Longitudinal structure function in the limit x=Q2/s

The longitudinal structure function for nucleons and nuclei is considered at fixed <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msqrt><a:mi>s</a:mi></a:msqrt></a:math> and <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msup><c:mi>Q</c:mi><c:mn>2</c:mn></c:msup></c:math> to the minimum value of <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>x</e:mi></e:math> given by <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msup><g:mi>Q</g:mi><g:mn>2</g:mn></g:msup><g:mo>/</g:mo><g:mi>s</g:mi></g:math>. This is done using the expansion method and color dipole model in the next-to-leading order approximation. The extracted longitudinal structure functions were consistent with HERA hepdata and the determination of <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:msub><i:mi>F</i:mi><i:mi>L</i:mi></i:msub></i:math> at <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi>x</k:mi><k:mo>=</k:mo><k:msup><k:mi>Q</k:mi><k:mn>2</k:mn></k:msup><k:mo>/</k:mo><k:mi>s</k:mi></k:math> [Taylor, ] at moderate and large <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:msup><m:mi>Q</m:mi><m:mn>2</m:mn></m:msup></m:math> values. The results, consistent with the dipole picture at low <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:msup><o:mi>Q</o:mi><o:mn>2</o:mn></o:msup></o:math> values, show that the longitudinal structure function is small as expected due to the transverse polarization of the exchanged photon and the strong suppression of the dominant gluon component. Nonlinear corrections to the nuclear longitudinal structure function at low values of <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:mi>x</q:mi></q:math> and <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:msup><s:mi>Q</s:mi><s:mn>2</s:mn></s:msup></s:math> are also considered. These results may enhance the deep inelastic scattering neutral current data in future colliders at low <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:mi>x</u:mi></u:math> and low <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>. The longitudinal structure functions for deuterium at low four-momentum transfer squared, <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"><y:msup><y:mi>Q</y:mi><y:mn>2</y:mn></y:msup><y:mo><</y:mo><y:mn>1</y:mn><y:mtext> </y:mtext><y:mtext> </y:mtext><y:msup><y:mi>GeV</y:mi><y:mn>2</y:mn></y:msup></y:math> at the leading order and next-to-leading order approximations are determined and compared with the JLab E00-002 data.