Novel cross section ratios as possible signals of saturation in ultraperipheral collisions

We propose new cross section ratios in ultraperipheral <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mrow><a:mi mathvariant="normal">A</a:mi><a:mo stretchy="false">+</a:mo></a:mrow><a:mi mathvariant="normal">A</a:mi></a:mrow></a:math> and <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:mrow><f:mi>p</f:mi><f:mo>+</f:mo><f:mi mathvariant="normal">A</f:mi></f:mrow></f:math> collisions (UPCs) as a potential experimental signal of saturation physics. We consider the ratio <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:msub><i:mi>R</i:mi><i:mn>1</i:mn></i:msub></i:math> of elastic vector meson photoproduction cross section to the inclusive hadron or jet photoproduction cross section. The ratio can be measured in the <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mrow><k:mi>γ</k:mi><k:mo>+</k:mo><k:mi mathvariant="normal">A</k:mi></k:mrow></k:math> and <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"><n:mi>γ</n:mi><n:mo>+</n:mo><n:mi>p</n:mi></n:math> collisions taking place in the UPCs. We label the ratios <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"><p:msub><p:mi>R</p:mi><p:mn>1</p:mn></p:msub><p:mo stretchy="false">(</p:mo><p:mi mathvariant="normal">A</p:mi><p:mo stretchy="false">)</p:mo></p:math> and <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:msub><u:mi>R</u:mi><u:mn>1</u:mn></u:msub><u:mo stretchy="false">(</u:mo><u:mi>p</u:mi><u:mo stretchy="false">)</u:mo></u:math>, respectively. Constructing the double ratio <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"><y:mrow><y:msub><y:mrow><y:mi>R</y:mi></y:mrow><y:mrow><y:mi>UPC</y:mi></y:mrow></y:msub><y:mo stretchy="false">(</y:mo><y:mi mathvariant="normal">A</y:mi><y:mo stretchy="false">)</y:mo><y:mo>=</y:mo><y:msub><y:mrow><y:mi>R</y:mi></y:mrow><y:mrow><y:mn>1</y:mn></y:mrow></y:msub><y:mo stretchy="false">(</y:mo><y:mi mathvariant="normal">A</y:mi><y:mo stretchy="false">)</y:mo><y:mo>/</y:mo><y:msub><y:mrow><y:mi>R</y:mi></y:mrow><y:mrow><y:mn>1</y:mn></y:mrow></y:msub><y:mo stretchy="false">(</y:mo><y:mi>p</y:mi><y:mo stretchy="false">)</y:mo></y:mrow></y:math>, and performing a small-<ib:math xmlns:ib="http://www.w3.org/1998/Math/MathML" display="inline"><ib:mi>x</ib:mi></ib:math> calculation both in the quasiclassical approximation and by including small-<kb:math xmlns:kb="http://www.w3.org/1998/Math/MathML" display="inline"><kb:mi>x</kb:mi></kb:math> evolution, we observe that <mb:math xmlns:mb="http://www.w3.org/1998/Math/MathML" display="inline"><mb:msub><mb:mi>R</mb:mi><mb:mi>UPC</mb:mi></mb:msub><mb:mo stretchy="false">(</mb:mo><mb:mi mathvariant="normal">A</mb:mi><mb:mo stretchy="false">)</mb:mo></mb:math> exhibits a markedly different dependence on the nuclear atomic number inside and outside the saturation region. This result indicates that <rb:math xmlns:rb="http://www.w3.org/1998/Math/MathML" display="inline"><rb:msub><rb:mi>R</rb:mi><rb:mi>UPC</rb:mi></rb:msub><rb:mo stretchy="false">(</rb:mo><rb:mi mathvariant="normal">A</rb:mi><rb:mo stretchy="false">)</rb:mo></rb:math> and <wb:math xmlns:wb="http://www.w3.org/1998/Math/MathML" display="inline"><wb:msub><wb:mi>R</wb:mi><wb:mn>1</wb:mn></wb:msub><wb:mo stretchy="false">(</wb:mo><wb:mi mathvariant="normal">A</wb:mi><wb:mo stretchy="false">)</wb:mo></wb:math> measurements in UPCs may help in the experimental searches for the evidence of saturation physics.