Heavy quark structure functions from unifying the color dipole picture and double asymptotic scaling approaches

We present an analysis of the heavy quark structure functions from the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:msub><a:mrow><a:mi>k</a:mi></a:mrow><a:mrow><a:mi>t</a:mi></a:mrow></a:msub></a:mrow></a:math> factorization scheme, using unifying the color dipole picture and double asymptotic scaling approaches at small <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>x</c:mi></c:math>. The gluon distribution is obtained from the Golec-Biernat-Wüsthoff and Bartels, Golec-Biernat and Kowalski models. The main elements are based on the color dipole picture and the generalized double asymptotic scaling approach for usual parton distribution functions. The comparisons with the HERA data are made and predictions for the proposed LHeC and FCC-he colliders are also provided in a wide range of the transverse separation <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>r</e:mi></e:math>. In particular, the ratio <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mrow><g:msup><g:mrow><g:mi>R</g:mi></g:mrow><g:mrow><g:mi>h</g:mi></g:mrow></g:msup><g:mo>=</g:mo><g:msubsup><g:mrow><g:mi>F</g:mi></g:mrow><g:mrow><g:mi>L</g:mi></g:mrow><g:mrow><g:mi>h</g:mi></g:mrow></g:msubsup><g:mo>/</g:mo><g:msubsup><g:mrow><g:mi>F</g:mi></g:mrow><g:mrow><g:mn>2</g:mn></g:mrow><g:mrow><g:mi>h</g:mi></g:mrow></g:msubsup><g:mo>,</g:mo><g:mi>h</g:mi><g:mo>=</g:mo><g:mi>c</g:mi><g:mo>,</g:mo><g:mrow><g:mi>b</g:mi></g:mrow><g:mo>,</g:mo><g:mrow><g:mi>t</g:mi></g:mrow></g:mrow></g:math> is well described by the dipole models and is sensitive to the collider energies from HERA until FCC-he. We derive correlated bounds on the ratio <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:msubsup><i:mi>F</i:mi><i:mn>2</i:mn><i:mi>c</i:mi></i:msubsup><i:mo>/</i:mo><i:msub><i:mi>F</i:mi><i:mn>2</i:mn></i:msub></i:math> and <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:msubsup><k:mi>F</k:mi><k:mn>2</k:mn><k:mi>b</k:mi></k:msubsup><k:mo>/</k:mo><k:msub><k:mi>F</k:mi><k:mn>2</k:mn></k:msub></k:math> and compared them with the BGK and impact-parameter dependent saturation models. The uncertainties are due to the renormalization and factorization scales at large and low <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mi>r</m:mi></m:math> values. The Sudakov form factor into the heavy quark structure functions is incorporated and the results are considered, which are dependent on the hard scale in a wide range of the transverse separation <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mi>r</o:mi></o:math>. Published by the American Physical Society 2024