# $B$-hadron fragmentation functions at next-to-next-to-leading order from global analysis of $e^+e^-$ annihilation data

## TL;DR

This paper derives precise nonperturbative fragmentation functions for B-hadrons at NNLO accuracy by fitting extensive e+e- annihilation data, enabling improved predictions for B-hadron production at colliders.

## Contribution

It provides the first NNLO B-hadron fragmentation functions fitted to experimental data, enhancing the accuracy of theoretical predictions in high-energy physics.

## Key findings

- NNLO FFs show reduced uncertainties compared to NLO.
- New FFs improve predictions for B-hadron energy distributions in top decays.
- Comparison with previous NLO FFs demonstrates significant advancements.

## Abstract

We present nonperturbative fragmentation functions (FFs) for bottom-flavored ($B$) hadrons both 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. They are determined by fitting all available experimental data of inclusive single $B$-hadron production in $e^+e^-$ annihilation, from the ALEPH, DELPHI, and OPAL Collaborations at CERN LEP1 and the SLD Collaboration at SLAC SLC. The uncertainties in these FFs as well as in the corresponding observables are estimated using the Hessian approach. We perform comparisons with available NLO sets of $B$-hadron FFs. We apply our new FFs to generate theoretical predictions for the energy distribution of $B$ hadrons produced through the decay of unpolarized or polarized top quarks, to be measured at the CERN LHC.