Fragmentation Functions for Pions, Kaons, and Protons at Next-to-Leading Order

TL;DR

The paper derives charged-hadron fragmentation functions for pions, kaons, and protons at LO and NLO by fitting to extensive e+e- annihilation data, including flavor-separated and gluon-tagged samples from LEP1/SLC and lower-energy PEP data to probe scaling violation. By modeling the starting FFs with a flexible x-dependence and evolving them with timelike DGLAP equations, the authors extract Lambda_MSbar^(5) and alpha_s(M_Z) consistent with world averages, and deliver updated gluon FFs constrained by gluon-tagged jets. They validate the FFs through momentum-sum checks, comparisons to the longitudinal cross section, and cross-dataset consistency with older and newer measurements, providing a practical toolset for predicting inclusive hadron production in other processes. The work extends previous analyses by fully exploiting flavor separation and gluon-tagged data, offering improved FFs for phenomenology at current and future colliders.

Abstract

We present new sets of fragmentation functions for charged pions, charged kaons, and protons, both at the leading and next-to-leading orders. They are fitted to the scaled-momentum distributions of these hadrons measured in e+e- annihilation on the Z-boson resonance at CERN LEP1 and SLAC SLC. These data partly come as light-, charm-, bottom-quark-enriched and gluon-jet samples, which allows us to treat all partons independently, after imposing the SU(2) flavour symmetry relations. In order to gain sensitivity to the scaling violation in fragmentation, we also include data from SLAC PEP, with center-of-mass energy root(s)=29 GeV, in our fits. This allows us to also determine the strong-coupling constant, with a competitive error. LEP1 data on the longitudinal cross section as well as DESY DORIS and PETRA data at lower energies nicely agree with theoretical predictions based on our fragmentation functions.

Figures (11)

• Figure 1: Normalized differential cross section of inclusive hadron production at $\sqrt{s}=91.2$ GeV as a function of $x$. The LO (dashed lines) and NLO (solid lines) fit results are compared with data from ALEPH 9 (triangles), DELPHI D (circles), and SLD S (squares). The upmost, second, third, and lowest curves refer to charged hadrons, $\pi^\pm$, $K^\pm$, and $p/\bar{p}$, respectively. Each pair of curves is rescaled relative to the nearest upper one by a factor of 1/5.
• Figure 2: Same as in Fig. 1, but for the light-quark-enriched samples from DELPHI D (circles) and SLD S (squares).
• Figure 3: Same as in Fig. 1, but for the $c$-quark-enriched samples from SLD S (squares). The last two points on the right belong to the charged-hadron sample.
• Figure 4: Same as in Fig. 1, but for the $b$-quark-enriched samples from DELPHI D (circles) and SLD S (squares).
• Figure 5: Gluon FF for charged-hadron production as a function of $x$ at $M_f=52.4$ and 80.2 GeV. The LO (dashed lines) and NLO (solid lines) predictions are compared with three-jet data from ALEPH gA, with $E_{\mathrm{jet}}=26.2$ GeV, (upper curves) and from OPAL gO, with $E_{\mathrm{jet}}=40.1$ GeV (lower curves). The OPAL data and the pertinent predictions are rescaled by a factor of 1/100.