Using analytic models to describe effective PDFs

TL;DR

This paper introduces machine-assisted methods to derive analytical models of parton distribution functions (PDFs) that incorporate scale evolution, reducing computational costs while maintaining accuracy in high-energy physics simulations.

Contribution

It presents a novel approach to directly compute PDFs with scale dependence using analytical approximations, eliminating the need to solve DGLAP equations separately.

Findings

Reduced computational cost in PDF calculations.

Accurate reproduction of HERAPDF2.0 set.

Maintained precision in simulations.

Abstract

Parton distribution functions play a pivotal role in hadron collider phenomenology. They are non-perturbative quantities extracted from fits to available data, and their scale dependence is dictated by the DGLAP evolution equations. In this article, we discuss machine-assisted strategies to efficiently compute PDFs directly incorporating the scale evolution without the need of separately solving DGLAP equations. Analytical approximations to the PDFs as a function of $x$ and $Q^2$, including up to next-to-leading order effects in Quantum Chromodynamics, are obtained. The methodology is tested by reproducing the $\texttt{HERAPDF2.0}$ set and implementing the analytical expressions in benchmarking codes. It is found that the computational cost is reduced while the precision of the simulations stays well under control.