Using analytic models to describe effective PDFs

Parton distribution functions play a pivotal role in hadron collider phenomenology. They are nonperturbative quantities extracted from fits to available data, and their scale dependence is dictated by the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution equations. In this article, we discuss machine-assisted strategies to efficiently compute parton distribution functions (PDFs) explicitly incorporating the scale dependence. Analytical approximations to the PDFs as functions of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>x</a:mi></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>, including up to next-to-leading-order effects in quantum chromodynamics, are obtained. The methodology is tested by reproducing the 2.0 set and implementing the analytical expressions in benchmarking codes. It is found that the computational time cost of evaluating the distributions is reduced by <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mo>∼</e:mo><e:mn>50</e:mn><e:mo>%</e:mo></e:math>, while the precision of the simulations stays well under control. Published by the American Physical Society 2024