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

TL;DR

This work delivers the NNLO QCD calculation of hadron multiplicities in light-quark jets at lepton colliders using the FMNLO framework together with the projection-to-Born (P2B) method. The authors validate the NLO implementation against a quark-tagged hemisphere benchmark for the hadron energy fraction and then compute NNLO predictions for the normalized asymmetry $D_{K^{-}}$, comparing with SLD data. Across several fragmentation-function sets, they find that SLD data are suppressed relative to NPC23 in the intermediate $z_h$ region, highlighting tensions that can help refine FFs, especially for strange quark fragmentation to $K^{-}$. The results demonstrate the potential of incorporating light-quark jet measurements into global NNLO fragmentation-function fits to achieve more precise, flavor-sensitive determinations of FFs.

Abstract

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.

Figures (5)

• Figure 1: Comparison of the NLO results obtained using the P2B method with the benchmark calculation of the hadron energy fraction distribution in the quark-tagged hemisphere. The middle panel displays the ratios of the P2B predictions to the benchmark, while the bottom panel shows the ratio of the LO prediction and of the first term in Eq. \ref{['eq:4']} to the benchmark.
• Figure 2: Comparison of the NNLO predictions for the hadron energy fraction distribution in the quark-tagged hemisphere for $\lambda$ values ranging from $0.005$ to $0.04$. The middle and lower panels show, respectively, the ratios of predictions at $\lambda=0.005$, $0.01$, and $0.04$ to the $\lambda=0.02$ reference, and the ratios of NLO results to NNLO ones at $\lambda=0.02$.
• Figure 3: Comparison of the normalized difference ($D_{K^{-}}$) between hadron and antihadron production in light-quark jets from SLD measurements and JETSET predictions. "Pure" denotes results excluding antiquark contributions in the quark-tagged hemisphere, while "Mixing" includes these contributions. The error bars include statistical and systematic uncertainties. The lower panel shows the ratio to the corresponding "Pure" predictions.
• Figure 4: Comparison of $D_{k^-}$ predictions at NNLO between the results obtained from different fragmentation function sets and the data from SLD at the $Z$-pole. The lower panel displays the ratio to the NPC23 predictions. The error bands indicate their one-$\sigma$ uncertainties, and the error bars include statistical and systematic uncertainties.
• Figure 5: Comparison of our NNLO predictions from various FFs at NLO, JETSET, and Pythia8 models to the NPC23 results from the FFs at NNLO. The lower panel displays the ratio to the NPC23 results. The error bands indicate their one-$\sigma$ uncertainties.