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Next-To-Leading Order Determination of Fragmentation Functions

L. Bourhis, M. Fontannaz, J. Ph. Guillet, M. Werlen

TL;DR

The paper addresses determining next-to-leading order fragmentation functions for charged hadrons by fitting $e^+e^-$ annihilation data within a QCD factorization framework and DGLAP evolution, using scale optimization via PMS. Since $e^+e^-$ data poorly constrain the gluon fragmentation function, the authors supplement the analysis with large-$p_T$ hadroproduction (UA1) data to constrain $D_g(z,Q^2)$, finding that multiple gluon-FF shapes can describe the hadroproduction data. They achieve a convergent NLO FF set after a two-step fitting procedure to manage parameter correlations, report explicit initial conditions at $Q_0^2=2\ \mathrm{GeV}^2$, and compare with prior FF sets, noting significant large-$z$ differences. The work demonstrates the necessity of including hadroproduction data to bound the gluon fragmentation function and provides a practical NLO FF set for charged hadrons along with a framework for uncertainty estimation.

Abstract

We analyse LEP and PETRA data on single inclusive charged hadron cross-sections to establish new sets of Next-to-Leading order Fragmentation Functions. Data on hadro-production of large-$p_{\bot}$ hadrons are also used to constrain the gluon Fragmentation Function. We carry out a critical comparison with other NLO parametrizations.

Next-To-Leading Order Determination of Fragmentation Functions

TL;DR

The paper addresses determining next-to-leading order fragmentation functions for charged hadrons by fitting annihilation data within a QCD factorization framework and DGLAP evolution, using scale optimization via PMS. Since data poorly constrain the gluon fragmentation function, the authors supplement the analysis with large- hadroproduction (UA1) data to constrain , finding that multiple gluon-FF shapes can describe the hadroproduction data. They achieve a convergent NLO FF set after a two-step fitting procedure to manage parameter correlations, report explicit initial conditions at , and compare with prior FF sets, noting significant large- differences. The work demonstrates the necessity of including hadroproduction data to bound the gluon fragmentation function and provides a practical NLO FF set for charged hadrons along with a framework for uncertainty estimation.

Abstract

We analyse LEP and PETRA data on single inclusive charged hadron cross-sections to establish new sets of Next-to-Leading order Fragmentation Functions. Data on hadro-production of large- hadrons are also used to constrain the gluon Fragmentation Function. We carry out a critical comparison with other NLO parametrizations.

Paper Structure

This paper contains 6 sections, 10 equations, 14 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Single Inclusive Cross Section in e$^+$e$^-$ Annihilation
  3. Analysis of e$^+$e$^-$-annihilation data
  4. Analysis of large-p$_{\bot}$ production rate
  5. Conclusion
  6. Appendix

Figures (14)

  • Figure 1: NLO inclusive charged particle production in $e^+e^- \to bX$ collisions at $\sqrt{s}=91.2$ GeV with optimized scales and with fragmentation functions obtained here (formula \ref{['8e']}) compared to data of the ALEPH aleph and OPAL collaboration opal98.
  • Figure 2: NLO inclusive charged particle production in $e^+e^- \to bX$ collisions at $\sqrt{s}=91.2$ GeV with optimized scales and with fragmentation functions obtained here (formula \ref{['8e']}) compared to data of the DELPHI collaboration taken in 1994 (top) del94 and in 1991-1993 del98.
  • Figure 3: NLO inclusive charged particle production in $e^+e^- \to u,d,sX$ collisions at $\sqrt{s}=91.2$ GeV with optimized scales and with fragmentation functions obtained here (formula \ref{['8e']}) compared to data of the ALEPH aleph, OPAL opal98 and DELPHI del98 collaboration.
  • Figure 4: NLO inclusive charged particle production in $e^+e^- \to cX$ collisions at $\sqrt{s}=91.2$ GeV with optimized scales and with fragmentation functions obtained here (formula \ref{['8e']}) compared to data of the ALEPH aleph, OPAL opal98 and DELPHI del98 collaboration.
  • Figure 5: NLO inclusive charged particle production in $e^+e^- \to hX$ collisions with optimized scales and with fragmentation functions obtained here (formula \ref{['8e']}) compared to data at $\sqrt{s}=35$ GeV from the CELLO collaboration cello and at $\sqrt{s}=44$ GeV from the TASSO collaboration tasso.
  • ...and 9 more figures