# NNLO charmed-meson fragmentation functions and their uncertainties in the presence of meson mass corrections

## TL;DR

This paper presents new NNLO fragmentation functions for D mesons, incorporating meson mass corrections, derived from OPAL data, with uncertainty estimates, and applies them to top quark decay predictions at the LHC.

## Contribution

It provides the first NNLO fragmentation functions for D mesons including meson mass effects, based on a comprehensive QCD fit to experimental data.

## Key findings

- New NNLO FFs for D mesons with mass corrections
- Improved theoretical predictions for charmed meson production at LHC
- Uncertainty estimates using the Hessian method

## Abstract

The main aim of this paper is to present new sets of non-perturbative fragmentation functions (FFs) for $D^0$ and $D^+$ mesons at next-to-leading (NLO) and, for the first time, at next-to-next-to-leading order (NNLO) in the $\overline{\mathrm{MS}}$ factorization scheme with five massless quark flavors. This new determination of FFs is based on the QCD fit to the {\tt OPAL} experimental data for hadron production in the electron-positron single-inclusive annihilation (SIA). We discuss in detail the novel aspects of the methodology used in our analysis and the validity of obtained FFs by comparing with previous works in literature which have been carried out up to NLO accuracy. We will also incorporate the effect of charmed meson mass corrections into our QCD analysis and discuss the improvements upon inclusion of these effects. The uncertainties in the extracted FFs as well as in the corresponding observables are estimated using the "Hessian" approach. For a typical application, we use our new FFs to make theoretical predictions for the energy distributions of charmed mesons inclusively produced through the decay of unpolarized top quarks, to be measured at the CERN LHC. As a result of this analysis, suggestions are discussed for possible future studies on the current topic to consider any theory improvements and other available experimental observables.