NNLO QCD calculation of hadron multiplicities in light-quark jets at lepton colliders

We present the calculation of next-to-next-to-leading-order (NNLO) QCD corrections to hadron multiplicities in light-quark jets at lepton colliders, employing the ``projection-to-Born" (P2B) method implemented in the FMNLO program. Taking the next-to-leading-order result as an example, we rigorously establish the validity of our P2B-based calculation. We then present NNLO predictions for the normalized asymmetry $D_{K^{-}}$ between hadron and antihadron production in light-quark jets and compare them with SLD data. We find that a suppression of these SLD measurements relative to NPC23 predictions for $D_{K^{-}}$ emerges in the intermediate $z_h$ domain ($0.2\lesssim z_h\lesssim 0.7$). We expect that incorporating these SLD data into global QCD fits will enable improved determination of fragmentation functions.