Precise QCD Predictions for Hadron-in-jet Production in $e^{+}{e}^{-}$ Collisions

The production of identified hadrons inside jets in $e^{+}{e}^{-}$ annihilation allows for detailed studies of parton-to-hadron fragmentation functions in a clean environment. We compute hadron-in-jets production cross sections for $e^{+}{e}^{-}\to 2\mathrm{j}\mathrm{e}\mathrm{t}\mathrm{s}$ and $e^{+}{e}^{-}\to 3\mathrm{j}\mathrm{e}\mathrm{t}\mathrm{s}$ to next-to-next-to-leading order (NNLO) in perturbative QCD. By comparing with data from the ALEPH experiment, we demonstrate the implications of the newly computed theory predictions for precision phenomenology.