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First determination of $D^{*+}$-meson fragmentation functions and their uncertainties at next-to-next-to-leading order

Maryam Soleymaninia, Hamzeh Khanpour, S. Mohammad Moosavi Nejad

TL;DR

The paper delivers the first NNLO determination of $D^{*\pm}$ fragmentation functions from a global $e^+e^-$ annihilation analysis within the ZM-VFN framework, using a Bowler parametrization and Hessian-based uncertainties. It demonstrates modest but meaningful improvements over NLO in fit quality and reduces theoretical scale sensitivity, with FFs constrained primarily by LEP data. Comparisons to KKKS08 and AKSRV17 illustrate the impact of dataset choices on charm and gluon fragmentation densities. The authors apply the extracted FFs to predict $D^{*\pm}$ spectra in top-quark decays, illustrating potential channels for top-quark property studies at the LHC. Overall, SKM18 provides a robust NNLO benchmark for charged $D^{*}$ fragmentation and informs future collider phenomenology involving heavy-flavor hadronization.

Abstract

We present, for the first time, a set of next-to-next-to-leading order (NNLO) fragmentation functions (FFs) describing the production of charmed-meson $D^{*+}$ from partons. Exploiting the universality and scaling violations of FFs, we extract the NLO and NNLO FFs through a global fit to all relevant data sets from single-inclusive $e^+e^-$ annihilation. The uncertainties for the resulting FFs as well as the corresponding observables are estimated using the Hessian approach. We evaluate the quality of the {\tt SKM18} FFs determined in this analysis by comparing with the recent results in literature and show how they describe the available data for single-inclusive $D^{*+}$-meson production in electron-positron annihilation. As a practical application, we apply the extracted FFs to make our theoretical predictions for the scaled-energy distributions of $D^{*+}$-mesons inclusively produced in top quark decays. We explore the implications of {\tt SKM18} for LHC phenomenology and show that our findings of this study can be introduced as a channel to indirect search for top-quark properties.

First determination of $D^{*+}$-meson fragmentation functions and their uncertainties at next-to-next-to-leading order

TL;DR

The paper delivers the first NNLO determination of fragmentation functions from a global annihilation analysis within the ZM-VFN framework, using a Bowler parametrization and Hessian-based uncertainties. It demonstrates modest but meaningful improvements over NLO in fit quality and reduces theoretical scale sensitivity, with FFs constrained primarily by LEP data. Comparisons to KKKS08 and AKSRV17 illustrate the impact of dataset choices on charm and gluon fragmentation densities. The authors apply the extracted FFs to predict spectra in top-quark decays, illustrating potential channels for top-quark property studies at the LHC. Overall, SKM18 provides a robust NNLO benchmark for charged fragmentation and informs future collider phenomenology involving heavy-flavor hadronization.

Abstract

We present, for the first time, a set of next-to-next-to-leading order (NNLO) fragmentation functions (FFs) describing the production of charmed-meson from partons. Exploiting the universality and scaling violations of FFs, we extract the NLO and NNLO FFs through a global fit to all relevant data sets from single-inclusive annihilation. The uncertainties for the resulting FFs as well as the corresponding observables are estimated using the Hessian approach. We evaluate the quality of the {\tt SKM18} FFs determined in this analysis by comparing with the recent results in literature and show how they describe the available data for single-inclusive -meson production in electron-positron annihilation. As a practical application, we apply the extracted FFs to make our theoretical predictions for the scaled-energy distributions of -mesons inclusively produced in top quark decays. We explore the implications of {\tt SKM18} for LHC phenomenology and show that our findings of this study can be introduced as a channel to indirect search for top-quark properties.

Paper Structure

This paper contains 11 sections, 19 equations, 9 figures, 4 tables.

Table of Contents

  1. Introduction
  2. QCD Analysis Framework up to NNLO accuracy
  3. Phenomenological parametrization up to NNLO
  4. Experimental input
  5. The calculation method of errors
  6. Discussion of SKM18 fit results
  7. SKM18 FFs and comparison with other FF sets
  8. Discussion of fit quality and data/theory comparison
  9. Importance of theoretical uncertainty at NNLO
  10. Energy spectrum of inclusive $D^{*\pm}$-mesons in polarized and unpolarized top decays
  11. Summary and Conclusions

Figures (9)

  • Figure 1: SKM18 fragmentation densities and their uncertainties (shaded bands) are shown for $zD^{D^{*\pm}}_i$ at the initial scale $\mu_0^2=18.5$ GeV$^2$ for $c$ and $b$ both at NLO (solid lines) and NNLO (dashed lines).
  • Figure 2: Fragmentation densities and their uncertainties (shaded bands) are shown for $zD^{D^{* \pm}}_i$ at $\mu ^2 =100$ GeV$^2$ for $c$, $b$ and gluon both at NLO (solid lines) and NNLO (dashed lines). Our results are also compared with the KKKS08 (dot-dashed lines) Kneesch:2007ey and the AKSRV17 (short dashed lines) Anderle:2017cgl results at NLO.
  • Figure 3: Fragmentation densities and their uncertainties (shaded bands) are shown for $zD^{D^{*\pm}}_i$ at $\mu ^2 =M_Z^2$ for $c$, $b$ and gluon at NLO (solid lines) and NNLO (dashed lines). Our results are also compared with the KKKS08 (dot-dashed lines) Kneesch:2007ey and the AKSRV17 (short dashed lines) Anderle:2017cgl results at NLO.
  • Figure 4: The NNLO/NLO ratios for SKM18 fragmentation densities and their uncertainties are shown for $zD^{D^{*\pm}}_i$ at $\mu ^2 =M_Z^2$ for $c$, $b$ and gluon at NLO (dashed lines) and NNLO (dot-dashed lines).
  • Figure 5: Our NLO (solid line) and NNLO (dashed line) results for the normalized total cross sections of $D^{*\pm}$-production compared with the KKKS08 ones Kneesch:2007ey (dot-dashed line) at the scale $Q=M_Z$. Data from ALEPH Barate:1999bg and OPAL Ackerstaff:1997ki are also shown in this scale. The shaded bands refer to our uncertainty results at NLO (green band) and NNLO (yellow band).
  • ...and 4 more figures