Polarized dipole scattering amplitudes meet the valence quark model

The recently revised small-<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>x</a:mi></a:math> helicity evolution [], resumming the double-logarithmic factor, <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mrow><c:msub><c:mrow><c:mi>α</c:mi></c:mrow><c:mrow><c:mi mathvariant="normal">s</c:mi></c:mrow></c:msub><c:msup><c:mrow><c:mi>ln</c:mi></c:mrow><c:mrow><c:mn>2</c:mn></c:mrow></c:msup><c:mo stretchy="false">(</c:mo><c:mn>1</c:mn><c:mo>/</c:mo><c:mi>x</c:mi><c:mo stretchy="false">)</c:mo></c:mrow></c:math>, allows for the study of helicity distributions of quarks and gluons at small Bjorken <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:mi>x</h:mi></h:math>, corresponding to high center-of-mass energy. In this work, we calculate the moderate-<j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"><j:mi>x</j:mi></j:math> initial conditions in the regime, <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"><l:msub><l:mi>α</l:mi><l:mi mathvariant="normal">s</l:mi></l:msub><l:msup><l:mi>ln</l:mi><l:mn>2</l:mn></l:msup><l:mo stretchy="false">(</l:mo><l:mn>1</l:mn><l:mo>/</l:mo><l:mi>x</l:mi><l:mo stretchy="false">)</l:mo><l:mo>∼</l:mo><l:mn>1</l:mn></l:math>, for the small-<q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:mi>x</q:mi></q:math> helicity evolution using a light-front valence quark model of the proton, which provides additional physical information about the target. The perturbative emission and absorption of a gluon by the valence quarks are also included. The results, given in Eqs. (35), provide a new set of initial conditions with a significantly reduced number of free parameters than conventional models []. Consequently, the predictive power of small-<s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:mi>x</s:mi></s:math> helicity evolution is expected to improve once the initial conditions from this work are incorporated. Published by the American Physical Society 2024