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Global analysis of fragmentation functions to light neutral hadrons

Jun Gao, ChongYang Liu, Mengyang Li, XiaoMin Shen, Hongxi Xing, Yuxiang Zhao, Yiyu Zhou

TL;DR

This work delivers a global NLO QCD analysis to extract FFs for light neutral hadrons ($K_S^0$, $\Lambda$, $\eta$, $\pi^0$) using diverse world data (SIA, SIDIS, $pp$), incorporating SIDIS and hadron-in-jet measurements for the first time to constrain the gluon FFs. It employs the NPC23 framework with two-loop timelike splitting kernels, FMNLO computations, and a carefully penalized parametrization enforcing physically motivated flavor relations, achieving good overall fits and enabling tests of momentum sum rules and isospin symmetry. The paper provides detailed FFs with Hessian uncertainties, tests of data compatibility, and predictions for in-jet fragmentation and kaon ratios, along with public LHAPDF grids, facilitating future cross-checks and experimental planning. Overall, the analysis strengthens the understanding of fragmentation to neutral hadrons, highlights remaining tensions and regions needing more data (notably flavor separation for $K_S^0$ and gluon-initiated $\ ext{η}$ fragmentation), and outlines concrete measurements to further constrain FFs. The results have practical impact on precision QCD predictions in collider phenomenology and on the interpretation of jet substructure observables involving neutral hadrons.

Abstract

Fragmentation functions (FFs) are crucial non-perturbative components in quantum chromodynamics (QCD), playing a vital role in predictions and understanding of the hadronization process. In this paper, we present the FFs for $K_S^0$, $η$, $π^0$ mesons, and $Λ$ baryons in the context of global QCD analysis. The data included in the fit are from single inclusive $e^+ e^-$ annihilation (SIA), semi-inclusive deep-inelastic scattering (SIDIS) and proton-proton collisions, with kinematic cuts carefully applied to ensure validity of collinear factorization and perturbative QCD expansion. For the first time, data from SIDIS and hadron-in-jet production in SIA have been incorporated into the extraction of FFs for light-flavor neutral hadrons. Our analysis reveals that these data play a critical role in constraining the gluon distribution, and in distinguishing between different quark flavors. Pulls from different datasets are also studied by performing alternative fits with systematically subtracting groups of data from the nominal fit. For the quality of the fit, good $χ^2$ values are achieved for most of the datasets, and FFs are generally well constrained within the momentum fraction region $\pqty{0.1, 0.5}$. The extracted $K_S^0$ fragmentation functions, together with the $K_S^0$ FFs constructed from $K^{\pm}$ FFs via isospin symmetry, are used to test isospin symmetry in kaon fragmentation. Although a definitive conclusion cannot be reached yet, these studies have identified several potential measurements that can be performed at existing facilities, which may ultimately help us to arrive at a conclusive answer. With the comprehensive species of FFs extracted within the NPC framework, we are able to perform a test on the momentum sum rule with the light-flavor charged and neutral hadrons.

Global analysis of fragmentation functions to light neutral hadrons

TL;DR

This work delivers a global NLO QCD analysis to extract FFs for light neutral hadrons (, , , ) using diverse world data (SIA, SIDIS, ), incorporating SIDIS and hadron-in-jet measurements for the first time to constrain the gluon FFs. It employs the NPC23 framework with two-loop timelike splitting kernels, FMNLO computations, and a carefully penalized parametrization enforcing physically motivated flavor relations, achieving good overall fits and enabling tests of momentum sum rules and isospin symmetry. The paper provides detailed FFs with Hessian uncertainties, tests of data compatibility, and predictions for in-jet fragmentation and kaon ratios, along with public LHAPDF grids, facilitating future cross-checks and experimental planning. Overall, the analysis strengthens the understanding of fragmentation to neutral hadrons, highlights remaining tensions and regions needing more data (notably flavor separation for and gluon-initiated fragmentation), and outlines concrete measurements to further constrain FFs. The results have practical impact on precision QCD predictions in collider phenomenology and on the interpretation of jet substructure observables involving neutral hadrons.

Abstract

Fragmentation functions (FFs) are crucial non-perturbative components in quantum chromodynamics (QCD), playing a vital role in predictions and understanding of the hadronization process. In this paper, we present the FFs for , , mesons, and baryons in the context of global QCD analysis. The data included in the fit are from single inclusive annihilation (SIA), semi-inclusive deep-inelastic scattering (SIDIS) and proton-proton collisions, with kinematic cuts carefully applied to ensure validity of collinear factorization and perturbative QCD expansion. For the first time, data from SIDIS and hadron-in-jet production in SIA have been incorporated into the extraction of FFs for light-flavor neutral hadrons. Our analysis reveals that these data play a critical role in constraining the gluon distribution, and in distinguishing between different quark flavors. Pulls from different datasets are also studied by performing alternative fits with systematically subtracting groups of data from the nominal fit. For the quality of the fit, good values are achieved for most of the datasets, and FFs are generally well constrained within the momentum fraction region . The extracted fragmentation functions, together with the FFs constructed from FFs via isospin symmetry, are used to test isospin symmetry in kaon fragmentation. Although a definitive conclusion cannot be reached yet, these studies have identified several potential measurements that can be performed at existing facilities, which may ultimately help us to arrive at a conclusive answer. With the comprehensive species of FFs extracted within the NPC framework, we are able to perform a test on the momentum sum rule with the light-flavor charged and neutral hadrons.

Paper Structure

This paper contains 28 sections, 21 equations, 51 figures, 15 tables.

Table of Contents

  1. Introduction
  2. Experimental data sets fitted
  3. $K_S^0$ data
  4. $\Lambda$ data
  5. $\eta$ data
  6. $\pi^0$ data
  7. Theoretical inputs to the NPC23 analysis
  8. Parametrization
  9. Theoretical computation method
  10. Goodness of fit function and the covariance matrix
  11. Quality of fit to data
  12. $K_S^0$ production
  13. $\Lambda$ production
  14. $\eta$ production
  15. $\pi^0$ production
  16. ...and 13 more sections

Figures (51)

  • Figure 1: The data over theory plot for $K_S^0$ production in SIA at $Z$-pole energy. The $x$-axis is plotted in logarithmic scale for $x_h$ defined in \ref{['ss.K0S-data']}. The data and experimental uncertainties are shown in green error bars, while the scale and Hessian uncertainties are shown in blue and orange bands, respectively. The data, scale and Hessian uncertainties are normalized to our best-fit theory values.
  • Figure 2: Same as \ref{['f.SIA-Z_pole-K0S']} but for $K_S^0$ production in SIA below $Z$-pole energy.
  • Figure 3: Same as \ref{['f.SIA-Z_pole-K0S']} but for $K_S^0$ production in SIDIS process. The ranges of photon virtuality, $Q^2$, are also labeled in each panel.
  • Figure 4: Same as \ref{['f.SIA-Z_pole-K0S']} but for $K_S^0$ production in $pp$ collisions. The first panel shows the data-theory comparison for the ALICE data of $K_S^0$ production ratio between $\sqrt{s} = 13~\mathrm{TeV}$ and $\sqrt{s} = 7~\mathrm{TeV}$. The second panel shows the data-theory comparison for the data of $K_S^0$ production over $\pi^{\pm}$ production at $\sqrt{s} = 13~\mathrm{TeV}$.
  • Figure 5: Same as \ref{['f.SIA-Z_pole-K0S']} but for $\Lambda$ production in SIA at $Z$-pole energy.
  • ...and 46 more figures