# A determination of the fragmentation functions of pions, kaons, and protons with faithful uncertainties

## TL;DR

This paper introduces NNFF1.0, a new set of fragmentation functions for pions, kaons, and protons derived from electron-positron data using advanced QCD calculations and the NNPDF methodology, with improved uncertainty quantification.

## Contribution

The paper presents the first NNFF1.0 fragmentation functions determined with a robust statistical framework and includes novel methodological improvements and validation procedures.

## Key findings

- Higher-order QCD corrections improve data description.
- NNFF1.0 shows good agreement with other FF sets but highlights key differences.
- Systematic uncertainties are effectively quantified using the NNPDF approach.

## Abstract

We present NNFF1.0, a new determination of the fragmentation functions (FFs) of charged pions, charged kaons, and protons/antiprotons from an analysis of single-inclusive hadron production data in electron-positron annihilation. This determination, performed at leading, next-to-leading, and next-to-next-to-leading order in perturbative QCD, is based on the NNPDF methodology, a fitting framework designed to provide a statistically sound representation of FF uncertainties and to minimise any procedural bias. We discuss novel aspects of the methodology used in this analysis, namely an optimised parametrisation of FFs and a more efficient $\chi^2$ minimisation strategy, and validate the FF fitting procedure by means of closure tests. We then present the NNFF1.0 sets, and discuss their fit quality, their perturbative convergence, and their stability upon variations of the kinematic cuts and the fitted dataset. We find that the systematic inclusion of higher-order QCD corrections significantly improves the description of the data, especially in the small-$z$ region. We compare the NNFF1.0 sets to other recent sets of FFs, finding in general a reasonable agreement, but also important differences. Together with existing sets of unpolarised and polarised parton distribution functions (PDFs), FFs and PDFs are now available from a common fitting framework for the first time.