Fragmentation Functions of neutral mesons $\pi^0$ and $k ^0$ with Laplace transform approach

TL;DR

This paper derives analytical fragmentation functions for neutral mesons $$ and $k^0$ at NLO using Laplace transforms, validating results against experimental data and global fits.

Contribution

It introduces a novel analytical Laplace transform approach to solve DGLAP equations for meson fragmentation functions at NLO.

Findings

Good agreement with experimental data

Consistent with global fit results

Analytical solutions provide new insights

Abstract

With an analytical solutions of DGLAP evolution equations based on the Laplace transform method , we find the fragmentation functions (FFs) of neutral mesons, $\pi^0$ and $k ^0$ at NLO approximation. We also calculated the total fragmentation functions of these mesons and compared them with experimental data and those from global fits. The results show a good agreements between our solutions and other models and also are compatible with experimental data.