Analytical approaches to the determination of spin-dependent parton distribution functions at NNLO approximation

TL;DR

This paper introduces the first NNLO spin-dependent parton distribution functions analysis using analytical solutions via Laplace transforms and Jacobi polynomials, incorporating recent experimental data and uncertainty estimations.

Contribution

It presents a novel analytical method for extracting NNLO spin-dependent PDFs and their uncertainties, utilizing Laplace transforms and Jacobi polynomials, with comprehensive data analysis.

Findings

Consistent spin-dependent PDFs across small and large x regions.

Inclusion of recent high-precision COMPASS16 data enhances accuracy.

Uncertainty estimates align with standard Hessian error propagation.

Abstract

In this paper, we present {\tt SMKA18} analysis which is a first attempt to extract the set of next-to-next-leading-order (NNLO) spin-dependent parton distribution functions (spin-dependent PDFs) and their uncertainties determined through the Laplace transform technique and Jacobi polynomial approach. Using the Laplace transformations, we present an analytical solution for the spin-dependent Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution equations at NNLO approximation. The results are extracted using a wide range of proton $g_1^{p}(x, Q^2)$, neutron $g_1^{n}(x, Q^2)$ and deuteron $g_1^{d}(x, Q^2)$ spin-dependent structure functions dataset including the most recent high-precision measurements from {\tt COMPASS16} experiments at CERN which are playing an increasingly important role in global spin-dependent fits. The careful estimations of uncertainties have been done using the standard 'Hessian error' propagation. We will compare our results with the available spin-dependent inclusive deep inelastic scattering dataset and other results for the spin-dependent PDFs in literature. The results obtained for the spin-dependent PDFs as well as spin-dependent structure functions are clearly explained both in the small and large values of $x$.