </t:mtext><t:mi>TeV</t:mi></t:math>, is of the order of <v:math xmlns:v="http://www.w3.org/1998/Math/MathML" display="inline"><v:mn>3</v:mn><v:mtext> </v:mtext><v:mtext> </v:mtext><v:mi mathvariant="normal">μ</v:mi><v:mi mathvariant="normal">b</v:mi></v:math>.