A global analysis of $\pi^0$, $K_S^0$ and $\eta$ fragmentation functions with BESIII data

Abstract

In this research, we conduct a global QCD analysis of fragmentation functions (FFs) for neutral pions ($\pi^0$), neutral kaons ($K_S^0$), and eta mesons ($\eta$), utilizing world data of single inclusive hadron production in $e^+e^-$ annihilation involving the most recent BESIII data with low collision energy, to test the operational region of QCD collinear factorization for single inclusive hadron production. We found that the QCD-based analysis at next-to-next-to leading order in perturbative QCD with parameterized higher-twist effects can explain both existing high-energy world data and the BESIII new measurements, while the latter cannot be explained with existing FFs extracted with high-energy data. To investigate the higher-twist contributions to this discrepancy, a direct functional approach is employed, providing testing framework for characterizing the experimental results over a wide range of energy scales, from low to high, thus extending the classical theoretical models to the BESIII domain.