Unifying the landscape of nucleon structure: An infrared-safe evolution scheme

A novel approach for describing the evolution of nucleon structure from low-<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msup><a:mi>Q</a:mi><a:mn>2</a:mn></a:msup></a:math> regime to high-<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> asymptotic region is proposed. This infrared-safe scheme modifies the parton distribution evolution equations to incorporate the corrections from emergent hadron mass mechanisms and parton-parton recombination at low <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msup><e:mi>Q</e:mi><e:mn>2</e:mn></e:msup></e:math>. The effective quark mass, generated by dynamical chiral symmetry breaking, slows the evolution of parton distributions in the infrared region, causing the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution to freeze when <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:msub><g:mi>M</g:mi><g:mrow><g:mi mathvariant="normal">q</g:mi><g:mo>/</g:mo><g:mi mathvariant="normal">g</g:mi></g:mrow></g:msub></g:math>. Notably, this scheme renders the high-<k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:msup><k:mi>Q</k:mi><k:mn>2</k:mn></k:msup></k:math> parton distributions insensitive to the choice of input hadronic scale. The parton-parton recombination effect is crucial in suppressing the rapid growth of parton distributions at small <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mi>x</m:mi></m:math>, consistent with experimental data. When applied to three valence quark distributions derived from a quark model, our scheme yields parton distributions that agree well with deep-inelastic scattering data in both large-<o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mi>x</o:mi></o:math> and small-<q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:mi>x</q:mi></q:math> regions, providing a unified description of nucleon structure across the entire <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> range. Published by the American Physical Society 2024