(medium-modified) Fragmentation Functions

TL;DR

The paper surveys how fragmentation functions, describing how partons turn into hadrons, are extracted and evolved in vacuum and how they may be modified by QCD media. It links extensive $e^+e^-$, DIS, and hadroproduction data to global FF fits (HKNS, DSS, AKK08), discusses small-$x$ resummation (MLLA/DLA) and heavy-quark fragmentation, and then surveys medium-modified fragmentation frameworks including energy-loss formalisms (BDMPS/AMY), quenching weights, and medium-modified showers. A key focus is how nuclear and hot-QCD media alter the parton shower and fragmentation, with photon–hadron correlations proposed as a clean probe to extract medium-modified FFs. The review highlights the need for differential jet- and photon-jet observables, dynamical medium modeling, and continued refinement of fragmentation functions in both vacuum and medium contexts to deepen our understanding of QCD in extreme conditions.

Abstract

In this short review paper, we discuss some of the recent advances in the field of parton fragmentation processes into hadrons as well as their possible modifications in QCD media. Hadron production data in e+e-, deep inelastic scattering and hadronic collisions are presented, together with global analyses of fragmentation functions into light and heavy hadrons and developments on parton fragmentation in perturbative QCD at small momentum fraction. Motivated by the recent RHIC data indicating a significant suppression of large-pT hadron production in heavy-ion collisions, several recent attempts to model medium-modified fragmentation, e.g. by solving "medium" evolution equations or through Monte Carlo studies, have been proposed and are discussed in detail. Finally we mention the possibility to extract medium-modified fragmentation functions using photon-hadron correlations.

Figures (14)

• Figure 1: BaBar preliminary measurements of scaled-energy distributions of data $\pi^\pm$, $K^\pm$, and $p$/$\bar{p}$ in $e^+e^-$ collisions at $\sqrt{s}=10.54$ GeV. Taken from Ref. Anulli:2004nm.
• Figure 2: KNO scaling of charged hadron multiplicity distributions measured in DIS events by ZEUS and compared to $e^+e^-$ data taken by TASSO and LEP experiments. Taken from Ref. Chekanov:2008hy.
• Figure 3: HKNS parametrization for charged pions, $D_i^{\pi^\pm}/2$, at NLO for all flavours, compared to the AKK05, KKP, and Kr sets previously available. The bands indicate the theoretical uncertainty of the HKNS fragmentation functions. Taken from Ref. Hirai:2007cx.
• Figure 4: Location of the peak of the single-inclusive distribution $xD(x,Q^2)$ as a function of the energy scale $Q$, measured in $e^+e^-$, DIS, and $p$--$\bar{p}$ collisions. The prediction in the Leading-Logarithmic Approximation (short-dashed line), MLLA (solid line), and neglecting coherence effects (long-dashed line) are shown for comparison. Figure taken from Ref. Acosta:2002gg.
• Figure 5: CDF preliminary measurements Jindariani:2006ye of $k_\perp$-distributions for hadrons inside a jet compared to MLLA (dashed line) and NMLLA (solid line) calculations. Figure taken from Ref. Arleo:2007wn.