Testing the Universality of Fragmentation Functions

TL;DR

The paper tests the universality and scaling violations of fragmentation functions in QCD by applying NLO predictions, based on FFs extracted from e^+e^- data, to inclusive charged-hadron production in par{p}, γp, and γγ processes across multiple experiments. It conducts a global analysis with standard PDFs and photon PDFs, examining scale uncertainties via a ξ parameter and comparing with alternative FF sets to gauge systematic effects. The results show overall agreement within uncertainties, supporting both the universality and timelike Altarelli-Parisi evolution of FFs, with the gluon fragmentation function playing a key role at low transverse momentum. The study also highlights current tensions in heavy-flavor FFs due to inconsistent flavor-tag data and emphasizes the need for more differential, flavor-separated measurements at higher p_T to further refine the fragmentation-function determinations.

Abstract

Using fragmentation functions for charged pions, charged kaons, and (anti)protons recently extracted from experimental data of e^+e^- annihilation at the Z-boson resonance and at centre-of-mass energy root(s) = 29 GeV, we perform a global study of inclusive charged-hadron production in p anti-p, gamma p, and gamma gamma collisions at next-to-leading order in the parton model of quantum chromodynamics. Comparisons of our results with p anti-p data from CERN S p anti-p S and the Fermilab Tevatron, gamma p data from DESY HERA, and gamma gamma data from CERN LEP2 allow us to test the universality of the fragmentation functions predicted by the factorization theorem. Furthermore, we perform comparisons with (e^+e^-)-annihilation data from LEP2 so as to test the scaling violations predicted by the Altarelli-Parisi evolution equations.

Figures (15)

• Figure 1: Normalized differential cross section $(1/\sigma_{\mathrm{tot}})d\sigma/dx$ (in pb) of inclusive charged-hadron production in $e^+e^-$ annihilation $e^+e^-\to h^\pm+X$ as a function of scaled momentum $x$ at CM energies $\sqrt s=133$, 161, 172, 183, and 189 GeV (from bottom to top in this order). The NLO predictions for $\xi=1/2$ (dashed lines), 1 (solid lines), and 2 (dot-dashed lines) are compared with data from DELPHI D2 (solid boxes) and OPAL O2 (open circles). Each set of curves is rescaled relative to the nearest upper one by a factor of 1/10.
• Figure 2: Differential cross section $Ed^3\sigma/d^3p$ (in mb/GeV$^2$) of inclusive charged-hadron hadroproduction in $p\bar{p}$ collisions $p\bar{p}\to h^\pm+X$ as a function of transverse momentum $p_T$ at CM energies $\sqrt s=540$ and 630 GeV, averaged over rapidity intervals $|y|<2.5$ and 3, respectively. The NLO predictions for $\xi=1/2$ (dashed lines), 1 (solid lines), and 2 (dot-dashed lines) are compared with data from UA1 UA1aUA1c. The lower set of curves is rescaled by a factor of 1/10.
• Figure 3: Differential cross section $Ed^3\sigma/d^3p$ (in mb/GeV$^2$) of inclusive charged-hadron hadroproduction in $p\bar{p}$ collisions $p\bar{p}\to h^\pm+X$ as a function of transverse momentum $p_T$ at CM energies $\sqrt s=200$, 500, and 900 GeV, averaged over rapidity interval $|y|<2.5$. The NLO predictions for $\xi=1/2$ (dashed lines), 1 (solid lines), and 2 (dot-dashed lines) are compared with data from UA1 UA1b. Each set of curves is rescaled relative to the nearest upper one by a factor of 1/10.
• Figure 4: Differential cross section $Ed^3\sigma/d^3p$ (in mb/GeV$^2$) of inclusive charged-hadron hadroproduction in $p\bar{p}$ collisions $p\bar{p}\to h^\pm+X$ as a function of transverse momentum $p_T$ at CM energy $\sqrt s=540$ GeV, averaged over rapidity intervals $|y|<0.63$ and $1<|y|<1.8$. The NLO predictions for $\xi=1/2$ (dashed lines), 1 (solid lines), and 2 (dot-dashed lines) are compared with data from UA2 UA2aUA2b. The lower set of curves is rescaled by a factor of 1/10.
• Figure 5: Differential cross section $Ed^3\sigma/d^3p$ (in mb/GeV$^2$) of inclusive charged-hadron hadroproduction in $p\bar{p}$ collisions $p\bar{p}\to h^\pm+X$ as a function of transverse momentum $p_T$ at CM energies $\sqrt s=630$ and 1800 GeV, averaged over rapidity interval $|y|<1$. The NLO predictions for $\xi=1/2$ (dashed lines), 1 (solid lines), and 2 (dot-dashed lines) are compared with data from CDF CDF. The lower set of curves is rescaled by a factor of 1/10.