CGC and saturation approach: Impact-parameter dependent model of perturbative QCD and combined HERA data

In this paper we confront the color glass condensate and saturation approach of Contreras [Non-linear equation in the re-summed next-to-leading order of perturbative QCD: The leading twist approximation, ] with the experimental combined HERA data and obtain its parameters. The model includes two features that are in accordance with our theoretical knowledge of deep inelastic scattering. These consist of: (<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mi>i</a:mi></a:mrow></a:math>) the use of analytical solution for the nonlinear Balitsky-Kovchegov evolution equation and () the exponential behavior of the saturation momentum on the impact parameter <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>b</c:mi></c:math>-dependence, characterized by <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msub><e:mi>Q</e:mi><e:mi>s</e:mi></e:msub><e:mo>∝</e:mo><e:mi>exp</e:mi><e:mrow><e:mo stretchy="false">(</e:mo><e:mo>−</e:mo><e:mi>m</e:mi><e:mi>b</e:mi><e:mo stretchy="false">)</e:mo></e:mrow></e:math> which reproduces the correct behavior of the scattering amplitude at large <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>b</i:mi></i:math> in accord with Froissart theorem. The model results are then compared to data at small-<k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi>x</k:mi></k:math> for the structure function of the proton <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:msub><m:mi>F</m:mi><m:mn>2</m:mn></m:msub></m:math>, the longitudinal structure function <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:msub><o:mi>F</o:mi><o:mi>L</o:mi></o:msub></o:math>, the charm structure function <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:msubsup><q:mi>F</q:mi><q:mn>2</q:mn><q:mrow><q:mi>c</q:mi><q:mover accent="true"><q:mi>c</q:mi><q:mo stretchy="false">¯</q:mo></q:mover></q:mrow></q:msubsup></q:math>, the exclusive vector meson (<u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:mi>J</u:mi><u:mo>/</u:mo><u:mi>ψ</u:mi><u:mo>,</u:mo><u:mi>ϕ</u:mi><u:mo>,</u:mo><u:mi>ρ</u:mi></u:math>) production and deeply virtual Compton scattering. We obtain a good agreement for the processes in a wide kinematic range of <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:msup><w:mi>Q</w:mi><w:mn>2</w:mn></w:msup></w:math> at small-<y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"><y:mi>x</y:mi></y:math>. Our results provide a strong guide for finding an approach, based on color glass condensate and saturation effective theory for high-energy QCD, to make reliable predictions from first principles and for forthcoming experiments like the Electron Ion Collider and the LHeC. Published by the American Physical Society 2024