KNO scaling in quark and gluon jets at the LHC

Abstract

The Koba-Nielsen-Olesen (KNO) scaling of hadron multiplicity distributions, empirically confirmed to hold approximately in $e^+e^-$ collisions and Deep Inelastic Scattering, has been observed to be violated in hadron-hadron collisions. In this work, we show that the universality of KNO scaling can be extended to hadron-hadron collisions when restricted to QCD jets. We present a comprehensive study of KNO scaling in QCD jets produced in proton-proton collisions at the LHC. Using perturbative QCD calculations in the double logarithmic approximation and PYTHIA simulations, we find that KNO scaling approximately holds for both quark and gluon jets across a broad jet $p_T$ range, from $0.1$ TeV to $2.5$ TeV, at both the parton and hadron levels. Especially, we highlight characteristic differences between the KNO scaling functions of quark and gluon jets, with the quark-jet scaling function lying above that of gluon jets at both low and high multiplicities. This distinction is essential for interpreting inclusive jet data at the LHC. Furthermore, we propose direct experimental tests of KNO scaling in QCD jets at the LHC through quark-gluon discrimination using jet substructure techniques, as demonstrated by applying energy correlation functions to PYTHIA-generated data.

Figures (4)

• Figure 1: KNO scaling in parton multiplicity distributions within DLA. Over a broad jet $p_T$ range of $p_T = 0.1$–$2.5$ TeV, $\bar{n} P(n)$ for both quark and gluon jets (computed up to $n = 1000$) converge to well-defined scaling functions, with minor deviations observed at lower $p_T$. They deviate slightly from the asymptotic scaling functions (dashed) approximated in Refs. Bassetto:1987fqDokshitzer:1993dc. Here, $R = 0.4$ and $Q_0 = 0.5$ GeV.
• Figure 2: Inclusive parton multiplicity distributions for dijets in DLA. Here, $\bar{n}$ and $P(n)$ represent the averages over leading dijets produced at a given $p_T$ within rapidity range $|\eta|<2.1$ in proton-proton collisions at $\sqrt{s} = 13$ TeV. These distributions are calculated using the mean multiplicities and multiplicity distributions for quark and gluon jets, as shown in Fig. \ref{['fig:KNO_DLA']}.
• Figure 3: Inclusive charged particle multiplicity distributions in leading dijets at the LHC. The top panel presents experimental data for $\bar{n}_{ch}P(n_{ch})$ as a function of $n_{ch}/\bar{n}_{ch}$ from Ref. ATLAS:2019rqw, with a bin size of $\Delta n_{ch} = 4$, where uncertainty bands are omitted for clarity. The bottom panel displays our PYTHIA results for inclusive charged hadron multiplicity distributions, with results shown for each individual value of $n_{ch}$.
• Figure 4: KNO scaling within quark and gluon jets using PYTHIA. The left panel displays parton-level results for quark and gluon jets without MPI effects. The central panel shows charged hadron results incorporating MPI effects, with noticeable $p_T$ dependence arising mostly from hadronization. The right panel presents charged hadron results for quark-rich and gluon-rich jets, discriminated using the energy correlation functions Larkoski:2013eya.